Correlation and Regression Analysis.pptx

Correlation and Regression analysis is one of the important concepts of statistics which could be used to understand the relationship between the variables.

1. Chapter-4 Correlation and Regression Analysis By, Namrata Gaidole , Assistant Professor MSc(Quantitative Economics) CSIBER, Kolhapur

2. CORRELATION or CORRELATION ANALYSIS

3. CONTENTS INTRODUCTION CORRELATION IMPORTANCE (OR UTILITY) OF CORRELATION KINDS OF CORRELATION MEASURES OF CORRELATION

4. Are two variables related? Does one increase as the other increases? e . g. skills and income Does one decrease as the other increases ? e . g. health problems and nutrition How can we get a numerical measure of the degree of relationship?

5. Correlation can defined in different ways: Correlation measures closeness of relationship between two variables, more exactly of the closeness of linear relationship. According to Crotex and Cowden , “ When the relationship is of quantitative nature the appropriate tool for discovering and measuring the relationship and expressing it in a brief formula as correlation”. CORRELATION

6. (3)According to Ferguson : “ Correlation is concerned with describing the degree of relation between two variables .” Hence, correlation is simply defined as a measure of the  linear  relationship between two quantitative variables. Often a slightly looser definition is used, whereby correlation simply means that there is some type of relationship between two variables. CORRELATION

7. IMPORTANCE OF CORRELATION Helps in measuring relationship between two variables. It enables us to predict for the future. We can estimate the one variable value given the value of another. Facilitates decision-making in business organizations. C ontributes to the understanding of economic behavior.

8. KINDS OF CORRELTION

9. 1) Based on Direction Positive Correlation : Two variables move in same direction. Negative Correlation : Two variables move in opposite direction. Eg . Relation between Price, Demand and Supply. PRICE DEMAND SUPPLY Negative correlation Positive correlation

10. 2) Based on Change in Proportion The degree of association between the movements of two or more series, need not to in proportionate change . Linear Correlation : For two variables x and y, the ratio of ∆y/∆x is always constant . Non-Linear Correlation : If the change in variable is not proportionate , the correlation is non-linear or curvilinear. Eg ., x 1 2 3 4 6 y 2 4 6 8 10 x 1 2 3 4 6 y 3 5 8 15 19 Linear Correlation Non-Linear Correlation

11. 2) Based on Change in Proportion 2) Based on Number of Variables Simple Correlation : Only two variables are involved and relation between those is studied. Partial Correlation : More than two variables are involved but relationship is studied between two variables only, keeping other variables constant. Multiple Correlation : The relationship among two or more variables is studied simultaneously. Eg . Production and all factors studied simultaneously.

12. Is Correlation Cause and Effect Relationship ? Between two variables : eg . Heat and temperature, price of rice (causing factor may be found ) Being affected by third variable : Eg ., price of rice and jute affected by their production. Related variables mutually affecting each other : Eg . In business & economics. DD due to shortage in future. Due to random or chances : eg . Sometimes small sample gives you high correlation Situation of Spurious or nonsense correlation : Sowing high degree of correlation between two almost independent variables.

13. MEASURES OF CORRELATION 1. Scatter Plot 2. Karl Pearson’s Coefficient for measuring linear correlation 3. Method of Rank differences (Spearman’s Rank Correlation Coefficient)

14. 1. SCATTER DIAGRAM/ PLOTS

15. 1. SCATTER PLOT Also called as Dot Diagram . It is graphical representation of pair of numerical values of two variables. Each value is represented by a dot on the graph. The scatter points and the direction of the scatter diagram reveals the nature and degree of correlation between two variables. Correlation Coefficient : A measure of degree of relationship. It lies between 1 and - 1 and sign refers to direction.

16. A statistic that quantifies a relation between two variables and is denoted by ‘r’. Can be either positive or negative The sign referents the direction. Falls between - 1 and 1 The value of the number (not the sign) indicates the strength of the relation. 1. SCATTER PLOT Correlation Coefficient

17. 1. SCATTER PLOT Linear Correlation Linear relationships Curvilinear relationships

18. Linear Correlation Strong relationships Weak relationships 1. SCATTER PLOT

19. Linear Correlation 1. SCATTER PLOT No relationship

20. Size of correlation coefficient General Interpretation 0.8 - 1.0 Very Strong 0.6 -0.8 Strong 0.4 - 0.6 Moderate 0.2 - 0.4 Weak 0.0 -0.2 Very Weak or no relationship Rules of Thumb The strength of the correlation depends on how many data points in the scatter plot are near or far in a pattern.

21. 2. Karl Pearson’s Coefficient for Measuring Linear Correlation For ungrouped data, Karl Pearson’s Coefficient of can be obtained by the three methods : Actual Mean Method Direct Method Short-Cut Method Calculation of Correlation Coefficient

22. Linear Relationship : Assumed linear relationship between two variables. In such case, the paired observations cluster around a straight line when plotted. Causal Relationship : Expecting cause and effect relationship between the values in the series. 2. Karl Pearson’s Coefficient for Measuring Linear Correlation Assumptions

23. Spearman’s Rank Correlation Coefficient It permits to correlate two sets of qualitative observations which are subject to ranking such as qualitative productive ratings ( poor, fair, good, bad, etc.). It gives an idea of whether the two observers have common or different taste in particular to attribute or characteristic. Ranks can be assigned either by two persons( eg . Judges) to a single characteristic or by a single person to two c haracteristics.

24. Spearman’s Rank Correlation Coefficient When Ranks are repeated , we use Spearman's coefficient is given by,