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10、Given the results from a multiple regression function: 24 ? 2 × X1i + 4 × X2i, which of the following are known to be true? Based upon the equation:

?            if the observed dependent variable equals 30 and X1i = 1, then X2i = 2.

?            if both independent variables equal zero, the fitted value for the dependent variable is 24.

?            there is a negative relationship between the dependent variable and X1i.

?            given X1i = 2 and X2i = 1 the fitted value for the dependent variable is 24.

A) II and III only.

B) I and III only.

C) II, III, and IV only.

D) I, II, III, and IV.

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What is the y-intercept term, b0?

A) 47.6712. 

B) 34.7400.

C) 92.2840.

D) 512.3600.

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The correct answer is A

The mean of the aggregate revenue (Y) is 3,645/10 = 364.50 and of the advertising expenditure (X) is 91.2/10 = 9.12. The y-intercept, b0 = MeanY – Slope * MeanX = 364.50 – 34.74 * 9.12 = 47.6712.

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Which of the following is the CORRECT value of the correlation coefficient between aggregate revenue and advertising expenditure?

A) 0.9500.

B) 0.3947.

C) 0.7780.

D) 0.6053.

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The correct answer is C

The R2 = (SST - SSE)/SST = RSS/SST = (20,922.5 - 8,257.374) / 20,922.5 = 0.6053.

The correlation coefficient is the square root of the R2 in a simple linear regression which is the square root of 0.6053 = 0.7780.

Which of the following reports the CORRECT value and interpretation of the R2 for this regression? The R2 is:

A) 0.3947 indicating that the variability of advertising expenditure explains about 39.47% percent of the variability of aggregate revenue.

B) 0.6053 indicating that the variability of advertising expenditure explains about 60.53% of the variability in aggregate revenue.

C) 0.6053 indicating that the variability of aggregate revenue explains about 60.53% of the variability in advertising expenditure.

D) 0.3947 indicating that the variability of aggregate revenue explains about 39.47% percent of the variability of advertising expenditure

aianjie

 

The correct answer is B

The R2 = (SST - SSE)/SST = (20,922.5 - 8,257.374) / 20,922.5 = 0.6053.

The interpretation of this R2 is that 60.53% of the variation in aggregate revenue (Y) is explained by the variation in advertising expenditure (X).

aianjie

 

The correct answer is B

Lower Limit = Coefficient - (1.96 x Standard Error of the coefficient)

 = 34.74 - (1.96 x 9.917)

 = 34.74 - 19.4373 = 15.30

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9、Cynthia Jones is Director of Marketing at Vancouver Industries, a large producer of athletic apparel and accessories. Approximately three years ago, Vancouver experienced increased competition in the marketplace, and consequently sales for that year declined nearly 20 percent. At that time, Jones proposed a new marketing campaign for the company, aimed at positioning Vancouver’s product lines toward a younger target audience. Although the new marketing effort was significantly more costly than previous marketing campaigns, Jones assured her superiors that the resulting increase in sales would more than justify the additional expense. Jones was given approval to proceed with the implementation of her plan.

Three years later, in preparation for an upcoming shareholders meeting, the CEO of Vancouver has asked Jones for an evaluation of the marketing campaign. Sales have increased since the inception of the new marketing campaign nearly three years ago, but the CEO is questioning whether the increase is due to the marketing expenditures or can be attributed to other factors. Jones is examining the following data on the firm's aggregate revenue and marketing expenditure over the last 10 quarters. Jones plans to demonstrate the effectiveness of marketing in boosting sales revenue. She chooses to utilize a simple linear regression model. The output is as follows:

	Aggregate Revenue (Y)	Advertising Expenditure (X)	Y2	XY	X2
	300	7.5	90,000	2,250	56.25
	320	9.0	102,400	2,880	81.00
	310	8.5	96,100	2,635	72.25
	335	8.2	112,225	2,747	67.24
	350	9.0	122,500	3,150	81.00
	400	8.5	160,000	3,400	72.25
	430	10.0	184,900	4,300	100.00
	390	10.5	152,100	4,095	110.25
	380	9.0	144,400	3,420	81.00
	430	11.0	184,900	4,730	121.00
TOTAL	3,645	91.2	1,349,525	33,607	842.24

Slope coefficient = 34.74 Standard error of slope coefficient = 9.916629313 Standard error of intercept = 92.2840128

ANOVA
	Df	SS	MS
Regression	1	12,665.125760	12,665.12576
Residual	8	8,257.374238	1,032.17178
Total	9	20,922.5

For the questions below, assume that the regression model was estimated using a large number of observations.

What is the upper limit of the 95 percent confidence interval for the slope coefficient?

A)    62.84.

B)    54.18.

C)   46.05.

D)   36.70.

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The correct answer is B

Upper Limit = coefficient + (1.96 x standard error of the coefficient) = 34.74 + (1.96 x 9.917) = 54.18

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What is the lower limit of the 95 percent confidence interval for the slope coefficient?

A) 32.78.

B) 15.30.

C) 12.24.

D) 19.89.