This document discusses correlation and regression. Correlation describes the strength and direction of a linear relationship between two variables, while regression allows predicting a dependent variable from an independent variable. It provides examples of calculating the correlation coefficient r to determine the strength and direction of relationships between variables like education and self-esteem or family income and number of children. The regression equation describes the linear regression line and can be used to predict values of the dependent variable from known values of the independent variable.
The document discusses regression analysis and its key concepts. Regression analysis is used to understand the relationship between two or more variables and make predictions. There are two main types: simple linear regression, which involves two variables, and multiple regression, which involves more than two variables. Regression lines show the average relationship between the variables and can be used to predict outcomes. The regression coefficients measure the change in the dependent variable for a unit change in the independent variable. The standard error of the estimate indicates how close the data points are to the regression line.
The document discusses different types of correlation and methods for studying correlation. It describes Karl Pearson's coefficient of correlation, which measures the strength and direction of a linear relationship between two variables. The coefficient ranges from -1 to 1, where -1 is a perfect negative correlation, 0 is no correlation, and 1 is a perfect positive correlation. The document also discusses other types of correlation coefficients like Spearman's rank correlation coefficient and methods for analyzing correlation like scatter plots.
Regression analysis is a statistical technique for investigating relationships between variables. Simple linear regression defines a relationship between two variables (X and Y) using a best-fit straight line. Multiple regression extends this to model relationships between a dependent variable Y and multiple independent variables (X1, X2, etc.). Regression coefficients are estimated to define the regression equation, and R-squared and the standard error can be used to assess the goodness of fit of the regression model to the data. Regression analysis has applications in pharmaceutical experimentation such as analyzing standard curves for drug analysis.
A binomial random variable is the number of successes x in n repeated trials of a binomial experiment. The probability distribution of a binomial random variable is called a binomial distribution. Suppose we flip a coin two times and count the number of heads (successes).
This document presents information about regression analysis. It defines regression as the dependence of one variable on another and lists the objectives as defining regression, describing its types (simple, multiple, linear), assumptions, models (deterministic, probabilistic), and the method of least squares. Examples are provided to illustrate simple regression of computer speed on processor speed. Formulas are given to calculate the regression coefficients and lines for predicting y from x and x from y.
The document discusses correlation and regression analysis. It defines correlation as the statistical relationship between two variables, where a change in one variable corresponds to a change in the other. The key types of correlation are positive, negative, simple, partial and multiple, and linear and non-linear. Regression analysis establishes the average relationship between an independent and dependent variable in order to predict or estimate values of the dependent variable based on the independent variable. Methods for studying correlation include scatter diagrams and Karl Pearson's coefficient of correlation, while regression analysis uses equations to model the linear relationship between variables.
The t-test is used to compare the means of two groups and has three main applications:
1) Compare a sample mean to a population mean.
2) Compare the means of two independent samples.
3) Compare the values of one sample at two different time points.
There are two main types: the independent-measures t-test for samples not matched, and the matched-pair t-test for samples in pairs. The t-test assumes normal distributions and equal variances between groups. Examples are provided to demonstrate hypothesis testing for each application.
The document discusses Spearman's rank correlation coefficient, a nonparametric measure of statistical dependence between two variables. It assumes values between -1 and 1, with -1 indicating a perfect negative correlation and 1 a perfect positive correlation. The steps involve converting values to ranks, calculating the differences between ranks, and determining if there is a statistically significant correlation based on the test statistic and critical values. An example calculates Spearman's rho using rankings of cricket teams in test and one day international matches.
Finding the relationship between two quantitative variables without being able to infer causal relationships
Correlation is a statistical technique used to determine the degree to which two variables are related
The document provides information about the Chi-square test, including:
- It is a non-parametric test used to evaluate categorical data using contingency tables. The test statistic follows a Chi-square distribution.
- It can test for independence between variables and goodness of fit to theoretical distributions.
- Key steps involve calculating expected frequencies, taking the difference between observed and expected, and summing the results.
- The test interprets higher Chi-square values as less likelihood the results are due to chance. Modifications like Yates' correction and Fisher's exact test address limitations for small sample sizes.
Regression analysis is a statistical technique used to estimate the relationships between variables. It allows one to predict the value of a dependent variable based on the value of one or more independent variables. The document discusses simple linear regression, where there is one independent variable, as well as multiple linear regression which involves two or more independent variables. Examples of linear relationships that can be modeled using regression analysis include price vs. quantity, sales vs. advertising, and crop yield vs. fertilizer usage. The key methods for performing regression analysis covered in the document are least squares regression and regressions based on deviations from the mean.
Satyaki Aparajit Mishra presented on the topic of standard error and predictability limits. Standard error is used to estimate the standard deviation from a sample. It is calculated by dividing the standard deviation by the square root of the sample size. A larger standard error means the sample mean is less reliable at estimating the population mean. Standard error helps determine how far sample estimates may be from the true population values. Mishra discussed estimating standard error from a single sample and how standard error is used to test hypotheses. He provided an example of testing if a coin flip was unbiased using the standard error of the proportion of heads observed.
This document discusses correlation and different types of correlation analysis. It defines correlation as a statistical analysis that measures the relationship between two variables. There are three main types of correlation: (1) simple and multiple correlation based on the number of variables, (2) linear and non-linear correlation based on the relationship between variables, and (3) positive and negative correlation based on the direction of change between variables. The degree of correlation is measured using correlation coefficients that range from -1 to +1. Common methods to study correlation include scatter diagrams and Karl Pearson's coefficient of correlation.
The chi-square test is used to compare observed data with expected data. It was developed by Karl Pearson in 1900. The chi-square test calculates the sum of the squares of the differences between the observed and expected frequencies divided by the expected frequency. The chi-square value is then compared to a critical value to determine if there is a significant difference between the observed and expected results. The degrees of freedom, which determine the critical value, are calculated based on the number of rows and columns in a contingency table. The chi-square test can be used to test goodness of fit, independence of attributes, and other hypotheses.
HOW IS IT USEFUL IN FIELD OF FORENSIC SCIENCE AND IN THIS I HAVE SHOWN THE TYPES OF CORRELATION, SIGNIFICANCE , METHODS AND KARL PEARSON'S METHOD OF CORRELATION
This document discusses correlation and the Pearson's coefficient of correlation. It defines correlation as the relationship between two variables, which can be positive, negative, or zero. The Pearson's coefficient of correlation, represented by r, measures the strength and direction of this relationship. The document provides examples of calculating r using the product-moment method for different sets of data. It interprets the resulting r values and discusses advantages and limitations of the product-moment correlation method.
This document provides an overview of statistical tests of significance used to analyze data and determine whether observed differences could reasonably be due to chance. It defines key terms like population, sample, parameters, statistics, and hypotheses. It then describes several common tests including z-tests, t-tests, F-tests, chi-square tests, and ANOVA. For each test, it outlines the assumptions, calculation steps, and how to interpret the results to evaluate the null hypothesis. The goal of these tests is to determine if an observed difference is statistically significant or could reasonably be expected due to random chance alone.
This document discusses various types of analysis of variance (ANOVA) statistical tests. It begins with an introduction to one-way ANOVA for comparing the means of three or more independent groups. Requirements for one-way ANOVA include a nominal independent variable with three or more levels and a continuous dependent variable. Assumptions of one-way ANOVA include normality and homogeneity of variances. The document then briefly discusses two-way ANOVA, MANOVA, ANOVA with repeated measures, and related statistical tests. Examples of each type of ANOVA are provided.
Simple Correlation : Karl Pearson’s Correlation co- efficient and Spearman’s ...RekhaChoudhary24
The document discusses correlation and different correlation coefficients. It defines correlation as a linear relationship between two variables and explains that correlation coefficients measure the strength and direction of this relationship. It describes Karl Pearson's correlation coefficient and Spearman's rank correlation coefficient as common methods to determine correlation. It provides examples of calculating correlation using these methods and discusses limitations of correlation analysis.
This document defines correlation and discusses different types of correlation. It states that correlation refers to the relationship between two variables, where their values change together. There can be positive correlation, where variables change in the same direction, or negative correlation, where they change in opposite directions. Correlation can also be linear, nonlinear, simple, multiple, or partial. The degree of correlation is measured by the coefficient of correlation, which ranges from -1 to 1. Graphic and algebraic methods like scatter diagrams and calculating the coefficient can be used to study correlation.
The document discusses correlation and regression, explaining that correlation describes the strength of a linear relationship between two variables, while regression tells us how to draw the straight line described by the correlation. It provides examples of using correlation coefficients to determine the strength and direction of relationships between independent and dependent variables, and discusses calculating correlation coefficients and using regression analysis to predict variable relationships and outcomes.
The document discusses correlation and regression analysis. It provides examples to calculate the simple correlation coefficient (r) between two quantitative variables, finding the correlation between weight and blood pressure using a sample data set. It also explains how to find the regression equation between two variables and use it to predict outcomes. For example, the regression equation is used to predict weight given age using another sample data set.
This document provides an overview of regression models and analysis techniques. It introduces simple and multiple linear regression, as well as logistic regression. It discusses assessing regression models, cross-validation, model selection, and using regression models for prediction. Additionally, it covers the similarities and differences between linear and logistic regression, and assessing correlation without inferring causation. Scatter plots, correlation coefficients, and computing regression equations are also summarized.
Unit-I, BP801T. BIOSTATISITCS AND RESEARCH METHODOLOGY (Theory)
Correlation: Definition, Karl Pearson’s coefficient of correlation, Multiple correlations -
Pharmaceuticals examples.
Correlation: is there a relationship between 2
variables.
Correlation by Neeraj Bhandari ( Surkhet.Nepal )Neeraj Bhandari
The regression coefficients are 0.8 and 0.2.
The coefficient of correlation r is the geometric mean of the regression coefficients, which is:
√(0.8 × 0.2) = 0.4
Therefore, the value of the coefficient of correlation is 0.4.
This document discusses correlation and regression analysis. It begins by outlining the chapter's objectives and providing an introduction to investigating relationships between variables using statistical analysis. The document then presents examples of collecting data to study potential relationships between variables like stone dimensions, human heights and weights, and sprint and long jump performances. It introduces various statistical measures for quantifying relationships in data, including covariance, Pearson's product moment correlation coefficient, and Spearman's rank correlation coefficient. Examples are provided to demonstrate calculating and interpreting these statistics. Limitations of correlation analysis are also noted.
The document discusses correlation and linear regression analysis. It provides examples to calculate correlation coefficients and find regression equations to describe the relationship between two variables. Specifically:
- It shows how to calculate the Pearson correlation coefficient (r) between two variables to determine the strength and direction of their linear relationship.
- An example calculates r between age and weight using a sample data set.
- It also demonstrates calculating the Spearman rank correlation coefficient (rs) as a non-parametric measure of correlation.
- Linear regression finds the best fitting line that predicts a dependent variable (y) from an independent variable (x). The regression equation describes this line.
- An example calculates the regression equation and uses it
Correlation and regression are statistical techniques used to describe relationships between variables:
- Correlation determines the strength and direction of relationships between two variables without implying causation.
- Scatter plots show the pattern of relationships as positive, negative, or no correlation.
- Regression predicts the value of an outcome or dependent variable based on the value of an independent variable.
- The regression equation defines the linear relationship between variables as y=mx+b, where m is the slope and b is the y-intercept.
This document provides an introduction to regression and correlation analysis. It discusses simple and multiple linear regression models, how to interpret regression coefficients, and how to check the assumptions and adequacy of regression models. Key aspects covered include computing the regression line using the least squares method, interpreting the slope and intercept, checking the normality of residuals, and examining residual plots to validate the model. The goal of regression analysis is to model the relationship between a dependent variable and one or more independent variables.
The document discusses various statistical concepts related to correlation and regression. It defines the coefficient of correlation as a measure of the strength and direction of the relationship between variables ranging from +1 to -1. A value close to 0 indicates no relationship, while values close to +1 or -1 indicate a strong positive or negative linear relationship, respectively. It also discusses the covariance and correlation of random variables, Pearson correlation coefficient, Spearman rank correlation, partial correlation coefficient, and multiple correlation coefficients. Finally, it provides a definition of regression as a technique to determine the mathematical relationship between two variables using a regression line equation.
This document provides an overview of correlation and the Pearson correlation coefficient. It discusses how the Pearson r describes the direction, form, and strength of the linear relationship between two variables. It explains how to calculate r using the sum of products formula and interpret the results. The text also covers hypothesis testing with r and reporting correlations. Alternatives to the Pearson r are mentioned but not covered in detail.
This presentation covered the following topics:
1. Definition of Correlation and Regression
2. Meaning of Correlation and Regression
3. Types of Correlation and Regression
4. Karl Pearson's methods of correlation
5. Bivariate Grouped data method
6. Spearman's Rank correlation Method
7. Scattered diagram method
8. Interpretation of correlation coefficient
9. Lines of Regression
10. regression Equations
11. Difference between correlation and regression
12. Related examples
Lesson 27 using statistical techniques in analyzing datamjlobetos
The document discusses statistical techniques for analyzing data, including scatter diagrams, correlation coefficients, regression analysis, and chi-square tests. It provides examples of using scatter diagrams to visualize the relationship between two variables, calculating the Pearson correlation coefficient to determine the strength of linear relationships, and using simple linear regression to find the regression equation that best predicts a dependent variable from an independent variable. It also explains how to perform a chi-square test to analyze relationships between categorical variables by comparing observed and expected frequencies.
This document provides an introduction to simple linear regression and correlation. It defines key terms like independent and dependent variables, and explains how to estimate regression coefficients using the least squares method. Graphs like scatter plots are used to visualize the linear relationship between two variables. The correlation coefficient measures the strength of the linear association. Regression seeks to predict a dependent variable from an independent variable, while correlation simply measures the degree of association between two variables.
The document discusses various methods of correlation analysis. It begins by defining correlation as a statistical technique used to measure the strength and direction of association between two quantitative variables. Some key points made in the document include:
- Correlation can be positive (variables move in the same direction), negative (variables move in opposite directions), or zero (no relationship).
- Methods for measuring correlation discussed include scatter diagrams, Karl Pearson's coefficient, and Spearman's rank correlation coefficient.
- Correlation can be simple, partial, or multiple depending on the number of variables studied. It can also be linear or non-linear based on the relationship between the variables.
- Correlation only measures association but does not determine
Correlation _ Regression Analysis statistics.pptxkrunal soni
This document discusses correlation and related statistical concepts. Correlation measures the strength and direction of association between two quantitative variables. A correlation of 0 means no association, 1 means perfect positive association, and -1 means perfect negative association. Correlation is independent of measurement units and scaling of variables. Hypothesis testing is used to make inferences about the population correlation based on a sample correlation. The null hypothesis is that the population correlation is 0, and alternative hypotheses specify a non-zero correlation. The test statistic used is Student's t distribution. The null is rejected if the calculated t exceeds the critical value or if the p-value is less than the significance level.
This document discusses various methods of determining correlation between two variables, including scatter diagram methods, Karl Pearson's correlation coefficient, and Spearman's rank correlation method. It provides examples of calculating Karl Pearson's coefficient using direct and shortcut methods. The key points covered are:
1. Correlation analysis determines the nature and strength of the relationship between two variables. Common methods include scatter diagrams, Karl Pearson's coefficient, and Spearman's rank correlation.
2. Karl Pearson's coefficient calculates the covariance between two variables and divides it by the product of their standard deviations, resulting in a value between -1 and 1.
3. Spearman's rank correlation method involves ranking the data values and calculating the differences between their ranks
Most of the variables show some kind of relationship. For example, there is relationship between profits and dividends paid, income and expenditure, etc. with the help of correlation analysis we can measure in one figure the degree of relationship existing between the variables.
Correlation analysis contributes to the understanding of economic behaviour, aids in locating the critically important variables on which others depend, may reveal to the economist the connection by which disturbances spread and suggest to him the paths through which stabilizing forces may become effective.
The document discusses regression analysis, including definitions, uses, calculating regression equations from data, graphing regression lines, the standard error of estimate, and limitations. Regression analysis is a statistical technique used to understand the relationship between variables and allow for predictions. The document provides examples of calculating regression equations from various data sets and determining the standard error of estimate.
This document describes 11 different types of diodes: Zener diode, varactor diode, light-emitting diode (LED), photodiode, laser diode, Schottky diode, PIN diode, tunnel diode, small signal diode, large signal diode, and Shockley diode. It provides details on each diode type, including its basic structure and functions, symbol, and common applications. The document also includes separate sections focused on describing the key characteristics and uses of LEDs, photodiodes, and laser diodes.
Transistors are electronic devices made of semiconductor material that can act as both an insulator and conductor. They have three layers - an emitter, base, and collector - and come in two types: NPN and PNP bipolar junction transistors (BJTs). BJTs use both holes and electrons as charge carriers. Transistors have different operating regions - cutoff, linear, and saturation - and can be used as electronic switches or amplifiers by controlling the base current to mimic an input signal with greater amplitude at the collector. Common transistor types include BJTs, JFETs, FETs, and MOS transistors.
The document discusses single diode circuits and diode equations. It provides the following key points:
- A conducting diode has a voltage drop of about 0.7V for silicon and 0.3V for germanium. To forward bias a diode, the anode must be more positive than the cathode. To reverse bias, the anode must be less positive.
- The diode equation relates diode current (iD) to voltage (vD) and includes parameters like reverse saturation current (IS), temperature, and the nonideality factor.
- An example circuit is solved using Kirchhoff's law to find the diode voltage (VD) and current (iD) at the operating point, calculating
The document discusses silicon controlled rectifiers (SCRs), which are four-layer semiconductor devices containing three PN junctions. SCRs can be switched on and off rapidly to control the delivery of power to a load. Unlike a diode, an SCR can be made to operate as either an open circuit or conducting rectifier depending on gate triggering. The SCR consists of alternating P-type and N-type layers with three junctions (J1, J2, J3). Applying a positive voltage to the gate terminal forward biases J3, allowing current to flow and triggering the SCR into its conducting on state. Common applications of SCRs include rectification, power supplies, static switches, motor speed controls
Rectifiers convert alternating current (AC) to direct current (DC). There are two main types: half-wave and full-wave rectifiers. Half-wave rectifiers only conduct current during one half of the AC cycle, resulting in lower power output. Full-wave rectifiers conduct current during both halves of the cycle, doubling the output frequency and improving power output. Common full-wave rectifier circuits include the center-tap and bridge rectifier configurations using different diode arrangements.
An operational amplifier (op-amp) is an integrated circuit that can amplify or compare signals. It consists of transistors, resistors, and capacitors. Op-amps are used to build amplifiers, summers, integrators, differentiators, and comparators. They obey golden rules to make the difference between their input pins zero. Op-amps are also used in analog to digital converters, which sample analog signals and convert them to digital signals for processing.
A voltage multiplier is an electrical circuit that uses capacitors and diodes to convert AC power to higher DC voltage. There are different types depending on the output voltage, including half-wave and full-wave doublers, and triplers and quadruplers that output higher multiples of the input voltage. Voltage multipliers function by charging capacitors on alternating half-cycles to add voltage levels. They are used to provide high voltages in applications like CRTs, lasers, x-rays, and particle accelerators. While lower current and delays are disadvantages, voltage multipliers provide high voltage at low cost as an alternative to transformers.
There are two main types of transistors: bipolar junction transistors (BJT) and field effect transistors (FET). BJTs use both holes and electrons as current carriers and include NPN and PNP types, while FETs use only one carrier type and include JFETs and MOSFETs. MOSFETs are particularly important as they can be easily integrated into circuits. MOSFETs operate in different modes depending on the voltage applied to the gate and include depletion, enhancement, linear, and saturation modes.
Clipper and clamper circuits are used to modify signal waveforms. Clipper circuits remove portions of a signal that exceed a reference level, cutting off either positive or negative portions. Clamper circuits shift the entire signal up or down without changing its shape, setting either the positive or negative peak at a desired level. Common circuit types include positive and negative clippers and clampers, which use diodes and capacitors to clip or shift the signal in a particular direction relative to the reference level.
The document discusses different types of probability distributions including binomial, Poisson, and normal distributions. It provides examples of how to calculate probabilities for each distribution and approximations that can be used. It also defines common random variables like the number of successes in a binomial experiment and the number of events occurring in a Poisson distribution.
- There are 52 cards in a standard deck with 4 suits (clubs, hearts, diamonds, spades) and 13 cards in each suit
- The document provides examples of calculating probabilities of drawing certain cards/card combinations from a deck both with and without replacement
- Probabilities are calculated by considering the number of desired cards relative to the total number of cards in the deck at each draw
This document provides an overview of estimation and hypothesis testing. It defines key statistical concepts like population and sample, parameters and estimates, and introduces the two main methods in inferential statistics - estimation and hypothesis testing.
It explains that hypothesis testing involves setting a null hypothesis (H0) and an alternative hypothesis (Ha), calculating a test statistic, determining a p-value, and making a decision to accept or reject the null hypothesis based on the p-value and significance level. The four main steps of hypothesis testing are outlined as setting hypotheses, calculating a test statistic, determining the p-value, and making a conclusion.
Examples are provided to demonstrate left-tailed, right-tailed, and two-tailed hypothesis tests
This document provides an overview of probability concepts including:
- Probability is a numerical measure of the likelihood of an event occurring, ranging from 0 (impossible) to 1 (certain).
- An experiment generates outcomes that make up the sample space. Events are collections of outcomes.
- Simple events have a defined probability based on being equally likely. The probability of an event is the sum of probabilities of the simple events it contains.
- Rules like the multiplication rule for independent events and additive rule for unions allow calculating probabilities of composite events.
- Complement and conditional probabilities relate the probabilities of events. Independent events do not influence each other's probabilities.
Here is the tree diagram and sample space for flipping a coin and rolling a die:
H
T
1
2
3
4
5
6
1
2
3
4
5
6
Sample space: {H1, H2, H3, H4, H5, H6, T1, T2, T3, T4, T5, T6}
There are 12 outcomes in the sample space.
The document discusses permutations and combinations. It provides examples of calculating permutations and combinations for different scenarios like selecting committees from a group of people and arranging books on a shelf. Formulas for permutations (nPr) and combinations (nCr) are given. Order matters for permutations but not for combinations. The key difference between the two is explained.
This document discusses analytical representation of data through descriptive statistics. It begins by showing raw, unorganized data on movie genre ratings. It then demonstrates organizing this data into a frequency distribution table and bar graph to better analyze and describe the data. It also calculates averages for each movie genre. The document then discusses additional descriptive statistics measures like the mean, median, mode, and percentiles to further analyze data through measures of central tendency and dispersion.
This document discusses frequency distributions and how to construct them from raw data. It provides examples of creating stem-and-leaf displays, frequency tables, relative frequency tables, and cumulative frequency tables from various data sets. Key concepts covered include class width, class boundaries, tallying data, and calculating relative frequencies and percentages. Overall, the document serves as a tutorial on how to organize and summarize data using various types of frequency distributions.
Graphical representations such as charts and graphs are used to display data in a visual format. They allow readers to focus on key aspects of the evidence or data at a higher level rather than getting caught up in minor details. However, some numeric detail and potential relationships within the data may be lost compared to a table. There are many different types of graphs used in statistics including box plots, histograms, pie charts, bar graphs and line graphs. Each graph has strengths for displaying certain types of data such as continuous versus discrete values.
This document provides an introduction to statistical theory. It discusses why statistics are studied and defines key statistical concepts such as populations, samples, parameters, statistics, descriptive statistics, inferential statistics, and the different types of data and variables. It also covers experimental design, methods for collecting data such as surveys and sampling, and different sampling methods like random, stratified, cluster, and systematic sampling.
The document discusses finite state machines (FSMs) and algorithmic state machines (ASMs). FSMs have a fixed set of states and can only be in one state at a time. ASMs provide a flowchart-like diagram representation of FSMs and are suitable for more complex FSMs with many inputs and outputs. ASMs have three main building blocks - state boxes, decision boxes, and conditional output boxes. State boxes represent states, decision boxes represent condition expressions, and conditional output boxes represent Mealy-type outputs that depend on state and inputs. The document provides examples of converting state diagrams to ASM charts and vice versa.
Social media management system project report.pdfKamal Acharya
The project "Social Media Platform in Object-Oriented Modeling" aims to design
and model a robust and scalable social media platform using object-oriented
modeling principles. In the age of digital communication, social media platforms
have become indispensable for connecting people, sharing content, and fostering
online communities. However, their complex nature requires meticulous planning
and organization.This project addresses the challenge of creating a feature-rich and
user-friendly social media platform by applying key object-oriented modeling
concepts. It entails the identification and definition of essential objects such as
"User," "Post," "Comment," and "Notification," each encapsulating specific
attributes and behaviors. Relationships between these objects, such as friendships,
content interactions, and notifications, are meticulously established.The project
emphasizes encapsulation to maintain data integrity, inheritance for shared behaviors
among objects, and polymorphism for flexible content handling. Use case diagrams
depict user interactions, while sequence diagrams showcase the flow of interactions
during critical scenarios. Class diagrams provide an overarching view of the system's
architecture, including classes, attributes, and methods .By undertaking this project,
we aim to create a modular, maintainable, and user-centric social media platform that
adheres to best practices in object-oriented modeling. Such a platform will offer users
a seamless and secure online social experience while facilitating future enhancements
and adaptability to changing user needs.
Response & Safe AI at Summer School of AI at IIITHIIIT Hyderabad
Talk covering Guardrails , Jailbreak, What is an alignment problem? RLHF, EU AI Act, Machine & Graph unlearning, Bias, Inconsistency, Probing, Interpretability, Bias
A brand new catalog for the 2024 edition of IWISS. We have enriched our product range and have more innovations in electrician tools, plumbing tools, wire rope tools and banding tools. Let's explore together!
How to Manage Internal Notes in Odoo 17 POSCeline George
In this slide, we'll explore how to leverage internal notes within Odoo 17 POS to enhance communication and streamline operations. Internal notes provide a platform for staff to exchange crucial information regarding orders, customers, or specific tasks, all while remaining invisible to the customer. This fosters improved collaboration and ensures everyone on the team is on the same page.
In May 2024, globally renowned natural diamond crafting company Shree Ramkrishna Exports Pvt. Ltd. (SRK) became the first company in the world to achieve GNFZ’s final net zero certification for existing buildings, for its two two flagship crafting facilities SRK House and SRK Empire. Initially targeting 2030 to reach net zero, SRK joined forces with the Global Network for Zero (GNFZ) to accelerate its target to 2024 — a trailblazing achievement toward emissions elimination.
Unblocking The Main Thread - Solving ANRs and Frozen FramesSinan KOZAK
In the realm of Android development, the main thread is our stage, but too often, it becomes a battleground where performance issues arise, leading to ANRS, frozen frames, and sluggish Uls. As we strive for excellence in user experience, understanding and optimizing the main thread becomes essential to prevent these common perforrmance bottlenecks. We have strategies and best practices for keeping the main thread uncluttered. We'll examine the root causes of performance issues and techniques for monitoring and improving main thread health as wel as app performance. In this talk, participants will walk away with practical knowledge on enhancing app performance by mastering the main thread. We'll share proven approaches to eliminate real-life ANRS and frozen frames to build apps that deliver butter smooth experience.
2. 2
Correlation and Regression
Correlation describes the strength of a
linear relationship between two variables
Regression tells us how to draw the straight
line described by the correlation
3. 3
Correlation and Regression
• For example:
A sociologist may be interested in the relationship
between education and self-esteem or Income and
Number of Children in a family.
Independent Variables
Education
Family Income
Dependent Variables
Self-Esteem
Number of Children
4. 4
Correlation and Regression
• For example:
• May expect: As education increases, self-esteem
increases (positive relationship).
• May expect: As family income increases, the number
of children in families declines (negative relationship).
Independent Variables
Education
Family Income
Dependent Variables
Self-Esteem
Number of Children
+
-
6. 6
Correlation
• Correlation is a statistical technique used to
determine the degree to which two variables
are related
• A correlation is a relationship between two
variables. The data can be represented by the
ordered pairs (x, y) where x is the independent
(or explanatory) variable, and y is the
dependent (or response) variable.
7. 7
Correlation
x 1 2 3 4 5
y – 4 – 2 – 1 0 2
A scatter plot can be used to determine
whether a linear (straight line) correlation
exists between two variables.
x
2 4
–2
– 4
y
2
6
Example:
8. 8
Linear Correlation
x
y
Negative Linear Correlation
x
y
No Correlation
x
y
Positive Linear Correlation
x
y
Nonlinear Correlation
As x increases,
y tends to
decrease.
As x increases,
y tends to
increase.
9. 9
Correlation Coefficient
• It is also called Pearson's correlation or
product moment correlation coefficient
• The correlation coefficient is a measure of
the strength and the direction of a linear
relationship between two variables. The
symbol r represents the sample correlation
coefficient. The formula for r is
2 22 2
.
n xy x y
r
n x x n y y
10. 10
The sign of r denotes the nature of
association
while the value of r denotes the strength of
association.
11. 11
If the sign is +ve this means the relation is
direct (an increase in one variable is
associated with an increase in the
other variable and a decrease in one
variable is associated with a
decrease in the other variable).
While if the sign is -ve this means an
inverse or indirect relationship (which
means an increase in one variable is
associated with a decrease in the other).
12. 12
The value of r ranges between ( -1) and ( +1)
The value of r denotes the strength of the
association as illustrated
by the following diagram.
-1 10-0.25-0.75 0.750.25
strong strongintermediate intermediateweak weak
no
relation
perfect
correlation
perfect
correlation
Directindirect
13. 13
If r = Zero this means no association or
correlation between the two variables.
If 0 < r < 0.25 = weak correlation.
If 0.25 ≤ r < 0.75 = intermediate correlation.
If 0.75 ≤ r < 1 = strong correlation.
If r = l = perfect correlation.
14. 14
Linear Correlation
x
y
Strong negative correlation
x
y
Weak positive correlation
x
y
Strong positive correlation
x
y
Nonlinear Correlation
r = 0.91 r = 0.88
r = 0.42
r = 0.07
15. 15
Calculating a Correlation Coefficient
2 22 2
.
n xy x y
r
n x x n y y
1. Find the sum of the x-values.
2. Find the sum of the y-values.
Calculating a Correlation Coefficient
In Words In Symbols
x
y
xy3. Multiply each x-value by its
corresponding y-value and find
the sum.
16. 16
Calculating a Correlation Coefficient
Calculating a Correlation Coefficient
In Words In Symbols
2
x
2
y
4. Square each x-value and
find the sum.
5. Square each y-value and
find the sum.
6. Use these five sums to
calculate the correlation
coefficient.
17. 17
Correlation Coefficient
x y xy x2 y2
1 – 3 – 3 1 9
2 – 1 – 2 4 1
3 0 0 9 0
4 1 4 16 1
5 2 10 25 4
Example:
Calculate the correlation coefficient r for the following
data.
15x 1y 9xy 2
55x 2
15y
18. 18
Correlation Coefficient
2 22 2
n xy x y
r
n x x n y y
Example:
Calculate the correlation coefficient r for the following
data.
22
5(9) 15 1
5(55) 15 5(15) 1
60
50 74
0.986
There is a strong positive linear correlation
between x and y.
19. 19
Correlation Coefficient
Hours,
x
0 1 2 3 3 5 5 5 6 7 7 10
Test score,
y
96 85 82 74 95 68 76 84 58 65 75 50
Example:
The following data represents the number of hours, 12
different students watched television during the
weekend and the scores of each student who took a test
the following Monday.
a.) Display the scatter plot.
b.) Calculate the correlation coefficient r.
22. 22
Correlation Coefficient
Example continued:
2 22 2
n xy x y
r
n x x n y y
22
12(3724) 54 908
12(332) 54 12(70836) 908
0.831
• There is a strong negative linear correlation.
• As the number of hours spent watching TV increases,
the test scores tend to decrease.
23. 23
Example:
A sample of 6 children was selected, data about their
age in years and weight in kilograms was recorded
as shown in the following table . It is required to find
the correlation between age and weight.
Weight
(Kg)
Age
(years)
serial
No
1271
862
1283
1054
1165
1396
29. 29
13
0
10
20
30
40
50
60
70
0 2 4 6 8 10 12 14
2
Trunk Diameter, x
Tree
Height,
y
Example
• r = 0.886 → relatively
strong positive linear
association between x
and y
32. 32
Regression Analyses
• Regression technique is concerned with
predicting some variables by knowing others
• The process of predicting variable Y using
variable X
33. 33
20
Types of Regression Models
Positive Linear Relationship
Negative Linear Relationship
Relationship NOT Linear
No Relationship
34. 34
Regression
Uses a variable (x) to predict some outcome
variable (y)
Tells you how values in y change as a
function of changes in values of x
35. 35
The regression line makes the sum of the squares of the
residuals smaller than for any other line
Regression minimizes residuals
80
100
120
140
160
180
200
220
60 70 80 90 100 110 120
Wt (kg)
SBP(mmHg)
36. 36
By using the least squares method (a procedure that
minimizes the vertical deviations of plotted points
surrounding a straight line) we are
able to construct a best fitting straight line to the scatter
diagram points and then formulate a regression equation
in the form of:
n
x)(
x
n
yx
xy
b 2
2
1
)xb(xyyˆ
bXayˆ
Regression equation describes the regression line
mathematically by showing Intercept and Slope
37. 37
Correlation and Regression
• The statistics equation for a line:
Y = a + bx
Where: Y = the line’s position on the
vertical axis at any point (estimated
value of dependent variable)
X = the line’s position on the
horizontal axis at any point (value of
the independent variable for which you
want an estimate of Y)
b = the slope of the line
(called the coefficient)
a = the intercept with the Y axis,
where X equals zero
^
^
39. 39
Exercise
A sample of 6 persons was selected the value of
their age ( x variable) and their weight is
demonstrated in the following table. Find the
regression equation and what is the predicted
weight when age is 8.5 years.
Weight (y)Age (x)Serial no.
12
8
12
10
11
13
7
6
8
5
6
9
1
2
3
4
5
6
43. 43
we create a regression line by plotting two estimated
values for y against their X component, then extending
the line right and left.
44. 44
Regression Line
Example:
a.) Find the equation of the regression line.
b.) Use the equation to find the expected value when
value of x is 2.3
x y xy x2 y2
1 – 3 – 3 1 9
2 – 1 – 2 4 1
3 0 0 9 0
4 1 4 16 1
5 2 10 25 4
15x 1y 9xy 2
55x 2
15y
46. 46
Regression Line
Example:
The following data represents the number of hours 12
different students watched television during the
weekend and the scores of each student who took a
test the following Monday.
a.) Find the equation of the regression line.
b.) Use the equation to find the expected test score
for a student who watches 9 hours of TV.
48. 48
• Find the correlation between age and blood
pressure using simple and Spearman's
correlation coefficients, and comment.
• Find the regression equation?
• What is the predicted blood pressure for a
man aging 25 years?
Exercise