Question

Q2. Run two multiple regression model using the following formulation, then interpret, and compare the two models. The models are 1) Sales, = Be + B Salese-2 + B2 Advertiset-1+€ and 2) Sales; = B. + BSalest-1 + B2 Advertise-2 and data set is PINKHAM. Answer the following questions. a. State the null and alternate hypothesis for both slopes. b. Interpret the P value and comparison at a = 0.05 significance level forB1, B2 for both models c. What are r squared value and its interpretation? Also, interpret the root mean squared error (RMSE) and compare them. d. What conclusions have you derived after performing hypothesis tests? e. What will you state to your Sales Director after running the hypothesis test?

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Answer 1

Model 1

Regression Analysis: Sales versus SalesT_2, AdvertiseT_1

Analysis of Variance

Source	DF	Adj SS	Adj MS	F-Value	P-Value
Regression	2	16450153	8225076	93.49	0.000
SalesT_2	1	1738154	1738154	19.76	0.000
AdvertiseT_1	1	3234076	3234076	36.76	0.000
Error	49	4310891	87977
Total	51	20761043

Model Summary

S	R-sq	R-sq(adj)	R-sq(pred)
296.610	79.24%	78.39%	76.08%

Coefficients

Term	Coef	SE Coef	T-Value	P-Value	VIF
Constant	168	133	1.26	0.214
SalesT_2	0.4177	0.0940	4.44	0.000	1.98
AdvertiseT_1	0.951	0.157	6.06	0.000	1.98

Regression Equation

Sales

=

168 + 0.4177 SalesT_2 + 0.951 AdvertiseT_1

Model 2

Regression Analysis: Sales versus SalesT_1, AdvertiseT_2

Analysis of Variance

Source	DF	Adj SS	Adj MS	F-Value	P-Value
Regression	2	17990758	8995379	159.11	0.000
SalesT_1	1	5656199	5656199	100.05	0.000
AdvertiseT_2	1	5715	5715	0.10	0.752
Error	49	2770285	56536
Total	51	20761043

Model Summary

S	R-sq	R-sq(adj)	R-sq(pred)
237.774	86.66%	86.11%	84.94%

Coefficients

Term	Coef	SE Coef	T-Value	P-Value	VIF
Constant	103	104	0.99	0.325
SalesT_1	0.9675	0.0967	10.00	0.000	3.36
AdvertiseT_2	-0.052	0.165	-0.32	0.752	3.36

Regression Equation

Sales

=

103 + 0.9675 SalesT_1 - 0.052 AdvertiseT_2

(a) H0: Beta1 = Beta2 = 0 vs H1: At least one of Beta1 and Beta2 is not zer
(b) For model1 p values for both the parameters are 0.000. That is, both are significant. While for model the p value for beta1 is 0.000 indicating its significance while p value for beta2 is 0.752 implying its insignificance.

(c) Model 1: R square = 0.7924 and RMSE = 2076.27

Model2: R square = 0.8666 and RMSE = 1664.42

For model1 79.24% of the variation in sales is explained by salesT-2 and AdvertiseT-1 while for model 86.66% of the variation in sales is explained by salesT-1 and AdvertiseT-2. This indicates model2 is better fit. The RMSE for model2 is smaller than that of model 1 implying that model 2 is better.

(d) conclusion is written in (b)

(e) As per model1 SalesT-2 and AdvertiseT-1 both the variables can be used to predict the sales and as per model2 SalesT-1 only can be used to predict the sales as AdvertiseT-2 is insignificant. Model2 is better fit than model1 if we compare the R square and RMSE values. Even though model1 is inferior to model2 both the variables in SalesT-2 and AdvertiseT-1 are significant. Hence it is suggested to fit another model with SalesT-1, SalesT-2 and AdvertiseT-1 as the predictors of the sales.