A Realtor examines the factors that influence the price of a house in Arlington,
ID: 3222274 • Letter: A
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. Use Table 2 and Table 4.
Estimate: Price = 0 + 1 Sqft + 2 Beds + 3 Baths + . (Round your answers to 2 decimal places.)
Choose the appropriate hypotheses to test whether the explanatory variables are jointly significant in explaining price.
Find the value of the appropriate test statistic. (Round your answer to 4 decimal places.)
At the 5% significance level, what is the conclusion to the test? Are the explanatory variables jointly significant in explaining Price?
Choose the appropriate hypotheses to test whether each of the explanatory variables are individually significant in explaining Price.
At the 5% significance level, are all explanatory variables individually significant in explaining Price?
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. Use Table 2 and Table 4.
Explanation / Answer
Answer:
Regression Analysis
R²
0.724
Adjusted R²
0.698
n
36
R
0.851
k
3
Std. Error
74984.984
Dep. Var.
Price
ANOVA table
Source
SS
df
MS
F
p-value
Regression
471,210,518,475.0910
3
157,070,172,825.0300
27.9348
4.59E-09
Residual
179,927,931,247.1320
32
5,622,747,851.4729
Total
651,138,449,722.2220
35
Regression output
confidence interval
variables
coefficients
std. error
t (df=32)
p-value
95% lower
95% upper
Intercept
153,348.2664
57,141.7937
2.684
.0114
36,954.2414
269,742.2914
Sqft
95.8559
35.3997
2.708
.0108
23.7490
167.9629
Beds
556.8907
20,280.3128
0.027
.9783
-40,752.7546
41,866.5360
Baths
92,022.9126
25,012.2976
3.679
.0009
41,074.5297
142,971.2955
a.
Estimate: Price = 0 + 1 Sqft + 2 Beds + 3 Baths + . (Round your answers to 2 decimal places.)
= 153,348.27 + 95.86 Sqft + 556.89 Beds + 92,022.91 Baths
b-1.
Choose the appropriate hypotheses to test whether the explanatory variables are jointly significant in explaining price.
H0: 1 = 2 = 3 = 0; HA: At least one j < 0
Answer: H0: 1 = 2 = 3 = 0; HA: At least one j 0
H0: 1 = 2 = 3 = 0; HA: At least one j > 0
b-2.
Find the value of the appropriate test statistic. (Round your answer to 4 decimal places.)
Test statistic 27.9348
b-3.
At the 5% significance level, what is the conclusion to the test? Are the explanatory variables jointly significant in explaining Price?
Answer: 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: j = 0; HA: j > 0
H0: j = 0; HA: j < 0
Answer: H0: j = 0; HA: j 0
c-2.
At the 5% significance level, are all explanatory variables individually significant in explaining Price?
Explanatory Variables
Significant in
Explaining Price
Sqft
Yes
Beds
No
Baths
Yes
Regression Analysis
R²
0.724
Adjusted R²
0.698
n
36
R
0.851
k
3
Std. Error
74984.984
Dep. Var.
Price
ANOVA table
Source
SS
df
MS
F
p-value
Regression
471,210,518,475.0910
3
157,070,172,825.0300
27.9348
4.59E-09
Residual
179,927,931,247.1320
32
5,622,747,851.4729
Total
651,138,449,722.2220
35
Regression output
confidence interval
variables
coefficients
std. error
t (df=32)
p-value
95% lower
95% upper
Intercept
153,348.2664
57,141.7937
2.684
.0114
36,954.2414
269,742.2914
Sqft
95.8559
35.3997
2.708
.0108
23.7490
167.9629
Beds
556.8907
20,280.3128
0.027
.9783
-40,752.7546
41,866.5360
Baths
92,022.9126
25,012.2976
3.679
.0009
41,074.5297
142,971.2955