Question

Data on advertising expenditures and revenue (in thousands of dollars) for the Four Seasons Restaurant follow. Advertising Expenditures Revenue 1 19 2 33 4 45 52 10 14 53 20 54 a. Let x equal advertising expenditures and y equal revenue. Complete the estimated regression equation below (to 2 decimals) b. Test whether revenue and advertising expenditures are related at a .05 level of significance. Compute the following (to 2 decimals). SSE SST SSR MSR MSE Compute the F test statistic (to 2 decimals). 40

Answer 1

(a)

Following table shows the calculations:

	X	Y	X^2	Y^2	XY
	1	19	1	361	19
	2	33	4	1089	66
	4	45	16	2025	180
	6	40	36	1600	240
	10	52	100	2704	520
	14	53	196	2809	742
	20	54	400	2916	1080
Total	57	296	753	13504	2847

n = 7 Sample size: From table we have: (Σ3). 753- ((57)A2/7) 288.85714 13504- ((296)A2/7) n 987.42857 S,-Σw-ΣΣ) 2847- ((296* 57)/7) = n 436.714286

The slope is: 436.714286/288.85714 b 1.5119 The intercept is: 1 (Σν-ΑΣ: y bo (296 (1.5119 * 57))/7 -- n bo 29.9745 The regression equation is: y' 1.5119 * x+ 29.9745

Answer: 1.51*x+29.97

(b)

The SSE is SSE =y-bEy-b,^xy = 13504 - (29.9745 * 296) - (1.5119 * 2847) -327.17

The SSR is: (Σ) (29.9745 296) + (1.5119 * 2847) - ((296)^2 7) 660.26 The SST is: SST S 987.43

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Since there is 2 variables so we have k=2. Therefore degree of freedoms are:

dfreg = k- 1=1

dfres n-k=7-2 5

dfrotal =51 6

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Now

SSR 660.26 MSR dfreg

SSE 65.434 MSE dfres

F test statistics is

MSR 10.09 F MSE