Question

A Realtor examines the factors that influence the price of a house in Arlington, Massachusetts. He collects data on recent house sales (Price) and notes each house’s square footage (Sqft) as well as its number of bedrooms (Beds) and number of bathrooms (Baths). A portion of the data is shown in the accompanying table.

Price	Sqft	Beds	Baths
840,000	2,768	4	3.5
822,000	2,500	4	2.5
⋮	⋮	⋮	⋮
307,500	850	1	1

Click here for the Excel Data File

a. Estimate: Price = β₀ + β₁Sqft + β₂Beds + β₃Baths + ε. (Round your answers to 2 decimal places.)

PriceˆPrice^ =  +  Sqft +  Beds +  Baths

b-1. Choose the appropriate hypotheses to test whether the explanatory variables are jointly significant in explaining price.

• H₀: β₁ = β₂ = β₃ = 0; H_A: At least one β_j < 0

• H₀: β₁ = β₂ = β₃ = 0; H_A: At least one β_j ≠ 0

• H₀: β₁ = β₂ = β₃ = 0; H_A: At least one β_j > 0

    
b-2. Calculate the value of the test statistic. (Round your answer to 3 decimal places.)

b-3. At the 5% significance level, what is the conclusion to the test? Are the explanatory variables jointly significant in explaining Price?

• Reject H₀; the explanatory variables are jointly significant in explaining Price.

• Reject H₀; the explanatory variables are not jointly significant in explaining Price.

• Do not reject H₀; the explanatory variables are jointly significant in explaining Price.

• Do not reject H₀; the explanatory variables are not jointly significant in explaining Price.

c-1. Choose the appropriate hypotheses to test whether each of the explanatory variables are individually significant in explaining Price.

• H₀: β_j = 0; H_A: β_j > 0

• H₀: β_j = 0; H_A: β_j < 0

• H₀: β_j = 0; H_A: β_j ≠ 0

c-2. At the 5% significance level, are all explanatory variables individually significant in explaining Price?

Answer 1

EXCEL > DATA > DATA ANALYSIS > REGRESSION  

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.850689001
R Square	0.723671776
Adjusted R Square	0.697766005
Standard Error	74984.98417
Observations	36
ANOVA
	df	SS	MS	F	Significance F
Regression	3	4.71211E+11	1.5707E+11	27.93477086	4.59052E-09
Residual	32	1.79928E+11	5622747851
Total	35	6.51138E+11
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	153348.2664	57141.79374	2.683644603	0.011433126	36954.24141	269742.2914	36954.24141	269742.2914
Sqft	95.85594255	35.39974687	2.707814349	0.010779404	23.74901779	167.9628673	23.74901779	167.9628673
Beds	556.8906656	20280.31276	0.027459669	0.978263646	-40752.75462	41866.53595	-40752.75462	41866.53595
Baths	92022.91259	25012.29756	3.679106742	0.000854652	41074.52969	142971.2955	41074.52969	142971.2955

a)

Price^ = 153348.27 + 95.86*Sqft + 556.89*Beds + 92022.91*Baths

b1)

H0: β1 = β2 = β3 = 0

HA: At least one βj ≠ 0

b2)

F stat = 27.935

b3)

P value = 0 < 0.05

Reject H0; the explanatory variables are jointly significant in explaining Price.

c1)

H0: βj = 0

HA: βj ≠ 0

c2)

Except beds remaining all explanatory variables individually significant in explaining Price

beds p value = 0.9783 > 0.05 (Remaining all explanatory variables P value < 0.05)