Question

www.s Foesponse/submitrdep Suppose a certain retailer sells several models of refrigerators. A random sample of the models sold by this retailer and their corresponding cubic feet (ou. ft.) and list price can be found below. Cu. Ft List Price Model Model 1 18.3 $899.99 Model 2 24.8 $1,699.99 Model 3 with Thru-the Door Ice and Water 25.4 $1,699.99 19.3 $749.99 Model 4 $599.99 17.7 Model 5 Model 6 with Thru-the-Door Ice and Water $1,619.99 19.6 25.0 $999.99 Model 7 $1,299.99 24.5 Model 8 Model 9 $1,299.99 25.4 with Thru-the-Door Ice and Water Model 10 with Thru-the-Door Ice and Water $1.299.99 26.0 $1.099.99 Model 11 25.6 with Thru-the-Door Ice and Water $679.99 18.0 Model 12 Model 13 with Thru-the Door Ice and Water $2.199.99 25.0 629 PM with Thru-the Door Ice and Water Model 14 20.2 $849.99 Model 15 15.5 $549.99 Model 16 with Thru the Door Ice and Water 28.2 $2,599.99 Model 17 27.8 $2,999.99 Model 18 26.6 $2,399.99 with Thru-the-Door Ice and Water Model 19 with Thru-the-Door Ice and Water $1,099.99 22.6 Model 20 with Thru-the-Door Ice and Water 21.8 $1,499.99 Model 21 20.9 $1.679.99 (a) Develop the estimated simple linear regression equation to show how list price is related to the independent variable cubic feet. (Round your numerical values to four decimal places. Let x, represent the cubic feet and y represent the list price.) -1538.542+130.2381x x (b) At the 0.05 level of significance, test whether the estimated regression equation developed in part (a) indicates a significant relationship between list price and cubic feet. State the nul and alternative hypotheses. H P, 2 0 Suassagatwitystldent/Assignment-Responses/submit?dep-21278551 Find the test statistic. (Round your answer to two decimal places.) Find the p value. (Round your answer to four decimal places.) State your conclusion. OReject H: There is sufficient evidence to conclude there is a significant relationship between list price and cubic feet. OReject Ho: There is insufficient evidence to conclude there is a significant relationship between list price and cubic feet. Do not reject Ha. There is sufficient evidence to conclude there is a significant relationship between list price and cubic feet. ODo not reject Ha. There is insufficient evidence to conclude there is a significant relationship between list price and cublc feet. (c) Develop a dummy variable that will account for whether the refrigerator has the thru-the-door ice and water feature. Code the dummy variable with a value of 1 if the refrigerator has the thru-the-door ice and water feature and with 0 otherwise. Use this dummy variablee to develop the estimated multiple regression equation to show how ist price is related to cubic feet and the thru-the-door ice and water feature. (Round your numerical values to four decimal places. Let x, represent the cubic feet, x, represent whether the refrigerator has the thru-the-door ice and water feature, and y represent the list price.) (d) At a 0.05, is the thru-the-door ice and water feature a significant factor in the list price of a refrigerator? State the null and alternative hypotheses Ho Pa 2 0 H, o Hoi 2s0 H: B,>o 632 PM giuhetywebySiont/rSSIghment-Foesponsessubmitrdep 21278551 (d) At a 0.05, is the thru-the-door ice and water feature a significant factor in the list price of a refrigerator? State the null and alternative hypotheses H B 2 0 H o H B,0 Find the test statistic. (Round your answer to two decimal places.) Find the p value. (Round your answer to four decimal places.) State your conclusion Reject H. There is sufficient evidence to conclude there is a significant relationship between list price and whether the refrigerator has the thru-the-door ice and water feature. Reject H. There is insufficient evidence to conclude there is a significant relationship between list price and whether the refrigerator has the thna-the-door ice and water feature. Do not reject Ho There is sufficient evidence to conclude there is a significant relationship between list price and whether the refrigerator has the thru the-door ice and water feature. Do not reject Ha There is insufficient evidence to conclude there is a significant relationship between list price and whether the refrigerator has the thru-the-door ice and water feature.

Answer 1

(c) y^=-1706.459+137.1297x1

(b) H0:$\beta$1=0 and H1:$\beta_1\ne 0$

test statistic=t=coeff(x1)/SE(x1)=137.1297/27.8581=4.92

p-value=0.0000

since p-value of x1 is less than alpha=0.05, so we

Reject H0 : There is sufficient evidence to conclude there is a significant relationship between cubic feet and list price

following regression analysis information has been generated

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.748661265
R Square	0.560493689
Adjusted R Square	0.537361778
Standard Error	460.4965348
Observations	21
ANOVA
	df	SS	MS	F	Significance F
Regression	1	5138211.126	5138211	24.23032	9.45589E-05
Residual	19	4029084.112	212057.1
Total	20	9167295.238
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	-1706.458964	642.2791505	-2.65688	0.015569	-3050.764673	-362.1532553
x1	137.1297119	27.8581298	4.922431	9.46E-05	78.82197627	195.4374476

(c)y^=-1805.183+143.4711x1-106.5837x2

(d) H0:$\beta$2=0 and Ha:

B20

test statistic t=-106.58/230.16=-0.46

p-value=0.6489

since p-value is more than alpha=0.05 so

Donot reject H0. There is insufficient evidence to conclude there is significant relationship between list price and whether the refrigerator has the thru the door ice and water feature

following regression analysis information has been generated using ms-excel

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.752109095
R Square	0.56566809
Adjusted R Square	0.517408989
Standard Error	470.3219258
Observations	21
ANOVA
	df	SS	MS	F	Significance F
Regression	2	5185646.389	2592823	11.72148	0.000550042
Residual	18	3981648.849	221202.7
Total	20	9167295.238
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	-1805.183355	689.7567174	-2.61713	0.017459	-3254.308443	-356.0582677
x1	143.4711294	31.57645227	4.543611	0.000252	77.13146502	209.8107938
x2	-106.5837369	230.1630014	-0.46308	0.648857	-590.1382587	376.9707849