Maths - Summary of Correlation and Regression analysis | 11th Business Mathematics and Statistics(EMS) : Chapter 9 : Correlation and Regression analysis
Chapter: 11th Business Mathematics and Statistics(EMS) : Chapter 9 : Correlation and Regression analysis
Summary of Correlation and Regression analysis
SUMMARY
The term
correlation refers to the degree of relationship between two or more variables.
Scatter
diagram is a graphic device for finding correlation between two variables.
Karl
Pearson correlation coefficient r(x,y)= 
Correlation
coefficient r lies between –1 and 1. (i.e) –1 =< r =< 1
When r=+1
, then the correlation is perfect positive
When r=–1
, then the correlation is perfect negative
When r=0,
then there is no relationship between the variables, (i.e) the variables are
uncorrelated.
Rank
correlation deals with qualitative characteristics.
Spearman’s
rank correlation coefficient formula ρ is given by
where d = The difference between two ranks = RX–RY
N =
Number of paired observations.
Correlation
represents linear relationship between the variables but the regression helps
to estimate (or predict) one variable by using the other variable.
Regression
lines of
The two
regression lines passing through their respective means of X and Y
Calculation
of the regression coefficients.
The Properties
of regression coefficients.
(i) 
(ii) both the
regression coefficients cannot be greater than one.
(iii) Both the
regression coefficients have same sign.
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