Question

The following data represent a company's yearly sales volume and its advertising expenditure over a period of 5 years.

(y) sales in millions of dollars (x) advertising in ($10,000)

15 32

16 33

18 35

17 34

16 36

Use the method of least squares to compute an estimated regression line between sales and advertising by computing b0 and b1.

If the company's advertising expenditure is $400,000, what are the predicted sales? Give the answer in dollars.

What does the slope of the estimated regression line indicate?

Answer 1

We have,

	X(in $10000)	Y	X^2	Y^2	XY
	32	15	1024	225	480
	33	16	1089	256	528
	35	18	1225	324	630
	34	17	1156	289	578
	36	16	1296	256	576
Total	170	82	5790	1350	2792

Where, Y = b0 + b1*X

Thus,

a = b0 = (82*5790 - 170*2792)/ (5*5790- 170^2) = 2.8

b = b1 = (5*2792 - 170*82)/(5*5790- 170^2) = 0.4

Thus, Y = 2.8 + 0.4*X

Where, slope = b1 = 0.4

Now, when company's advertising expenditure is $400,000

i.e x = 40

then Y = 2.8+ 0.4*40

Y = 18.8

Thus, predicted sales is $18.8 million

Slope of regression line is proportion of change in Y per unit change in X. Thus, slope in this regression indicates for each additional advertising expenditure of $10,000 (i.e. x = 1), predicted sales increases by 0.4 million dollars (y = 0.4)