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

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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See the attached image for the introduction.

In terms of variables xi and parameters βi, write the null and alternative hypotheses for testing whether, after including Price/Square Feet(x2) in the model already, the further incorporation of the other 2 explanatory variables (x1, x3) adds any useful information for explaining pricey. Also, give the value of the F statistic and its degrees of freedom (df).

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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