Question

This problem has several parts.

The table below shows a firm’s advertising budget, in thousands of dollars, and its sales, also in thousands of dollars, for one year.

Advertising	5.5	5.9	6	5.8	6.3	6.3	6.4	6.5	6.5	6.5	6.7	6.9
Sales	98	108	111	114	118	115	118	120	122	119	117	124

Find the correlation coefficient to two decimal places:

Which of the following is the equation of the regression line?

A. y=−15.652x−17.116
B. y=−15.652x+17.116
C. y=17.116x−15.652
D. y=17.116x+15.652
E. y=15.652x+17.116
F. y=15.652x−17.116

Using the regression line, estimate sales if the advertising budget is increased to 7.0 (i.e., $7,000).
	Estimate:  (Round to the nearest thousand dollars. E.g., if the regression line predicted 117.235, you would round to 117.)
Did you just perform interpolation or extrapolation?
A. extrapolation B. interpolation

Answer 1

Following table shows the calculations:

	Advertising, X	Sales, Y	X^2	Y^2	XY
	5.5	98	30.25	9604	539
	5.9	108	34.81	11664	637.2
	6	111	36	12321	666
	5.8	114	33.64	12996	661.2
	6.3	118	39.69	13924	743.4
	6.3	115	39.69	13225	724.5
	6.4	118	40.96	13924	755.2
	6.5	120	42.25	14400	780
	6.5	122	42.25	14884	793
	6.5	119	42.25	14161	773.5
	6.7	117	44.89	13689	783.9
	6.9	124	47.61	15376	855.6
Total	75.3	1384	474.29	160168	8712.5

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Correct option is:

E. y=15.652x+17.116

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The predicted value for x = 7.0 is

y=15.652 * 7.0 +17.116 = 126.68

Answer: 127

A. extrapolation (because 7.0 is not in the range of x used to make the model).