Data on advertising expenditures and revenue (in thousands of dollars) for the Four Seasons Restaurant follow....

Data on advertising expenditures and revenue (in thousands of dollars) for the Four Seasons Restaurant follow. Advertising Expenditures Revenue 1 20 2 33 4 44 6 40 10 52 14 53 20 54

a. Let X equal advertising expenditures and Y equal revenue. Complete the estimated regression equation below (to 2 decimals). y =( )+( )x b. Compute the following (to 1 decimal). SSE ( ) SST ( ) SSR ( )MSR ( ) MSE ( )

c. Test whether revenue and advertising expenditures are related at a .05 level of significance. Compute the F test statistic ( to 2 decimals).

Solutions

Expert Solution

	x	y	(x-xbar)^2	(y-ybar)^2	(x-xbar)*(y-ybar)
	1	20	51.020408	496.65306	159.1836735
	2	33	37.734694	86.22449	57.04081633
	4	44	17.163265	2.9387755	-7.102040816
	6	40	4.5918367	5.2244898	4.897959184
	10	52	3.4489796	94.367347	18.04081633
	14	53	34.306122	114.79592	62.75510204
	20	54	140.59184	137.22449	138.8979592
sum	57	296	288.85714	937.42857	433.7142857
mean	8.142857143	42.28571429	sxx	syy	sxy

	slope=b1=sxy/sxx	1.50148368
	intercept=b0=ybar-(slope*xbar)	30.05934718
	SST	SYY	937.42857
	SSR	sxy^2/sxx	651.21492
	SSE	syy-sxy^2/sxx	286.21365

The Fitted model is

y=30.1+1.50(Expenditure)

Ansb:

SSE=286.22

SST=937.43

SSR=651.21

#MSR=SSR/1=651.21

#MSE=SSE/(n-2)=57.24273

ANOVA
	df	SS	MS	F
Regression	1	651.2149216	651.2149	11.37638
Residual	(n-2)=5	286.2136499	57.24273
Total	6	937.4285714

Ansc:

F-statistics=MSR/MSE=11.38

F-critical=6.608----using FINV(0.05,1,5)

P-value=0.0074

#P-value<0.05 hence we reject the null hypothesis at 5% l.o.s

#we reject the H0. Hence claim is significant

orchestra answered 1 year ago

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