Question

Number 2 A regression analysis of 62 months’ data relating a company's monthly advertising expenses (x, in thousands of dollars) to its sales (y, in thousands of dollars) yields the following output:

• • ?0=100
• • ?1=5.3
• • Standard error of the estimate ?=??=56
• • Standard error for ?1, ???1=0.3

Furthermore, when ?∗=9, the standard error for a confidence interval for the estimated mean response is given by ???̂=29, while the standard error for a prediction interval is ???̂=63.1.

• (a) (3 pts) Is the regression significant at a 5% level of significance?
• (b) (3 pts) Say that the company spends $9000 on advertising in a given month. What would you expect their sales to be?
• (c) (3 pts) Find a 95% confidence interval for the average sales over all months in which they plan to spend $9000 on advertising.
• (d) (3 pts) Assume that you know that in January of 2020, they spent $9000 on advertising, but you don’t have

Answer 1

y^ = 100 + 5.3 x

a)

TS = b1^ / se(b1^)

= 5.3 / 0.3 = 17.6667

p-value = 2 P(t > |TS| ) = 0

since p-value < alpha

regression is significant

b)

y^ = 100 + 5.3* x

= 100 + 5.3 * 9 = 147.7

c)

df =n-2 = 60

(147.7 +- 63.1)

= (84.6,210.8)

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