Regression - 17 From means, variances and r regression lines after changing origin and scale

Published: 25 March 2017
on channel: PUAAR Academy

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#Statistics
#Regression
#Linear Regression
#Coefficients of Regression and Correlation

Special type of problem

Case
The means of two variables x and y are 10 and 20 respectively while their variances are 16 and 36 respectively. The coefficient of correlation is 0.8. Obtain the equations of lines of regression of the two variables Zi and Wi. Zi = (Xi – 4)2; Wi = (Yi – 5)/3

In solving this type of problems few steps are important:

(1) We have to find the means of the new variables from the means of the old variables taking the effect of change of origin and scale into consideration. Mean is not independent of change or origin and scale. So, we have to take the effects of these changes while calculating means of the new variable.

(2) We have to find the standard deviations of the new variables from the SDs of the old variables by taking the change of scale into consideration. Standard Deviation is independent of change of origin but not scale. So, we have to give the effect of change of scale while calculating the SD of the new variable.

(3) Since the coefficient of correlation is independent of change of origin and scale, r(xy) = r(vw) of any new variables which are the results of the change of origin and scale in x and y.

(4) From the coefficient of correlation and the SDs of the new variables, we can now calculate the coefficients of regression of the new variable by using the formulae by definition.

(5) With the help of the means and the coefficients of regression of the new variables, now, we can obtain the lines of regression for the new variables and we can also find their estimated values corresponding to the known values.

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