[Regression Analysis] How do you solve this? The values in R have been provided in the pictures a) Test the null hypothesis that, in the presence of X1 and X3, X2 contributes no useful information for predicting Y . Please, provide: hypotheses, test statistic, p-value (or rejection region), and conclusion. Use α = 0.05. Could X2 be removed from the model? Justify your answers. b) Test the null hypothesis that, in the presence of X3 = the number of square feet of living space, the two independent variables X1 = the number of bedrooms and X2 = the number of bathrooms are insignificant predictors of Y . Please, provide: hypotheses, test statistic, p-value (or rejection region), and conclusion. Use α = 0.05. Justify your answers.
[Regression Analysis] How do you solve this? The values in R have been provided in the pictures a) Test the null hypothesis that, in the presence of X1 and X3, X2 contributes no useful information for predicting Y . Please, provide: hypotheses, test statistic, p-value (or rejection region), and conclusion. Use α = 0.05. Could X2 be removed from the model? Justify your answers. b) Test the null hypothesis that, in the presence of X3 = the number of square feet of living space, the two independent variables X1 = the number of bedrooms and X2 = the number of bathrooms are insignificant predictors of Y . Please, provide: hypotheses, test statistic, p-value (or rejection region), and conclusion. Use α = 0.05. Justify your answers.
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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a) Test the null hypothesis that, in the presence of X1 and X3, X2 contributes no useful information for predicting Y . Please, provide: hypotheses, test statistic, p-value (or rejection region), and conclusion. Use α = 0.05. Could X2 be removed from the model? Justify your answers.
b) Test the null hypothesis that, in the presence of X3 = the number of square feet of living space, the two independent variables X1 = the number of bedrooms and X2 = the number of bathrooms are insignificant predictors of Y . Please, provide: hypotheses, test statistic, p-value (or rejection region), and conclusion. Use α = 0.05. Justify your answers.
Transcribed Image Text:6. The selling prices (Y), in thousands of dollars, of 24 apartments in Edmonton, Alberta
and data on the independent variables X₁, the number of bedrooms, X2, the number of
bathrooms, and X3, the number of square feet of living space, are recorded in the following
table:
##
Price Bedrooms Bathrooms Square_feet
## 1
62.0
## 2
57.5
## 3
62.0
## 4 60.0
70.4
68.0
64.0
70.0
71.5
74.5
72.0
63.9
56.7
## 14 61.0
## 15
61.7
## 16
67.9
## 17 75.0
## 18
81.0
## 19
83.0
## 5
## 6
## 7
## 8
## 9
## 10
## 11
## 12
## 13
## 20
81.9
## 21
75.0
## 22
70.0
## 23
66.5
## 24 78.5
3
wo wo wo wo wo wo wo wo wo wo wo
3
3
3
3
3
3
3
3
3
3
3
3
4
4
4
4
4
4
4
4
4
4
4
2.0
2.0
2.0
2.0
2.0
2.0
2.0
2.0
2.0
2.0
1.5
1.5
1.5
2.0
2.0
2.0
2.0
2.5
2.5
2.5
2.5
2.5
2.5
2.5
1570
1500
1450
1466
1500
1708
1600
##
## Bedrooms
## Bathrooms
## Square feet
## Residuals 20 592.47 29.62
1617
1700
1768
1990
1470
1470
1580
2000
2000
2000
2050
2346
2415
2200
2150
2400
2085
modC=1m (Price Bedrooms+Bathrooms+Square_feet);
anova (modC);
Df Sum Sq Mean Sq F value
1 316.36 316.36 10.6796
1 185.27 185.27 6.2540
1 263.16 263.16 8.8835
Transcribed Image Text:summary (modC);
##
## (Intercept)
## Bedrooms
## Bathrooms
## Square feet
Estimate Std. Error t value
38.54714637 8.336218482 4.624057
-5.17269592 3.903698651 -1.325076
6.65774042 5.298320984 1.256576
0.01874226 0.006288257 2.980517
modR=1m (Price Square_feet);
anova (modR);
##
Df Sum Sq Mean Sq F value
## Square feet 1 688.25 688.25 22.633
## Residuals 22 669.00 30.41
summary (modR);
##
Estimate Std. Error t value
## (Intercept) 37.94708632 6.606324719 5.744054
## Square feet 0.01687907 0.003547935 4.757435
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