For the same houses from Question 1, a multiple regression model is now used to predict the price y (in $1000) of the n = 28 Seatle home prices based on two more explanatory variables in addition to square feet. The explanatory variables are then I1 = square feet; Price/Square Feet ; Bathrooms (Number of bathrooms). I2 = Bi, B2 and 33 are the corresponding parameters in the model. For all the testing problem hereby, set significance level a = 0.05. Response Price ($000) Summary of Fit RSquare RSquare Adj Root Mean Square Error Mean of Response Observations (or Sum Wgts) 0.9534 - Response Price (So00) 0.947575 29.38132 356.8214 Summary of Fit 28 RSquare RSquare Adj Root Mean Square Error Mean of Response Observations (or Sum Wgts) 0.131114 - Analysis of Variance 0.097695 121.8935 Sum of Squares Mean Square 3 423883.82 356.8214 Source DF F Ratio 28 Model 141295 163.6752 863 Prob > F Analysis of Variance Error 24 20718.29 C. Total - Parameter Estimates 27 444602.11 <.0001 Sum of Source DF F Ratio Squares Mean Square 58293.36 Model 58293.4 3.9234 Estimate Std Error tRatio Prob>lt| -8.13 <.0001 17.16 <.0001 12,51 <.0001 Term Error 26 386308.75 14858.0 Prob >F Intercept Square Feet 0.1895693 0.011048 Price/Sq Ft 1961.0355 156.728 Bathrooms -371.4508 45.67288 C. Total 27 444602.11 0.0583 Parameter Estimates -3.798639 11.36416 -0.33 0.7411 Term Estimate Std Error t Ratio Prob>t| 1.40 0.1731 1.98 0.0583 v Effect Tests Intercept Price/Sq Ft 1089.7999 550.1965 149.87283 106.9894 Sum of F Ratio Prob >F Effect Tests Source Nparm DF Squares Square Feet Price/Sq Ft Bathrooms 254169.70 294.4294 <.0001" <.0001" Sum of 135151.41 156.5590 Source Nparm DF Squares F Ratio Prob >F 96.45 0.1117 0.7411 Price/Sq Ft 58293.360 3.9234 0.0583

College Algebra

7th Edition

ISBN:9781305115545

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter1: Equations And Graphs

Section: Chapter Questions

Problem 10T: Olympic Pole Vault The graph in Figure 7 indicates that in recent years the winning Olympic men’s...

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See the attached image for the introduction.

Is there evidence that Square Feet(x1), Price/Square Feet(x2), and Bathrooms(x3) together provide important information for predicting price? In terms of variables xi and parameters βi, write the null and alternative hypotheses. Find the statistics and its corresponding p-value.
State your conclusion.

For the same houses from Question 1, a multiple regression model is now used to predict the price
y (in $1000) of the n = 28 Seatle home prices based on two more explanatory variables in addition
to square feet. The explanatory variables are then
I1 = square feet;
Price/Square Feet ;
Bathrooms (Number of bathrooms).
I2 =
Bi, B2 and 33 are the corresponding parameters in the model. For all the testing problem hereby,
set significance level a = 0.05.
Response Price ($000)
Summary of Fit
RSquare
RSquare Adj
Root Mean Square Error
Mean of Response
Observations (or Sum Wgts)
0.9534
- Response Price (So00)
0.947575
29.38132
356.8214
Summary of Fit
28
RSquare
RSquare Adj
Root Mean Square Error
Mean of Response
Observations (or Sum Wgts)
0.131114
- Analysis of Variance
0.097695
121.8935
Sum of
Squares Mean Square
3 423883.82
356.8214
Source
DF
F Ratio
28
Model
141295 163.6752
863 Prob > F
Analysis of Variance
Error
24
20718.29
C. Total
- Parameter Estimates
27 444602.11
<.0001
Sum of
Source
DF
F Ratio
Squares Mean Square
58293.36
Model
58293.4
3.9234
Estimate Std Error tRatio Prob>lt|
-8.13 <.0001
17.16 <.0001
12,51 <.0001
Term
Error
26 386308.75
14858.0 Prob >F
Intercept
Square Feet 0.1895693 0.011048
Price/Sq Ft 1961.0355 156.728
Bathrooms
-371.4508 45.67288
C. Total
27 444602.11
0.0583
Parameter Estimates
-3.798639 11.36416
-0.33 0.7411
Term
Estimate Std Error t Ratio Prob>t|
1.40 0.1731
1.98 0.0583
v Effect Tests
Intercept
Price/Sq Ft 1089.7999 550.1965
149.87283 106.9894
Sum of
F Ratio Prob >F
Effect Tests
Source
Nparm
DF
Squares
Square Feet
Price/Sq Ft
Bathrooms
254169.70 294.4294
<.0001"
<.0001"
Sum of
135151.41 156.5590
Source
Nparm
DF
Squares
F Ratio Prob >F
96.45
0.1117
0.7411
Price/Sq Ft
58293.360
3.9234
0.0583

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