Question

4. (a)	A random sample of 79 companies from the Forbes 500 list (which actually consists of nearly 800 companies) was selected, and the relationship between sales (in hundreds of thousands of dollars) and profits (in hundreds of thousands of dollars) was investigated by regression. The following results were obtained from statistical software. R2 = 0.662 s = 466.2 Variable Parameter estimate Standard error Constant –176.644 61.16 Sales 0.092498 0.0075 Is there strong evidence of a straight-line relationship between sales and profits? Explain briefly.
	A)	Yes, because the slope of the least-squares line is positive
	B)	Yes, because the P-value for testing if the slope is zero is quite small
	C)	No, because the value of the square of the correlation is relatively small
	D)	It is impossible to say because we are not given the actual value of the correlation.

(b)	Use the same data as for problem 4. Suppose the researchers conducting this study wish to estimate the profits (in hundreds of thousands of dollars) for companies that had sales (in hundreds of thousands of dollars) of 500. The following results were additionally obtained from statistical software. Sales Predicted profit Standard error 95.0% C.I. 95.0% P.I. 500 –130.4 59.3 (–248.5, –12.3) (–1066.4, 805.6) If the researchers wish to estimate the mean profits for all companies that had sales of 500, what would be a 95% confidence interval for the mean profits?
	A)	(–1066.4, 805.6)
	B)	(–248.5, –12.3)
	C)	–130.4 ± 59.3
	D)	500 ± 59.3

Answer 1