Correlation and regression
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This document discusses correlation and linear regression. It defines correlation as a measure of the linear association between two variables. The strength of the correlation is quantified from 0 (no association) to 1 (perfect association). Regression analysis predicts the value of a dependent variable based on independent variables. Simple linear regression fits a linear equation to the data of the form Y=β0 + β1X + ε, where β0 is the Y-intercept and β1 is the slope of the regression line. The coefficient of determination, R-squared, indicates how much of the variation in the dependent variable is explained by the independent variable.
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This document discusses correlation coefficient and regression analysis. It defines correlation coefficient as representing the relationship between two variables with a straight line and ranging from -1 to 1. Regression analysis predicts changes in a dependent variable from changes in independent variables. The coefficient of determination measures the proportion of variance explained by the regression model. Multiple regression uses two or more explanatory variables to predict an outcome.
Linear regression
Linear regression analysis allows researchers to predict scores on a dependent or criterion variable (Y) based on knowledge of an independent or predictor variable (X). Simple linear regression involves using one predictor variable to predict scores on the dependent variable. Multiple regression expands this to use multiple predictor variables. Key aspects of regression analysis covered in the document include the correlation between variables, using the least squares method to determine the best fitting regression line, computing predicted Y scores, explaining and unexplained variance, and the importance of multiple regression in understanding how well predictor variables predict the criterion variable.
RANDOM SIGNALS ANALYSIS pdf.pdf
This document summarizes topics that will be covered by a group of EXTC students in 2022-2023 for their Random Signals Analysis course. The topics include: ergodicity, Markov chains, and statistical learning and its applications. Ergodicity concepts such as mean ergodic processes and correlation ergodic processes will be discussed. Markov chains will be defined and different classifications will be examined. Statistical learning techniques like simple and multiple regression analysis will also be explored, along with comparing correlation and regression.
Correlation
This document discusses correlation and regression. It defines correlation as measuring the degree of relationship between two variables. There are several methods to measure correlation including scatter diagrams, covariance, Karl Pearson's coefficient of correlation, and Spearman's rank correlation coefficient. Regression finds the functional relationship between two correlated variables by estimating the value of one variable based on the other. There are two regression equations: regression of y on x and regression of x on x, where y is the dependent variable and x is the independent variable in each case.
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Introduction to objective, scope and outcome the subject
Chapter 2
Introduction: Scope and Specialization of Civil Engineering, Role of civil Engineer in Society, Impact of infrastructural development on economy of country.
Chapter 3
Surveying: Object Principles & Types of Surveying; Site Plans, Plans & Maps; Scales & Unit of different Measurements.
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Chapter 5
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Chapter 6
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Water Pollution: Water Quality standards, Introduction to Treatment & Disposal of Waste Water. Reuse and Saving of Water, Rain Water Harvesting. Solid Waste Management: Classification of Solid Waste, Collection, Transportation and Disposal of Solid. Recycling of Solid Waste: Energy Recovery, Sanitary Landfill, On-Site Sanitation. Air & Noise Pollution: Primary and Secondary air pollutants, Harmful effects of Air Pollution, Control of Air Pollution. . Noise Pollution Harmful Effects of noise pollution, control of noise pollution, Global warming & Climate Change, Ozone depletion, Greenhouse effect
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1. Palancharmy, Basic Civil Engineering, McGraw Hill publishers.
2. Satheesh Gopi, Basic Civil Engineering, Pearson Publishers.
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Correlation and regression
- 1. CORRELATION AND LINEAR REGRESSION SIMPLE CORRELATION AND REGRESSION ANALYSIS AJENDRA SHARMA
- 2. CONTENTS • WHAT IS CORRELATION • TYPE OF RELATIONSHIP AND STRENGTH OF ASSOCIATION • PROPERTIES OF CORRELATION • WHAT IS REGRESSION • SIMPLE LINEAR REGRESSION • REGRESSION LINE • COEFFICIENT OF DETERMINATION
- 3. What is need of correlation? What happens to Sweater sales with increase in temperature? What is the strength of association between them? Ice-cream sales vs temperature ? What is the strength of association between them? Which one of these two is stronger? How to quantify the association?
- 4. What is Correlation It is a measure of association (linear association only) Formula for correlation coefficient r is the ratio of variance together and product of separate variances r= cov(XY)/sd(x)*sd(y) r = [n(∑xy) – (∑ x)(∑ y)] / {[n(∑ x2 ) – (∑ x)2 ][n(∑ y2 ) – (∑ y)2 ]}1/2 Where n is the number of data pairs, x is the independent variable and y the dependent variable.
- 8. STRENGTH OF ASSOCIATION Correlation 0 - No linear association Correlation 0 to 0.25 - Negligible positive association Correlation 0.25-0.5 - Weak positive association Correlation 0.5-0.75 - Moderate positive association Correlation >0.75 - Very Strong positive association
- 9. PROPERTIES OF CORRELATION • -1 ≤ r ≤ +1 • r=0 represents no linear relationship between the two Variables • Correlation is unit free Limitations: • Though r measures how closely the two variables approximate a straight line, it does not validly measures the strength of nonlinear relationship • When the sample size, n, is small we also have to be careful with the reliability of the correlation • Outliers could have a marked effect on r
- 10. REGRESSION • Regression analysis is used to predict the value of one variable (the dependent variable) on the basis of other variables (the independent variables). • In correlation, the two variables are treated as equals. In regression, one variable is considered independent (=predictor) variable (X) and the other the dependent (=outcome) variable Y. • Dependent variable: denoted Y • Independent variables: denoted X1, X2, …, Xk Y=β0 + β1X + ε • Above model is referred to as simple linear regression. We would be interested in estimating β0 and β1 from the data we collect.
- 11. SIMPLE LINEAR REGRESSION ANALYSIS • If you know something about X, this knowledge helps you predict something about Y. Y=β0 + β1X + ε Variables: • X = Independent Variable (we provide this) • Y = Dependent Variable (we observe this) Parameters: • β0 = Y-Intercept • β1 = Slope
- 12. REGRESSION LINE
- 13. COEFFICIENT OF DETERMINATION The coefficient of determination is the portion of the total variation in the dependent variable that is explained by variation in the independent variable The coefficient of determination is also called R- squared and is denoted as R2