Question

The president of a company was interested in determining whether there is a correlation between sales made by different sales teams and hours spent on employee training. These figures are shown.

Sales (in thousands)	Training Hours
11	7
33	11
27	10
38	15
8	3

1. Compute the correlation coefficient for the data. (Round your answer to 4 decimal places, the tolerance is +/-0.0001.)
   The correlation coefficient is

2. Using the data, what would you expect sales to be if training was increased to eighteen hours? Use the linear regression model. (Round your answer to 2 decimal places, the tolerance is +/-0.01.)
Sales = . (in thousands)

Answer 1

Let the training hours be denoted by x and sales by y

Let the Regression line be y = b_o + b₁x

where,

b_o = ( Σy Σx² - Σx Σxy ) / ( nΣx² - (Σx)² )

b₁ = ( nΣxy - ΣxΣy ) / ( nΣx² - (Σx)² )

	Sales(y)	Training Hours(x)	x2	xy	y2
	11	7	49	77	121
	33	11	121	363	1089
	27	10	100	270	729
	38	15	225	570	1444
	8	3	9	24	64
Σ	117	46	504	1304	3447

=> b_o = ( 117*504 - 46*1304 ) / ( 5*504 - 46² ) = -2.51

b₁ = ( 5*1304 - 46*117 ) / ( 5*504 - 46² ) = 2.82

=> y = -2.51 + 2.82x

Correlation coefficient r = ( nΣxy - ΣxΣy ) / sqrt(( nΣx² - (Σx)² ) ( nΣy² - (Σy)² ))

=> r = ( 5*1304 - 46*117 ) / sqrt(( 5*504 - 46² ) ( 5*3447 - 117² )) = 0.9508

2. We found the regression line y = -2.51 + 2.82x

when training hours x = 18,

Sales y = -2.51 + 2.82*8 = 20.05