1. JMP output appears below for simple linear regression with data from the price, y (in $1000), of n = 28 Seattle home prices. The explanatory variable is the total number of square feet in the home. VOResponse Price ($000) v Regression Plot 600 500 400 300 200 1000 1500 2000 2500 3000 3500 DDistributions Square Feet Square Feet Summary of Fit RSquare RSquare Adj Root Mean Square Error Mean of Response Observations (or Sum Wgts) 0.560503 0.543599 356.8214 28 v Analysis of Variance Sum of 1000 1500 2000 2500 3000 3500 Source DF Squares Mean Square F Ratio Model 249200,64 249201 33.1585 Prob > F Summary Statistics Error 26 C. Total 27 <.0001* Mean 1923.1071 653,11574 123.42727 Std Dev - Parameter Estimates Std Err Mean Term Estimate Std Error t Ratio Prob>lt| Upper 95% Mean Lower 95% Mean 1669.8553 2176.359 1.43 0.1653 Intercept Square Feet 0.1470966 0.025545 73.938964 51.78554 5.76 <.0001" 28 Price ($000) 2. 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 X1 = square feet ; Price/Square Feet; Bathrooms (Number of bathrooms). B1, B2 and B3 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 0.947575 29.38132 Response Price ($000) Summary of Fit 356.8214 28 RSquare RSquare Adj Root Mean Square Error Mean of Response Observations (or Sum Wgts) 0.131114 0.097695 v Analysis of Variance 121.8935 Sum of 356.8214 Source DF Squares Mean Square F Ratio 28 Model 423883.82 141295 163.6752 Analysis of Variance Error 24 20718.29 863 Prob > F C. Total 27 444602.11 <.0001* Sum of Source DF Squares Mean Square F Ratio v Parameter Estimates Model 58293.36 58293.4 3.9234 Term Estimate Std Error t Ratio Prob>|t| 14858.0 Prob > F 0.0583 Error 26 386308.75 C. Total Intercept Square Feet 0.1895693 0.011048 Price/Sq Ft -371.4508 45.67288 -8.13 <.0001* 27 444602.11 17.16 <.0001* v Parameter Estimates 12.51 <.0001* -0.33 0.7411 1961.0355 156.728 Bathrooms -3.798639 11.36416 Term Estimate Std Error t Ratio Prob>|t| Intercept Price/Sq Ft 1089.7999 550.1965 v Effect Tests 149.87283 106.9894 1.40 0.1731 1.98 0.0583 Sum of Nparm F Ratio Prob > F Effect Tests Source DF Squares Square Feet Price/Sq Ft Bathrooms 254169.70 294.4294 <.0001* Sum of 135151.41 156.5590 <.0001* Source Nparm DF Squares F Ratio Prob > F 1 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
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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 Bi, write the NULL and ALTERNATIVE hypotheses. Find the statistics and its corresponding p-value. State your conclusion.

1. JMP output appears below for simple linear regression with data from the price, y (in $1000), of
n = 28 Seattle home prices. The explanatory variable is the total number of square feet in the
home.
VOResponse Price ($000)
v Regression Plot
600
500
400
300
200
1000
1500
2000
2500
3000
3500
DDistributions
Square Feet
Square Feet
Summary of Fit
RSquare
RSquare Adj
Root Mean Square Error
Mean of Response
Observations (or Sum Wgts)
0.560503
0.543599
356.8214
28
v Analysis of Variance
Sum of
1000
1500
2000
2500
3000
3500
Source
DF
Squares Mean Square
F Ratio
Model
249200,64
249201
33.1585
Prob > F
Summary Statistics
Error
26
C. Total
27
<.0001*
Mean
1923.1071
653,11574
123.42727
Std Dev
- Parameter Estimates
Std Err Mean
Term
Estimate Std Error t Ratio Prob>lt|
Upper 95% Mean
Lower 95% Mean 1669.8553
2176.359
1.43 0.1653
Intercept
Square Feet 0.1470966 0.025545
73.938964 51.78554
5.76 <.0001"
28
Price ($000)
Transcribed Image Text:1. JMP output appears below for simple linear regression with data from the price, y (in $1000), of n = 28 Seattle home prices. The explanatory variable is the total number of square feet in the home. VOResponse Price ($000) v Regression Plot 600 500 400 300 200 1000 1500 2000 2500 3000 3500 DDistributions Square Feet Square Feet Summary of Fit RSquare RSquare Adj Root Mean Square Error Mean of Response Observations (or Sum Wgts) 0.560503 0.543599 356.8214 28 v Analysis of Variance Sum of 1000 1500 2000 2500 3000 3500 Source DF Squares Mean Square F Ratio Model 249200,64 249201 33.1585 Prob > F Summary Statistics Error 26 C. Total 27 <.0001* Mean 1923.1071 653,11574 123.42727 Std Dev - Parameter Estimates Std Err Mean Term Estimate Std Error t Ratio Prob>lt| Upper 95% Mean Lower 95% Mean 1669.8553 2176.359 1.43 0.1653 Intercept Square Feet 0.1470966 0.025545 73.938964 51.78554 5.76 <.0001" 28 Price ($000)
2. 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
X1 = square feet ;
Price/Square Feet;
Bathrooms (Number of bathrooms).
B1, B2 and B3 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
0.947575
29.38132
Response Price ($000)
Summary of Fit
356.8214
28
RSquare
RSquare Adj
Root Mean Square Error
Mean of Response
Observations (or Sum Wgts)
0.131114
0.097695
v Analysis of Variance
121.8935
Sum of
356.8214
Source
DF
Squares Mean Square
F Ratio
28
Model
423883.82
141295 163.6752
Analysis of Variance
Error
24
20718.29
863 Prob > F
C. Total
27
444602.11
<.0001*
Sum of
Source
DF
Squares Mean Square
F Ratio
v Parameter Estimates
Model
58293.36
58293.4
3.9234
Term
Estimate Std Error t Ratio Prob>|t|
14858.0 Prob > F
0.0583
Error
26
386308.75
C. Total
Intercept
Square Feet 0.1895693 0.011048
Price/Sq Ft
-371.4508 45.67288
-8.13 <.0001*
27
444602.11
17.16 <.0001*
v Parameter Estimates
12.51 <.0001*
-0.33 0.7411
1961.0355
156.728
Bathrooms
-3.798639 11.36416
Term
Estimate Std Error t Ratio Prob>|t|
Intercept
Price/Sq Ft 1089.7999 550.1965
v Effect Tests
149.87283 106.9894
1.40 0.1731
1.98 0.0583
Sum of
Nparm
F Ratio Prob > F
Effect Tests
Source
DF
Squares
Square Feet
Price/Sq Ft
Bathrooms
254169.70 294.4294
<.0001*
Sum of
135151.41 156.5590
<.0001*
Source
Nparm
DF
Squares
F Ratio Prob > F
1
96.45
0.1117
0.7411
Price/Sq Ft
58293.360
3.9234
0.0583
Transcribed Image Text:2. 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 X1 = square feet ; Price/Square Feet; Bathrooms (Number of bathrooms). B1, B2 and B3 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 0.947575 29.38132 Response Price ($000) Summary of Fit 356.8214 28 RSquare RSquare Adj Root Mean Square Error Mean of Response Observations (or Sum Wgts) 0.131114 0.097695 v Analysis of Variance 121.8935 Sum of 356.8214 Source DF Squares Mean Square F Ratio 28 Model 423883.82 141295 163.6752 Analysis of Variance Error 24 20718.29 863 Prob > F C. Total 27 444602.11 <.0001* Sum of Source DF Squares Mean Square F Ratio v Parameter Estimates Model 58293.36 58293.4 3.9234 Term Estimate Std Error t Ratio Prob>|t| 14858.0 Prob > F 0.0583 Error 26 386308.75 C. Total Intercept Square Feet 0.1895693 0.011048 Price/Sq Ft -371.4508 45.67288 -8.13 <.0001* 27 444602.11 17.16 <.0001* v Parameter Estimates 12.51 <.0001* -0.33 0.7411 1961.0355 156.728 Bathrooms -3.798639 11.36416 Term Estimate Std Error t Ratio Prob>|t| Intercept Price/Sq Ft 1089.7999 550.1965 v Effect Tests 149.87283 106.9894 1.40 0.1731 1.98 0.0583 Sum of Nparm F Ratio Prob > F Effect Tests Source DF Squares Square Feet Price/Sq Ft Bathrooms 254169.70 294.4294 <.0001* Sum of 135151.41 156.5590 <.0001* Source Nparm DF Squares F Ratio Prob > F 1 96.45 0.1117 0.7411 Price/Sq Ft 58293.360 3.9234 0.0583
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