A real estate agent wants to determine the factors that influence house prices in Adelaide. A random sample of 200 houses was selected to estimate the multiple regression model: y =B₁ + B₁x₁ + B₂log(x₂) + B3X3 + B4x4 + B5X5 + U Where, y = House price (in $10,000s). x₁ = Distance from the city center (in kilometers). x₂ = Number of bedrooms. x3 = Age of the house (in years). x₁= Dummy variable equal to 1 if the house has a backyard. x= Proxy for the quality of the neighborhoods' schools The estimation results are shown below when excluding x, and xs of the regression (Model 1) and when including them (Model 2). Standard errors are in parentheses. Explanatory Variables Model 1 Model 2 Bo B₁ B₂ B3 B₁ Bs N SSR SST 25.3 (10.7) -0.032 (0.009) 15.1 (2.3) -1.8 (0.5) 100 432 798 20.1 (15.2) -0.028 (0.001) 12.4 (1.8) -1.5 (0.6) 5.2 (2.1) 4.6 (1.9) 100 390 798 (a) Write down the Sample Regression Function (SRF) for Model 1 in an equation form and interpret each of the estimated slope coefficients.
A real estate agent wants to determine the factors that influence house prices in Adelaide. A random sample of 200 houses was selected to estimate the multiple regression model: y =B₁ + B₁x₁ + B₂log(x₂) + B3X3 + B4x4 + B5X5 + U Where, y = House price (in $10,000s). x₁ = Distance from the city center (in kilometers). x₂ = Number of bedrooms. x3 = Age of the house (in years). x₁= Dummy variable equal to 1 if the house has a backyard. x= Proxy for the quality of the neighborhoods' schools The estimation results are shown below when excluding x, and xs of the regression (Model 1) and when including them (Model 2). Standard errors are in parentheses. Explanatory Variables Model 1 Model 2 Bo B₁ B₂ B3 B₁ Bs N SSR SST 25.3 (10.7) -0.032 (0.009) 15.1 (2.3) -1.8 (0.5) 100 432 798 20.1 (15.2) -0.028 (0.001) 12.4 (1.8) -1.5 (0.6) 5.2 (2.1) 4.6 (1.9) 100 390 798 (a) Write down the Sample Regression Function (SRF) for Model 1 in an equation form and interpret each of the estimated slope coefficients.
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter4: Equations Of Linear Functions
Section4.5: Correlation And Causation
Problem 2AGP
Related questions
Question
Transcribed Image Text:(b) Using Model 1 estimates, calculate the predicted dollar value of a 20-year-old
house situated 20km from the city, which has 3 bedrooms.
(c) Is there sufficient evidence at the 1% significance level to indicate that the
distance from the city center affects house prices? Specify all relevant steps of
the hypothesis testing procedure.
(d) Is there sufficient evidence at the 10% significance level to indicate that the
number of bedrooms affects house prices? Again, specify all relevant steps of
the hypothesis testing procedure.
(e) Test whether x, and x5 are jointly significant at the 1% level.
(f) Given the information provided in the regression results table above, determine
the goodness of fit of model 1 and explain its meaning.
(g) Test the overall significance of the regression model used in Model 1 at the
5% level. Specify all relevant steps of the hypothesis testing procedure.
Transcribed Image Text:Question 2
A real estate agent wants to determine the factors that influence house prices in
Adelaide. A random sample of 200 houses was selected to estimate the multiple
regression model:
y =B₁ + B₁x₁ + B₂log(x₂) + B3x3 + B4x4 + Bsxs +u
Where,
y = House price (in $10,000s).
x₁ = Distance from the city center (in kilometers).
x₂ = Number of bedrooms.
x3 = Age of the house (in years).
X4= Dummy variable equal to 1 if the house has a backyard.
x= Proxy for the quality of the neighborhoods' schools
The estimation results are shown below when excluding x, and x5 of the regression
(Model 1) and when including them (Model 2). Standard errors are in parentheses.
Explanatory Variables Model 1
Model 2
Bo
B₁
B₂
B3
B₁
Bs
N
SSR
SST
25.3
(10.7)
-0.032
(0.009)
15.1
(2.3)
-1.8
(0.5)
100
432
798
20.1
(15.2)
-0.028
(0.001)
12.4
(1.8)
-1.5
(0.6)
5.2
(2.1)
4.6
(1.9)
100
390
798
(a) Write down the Sample Regression Function (SRF) for Model 1 in an equation
form and interpret each of the estimated slope coefficients.
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VIEWStep 2: Determine the Sample Regression Function for Model 1 in equation form and interpret coefficients
VIEWStep 3: Estimate the house price and check the significance of distance from the city center
VIEWStep 4: Determine the significance of number of bedrooms and checking x4 and x5 are jointly significant
VIEWStep 5: Determine the goodness of fit of model 1 and the overall significance of the regression model 1
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