Question

The management of a large furniture store would like to determine sales (in thousands of ₹) (X) on a given day on the basis of number of people (Y) that visited the store on that day. The necessary records were kept, and a random sample of ten days was selected for the study. The summary results were as follows:

`sumx_i = 370 , sumy_i = 580, sumx_i^2 = 17200 , sumy_i^2 = 41640, sumx_iy_i = 11500, n = 10`

Answer 1

Line of regression of X on Y is `X = a + b_(xy) Y`

Where `b_(xy)= (cov(X,Y))/sigma_Y^2`

`= ((sumx_iy_i)/n - barxbary)/(((sumy_i^2)/n) - (bary)^2)`

`= (((11,500)/10) - (370/10)(580/10))/(((41,640)/10) - (510/10)^2)`

`= (-996)/800`

`=-1.245`

and `a^' = barx - b_(xy)bary`

`= 37 - (-1.245)(58)`

∴ Line of regression of X on Y is,

`X = 109.21 - 1.245 Y`