Question

please show work

anager of a bookstore wants to predict sales (in $1000) from Number Sales People Working using the accompanying data. Complete the parts below: Sales (in $1000) (y) 55 Number of sales people (x) 55 Mean Standard Deviation 17.90 5.40 11.00 5.96 (x-7)(y-7) = 1666.680624 a) Find the correlation coefficient between sales and number of sales peo ple working in the shop. b) Compute coefficient of determination (R) and interpret it. c) Comment on your results in (a) and (b) above.

Answer 1

$\textbf{a)}$

1666.680624/55 Cov(,y) correlation (R) = – var(.) x var(y) (x-7)(y-y)/n 5.402 x 5.962 =0.941563636 5.40 x 5.96

$\textbf{b)}$

coefficient of determination R2) = 0.941563636% = 0.886542081322314

Thus it can stated that almost 0.89 part of the total variability of the sales is accounted for by

its linear regression on the number of sales person.

$\textbf{c)}$

There is a high positive correlation between the sales and the number sales people. This indicates

that increasing the number of sales people is supposed to increase the sales with it.

The coefficient of determination is high, close to 1. So it implies that the linear regression model

explains very well the relation between sales and the number of sales people, and the prediction

of sales from the number of sales people will be highly accurate,