a) Test the null hypothesis that, in the presence of X1 and X3, X2 contributes no use- ful 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? b)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.
a) Test the null hypothesis that, in the presence of X1 and X3, X2 contributes no use- ful 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? b)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.
Big Ideas Math A Bridge To Success Algebra 1: Student Edition 2015
1st Edition
ISBN:9781680331141
Author:HOUGHTON MIFFLIN HARCOURT
Publisher:HOUGHTON MIFFLIN HARCOURT
Chapter9: Solving Quadratic Functions
Section: Chapter Questions
Problem 4CA
Related questions
Question
a) Test the null hypothesis that, in the presence of X1 and X3, X2 contributes no use-
ful 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?
b)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.
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:
##
## 1
## 2
## 3
## 4
## 5
## 6
## 7
Price Bedrooms Bathrooms Square_feet
62.0
## 8
## 9
57.5
62.0
60.0
70.4
68.0
64.0
70.0
71.5
## 10
74.5
## 11 72.0
## 12
63.9
## 13
56.7
## 14 61.0
## 15
61.7
## 16
67.9
## 17
75.0
## 18 81.0
## 19 83.0
## 20 81.9
## 21 75.0
## 22 70.0
## 23 66.5
## 24 78.5
3
3
3
##
## Bedrooms
## Bathrooms
3
wo wo wo wo wo wo wo
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
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
## Square feet 1 263.16 263.16 8.8835
## Residuals 20 592.47
29.62
Transcribed Image Text:summary (modC);
Estimate Std. Error
38.54714637 8.336218482
t value
4.624057
-5.17269592 3.903698651 -1.325076
## Bathrooms
6.65774042 5.298320984 1.256576
## Square feet 0.01874226 0.006288257 2.980517
##
## (Intercept)
## Bedrooms
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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