![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.](https://image.slidesharecdn.com/correlationandregression-180119033043-230105175802-ff151040/85/correlationandregression-180119033043-pdf-4-320.jpg)
correlationandregression-180119033043.pdf
- 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