(House Selling Price) The data below show the selling price, square footage, bed
ID: 3158894 • Letter: #
Question
(House Selling Price) The data below show the selling price, square footage, bedrooms, and age of houses that have sold in a neighborhood in the last six months.
64,000
1,670
2
30
59,000
1,339
2
25
61,500
1,712
3
30
79,000
1,840
3
40
87,500
2,300
3
18
92,500
2,234
3
30
95,000
2,311
3
19
113,000
2,377
3
7
115,000
2,736
4
10
138,000
2,500
3
1
142,500
2,500
4
3
144,000
2,479
3
3
145,000
2,400
3
1
147,500
3,124
4
0
144,000
2,500
3
2
155,500
4,062
4
10
165,000
2,854
3
3
Develop seven regression models as below using the corresponding Excel data.
(Model 4) Y = selling price, X1 = square footage, X2 = bedrooms (House Selling Price Model 4 Data)
(Model 5) Y = selling price, X1 = square footage, X3 = age (House Selling Price Model 5 Data)
(Model 6) Y = selling price, X2 = bedrooms, X3 = age (House Selling Price Model 6 Data)
(Model 7) Y = selling price, X1 = square footage, X2 = bedrooms, X3 = age (House Selling Price Model 7 Data)
(House Selling Price) Models 4, 5, and 6 are multiple regression models with two independent variables. Model 7 is a multiple regression model with three independent variables.
(a) The adjusted r2 value of model 4 is ___. [Answer format: one decimal place]
(b) The adjusted r2 value of model 5 is ___. [Answer format: two decimal places]
(c) The adjusted r2 value of model 6 is ___. [Answer format: one decimal place]
(d) The adjusted r2 value of model 7 is ___. [Answer format: two decimal places]
Write your answer(s) as 1.2, 3.45, 6.7, 8.91
64,000
1,670
2
30
59,000
1,339
2
25
61,500
1,712
3
30
79,000
1,840
3
40
87,500
2,300
3
18
92,500
2,234
3
30
95,000
2,311
3
19
113,000
2,377
3
7
115,000
2,736
4
10
138,000
2,500
3
1
142,500
2,500
4
3
144,000
2,479
3
3
145,000
2,400
3
1
147,500
3,124
4
0
144,000
2,500
3
2
155,500
4,062
4
10
165,000
2,854
3
3
Explanation / Answer
> tt <- read.csv("clipboard",sep=" ")
> head(tt)
Selling.price Square.footage Bedrooms Age
1 64000 1670 2 30
2 59000 1339 2 25
3 61500 1712 3 30
4 79000 1840 3 40
5 87500 2300 3 18
6 92500 2234 3 30
> m4 <- lm(Selling.price~Square.footage+Bedrooms,tt)
> m5 <- lm(Selling.price~Square.footage+Age,tt)
> m6 <- lm(Selling.price~Bedrooms+Age,tt)
> m7 <- lm(Selling.price~Square.footage+Bedrooms+Age,tt)
> summary(m4);summary(m5);summary(m6);summary(m7)
Call:
lm(formula = Selling.price ~ Square.footage + Bedrooms, data = tt)
Residuals:
Min 1Q Median 3Q Max
-37069 -15176 -6569 24656 30507
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 5701.45 30165.65 0.189 0.85280
Square.footage 48.51 14.53 3.338 0.00488 **
Bedrooms -2540.39 14985.90 -0.170 0.86781
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 22820 on 14 degrees of freedom
Multiple R-squared: 0.6465, Adjusted R-squared: 0.596
F-statistic: 12.8 on 2 and 14 DF, p-value: 0.0006902
Call:
lm(formula = Selling.price ~ Square.footage + Age, data = tt)
Residuals:
Min 1Q Median 3Q Max
-17006 -8160 -4638 8955 23350
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 79391.752 19269.817 4.120 0.00104 **
Square.footage 24.319 6.662 3.650 0.00262 **
Age -1712.209 315.998 -5.418 9.06e-05 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 12980 on 14 degrees of freedom
Multiple R-squared: 0.8856, Adjusted R-squared: 0.8693
F-statistic: 54.2 on 2 and 14 DF, p-value: 2.562e-07
Call:
lm(formula = Selling.price ~ Bedrooms + Age, data = tt)
Residuals:
Min 1Q Median 3Q Max
-20019 -13917 -1578 8642 29642
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 98390.4 26770.2 3.675 0.0025 **
Bedrooms 14432.7 7655.6 1.885 0.0803 .
Age -2110.2 352.1 -5.994 3.29e-05 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 16190 on 14 degrees of freedom
Multiple R-squared: 0.822, Adjusted R-squared: 0.7965
F-statistic: 32.32 on 2 and 14 DF, p-value: 5.671e-06
Call:
lm(formula = Selling.price ~ Square.footage + Bedrooms + Age,
data = tt)
Residuals:
Min 1Q Median 3Q Max
-17087 -8160 -5857 9097 24000
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 82185.649 23008.767 3.572 0.003410 **
Square.footage 25.941 9.583 2.707 0.017955 *
Bedrooms -2151.742 8826.087 -0.244 0.811196
Age -1711.537 327.191 -5.231 0.000162 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 13440 on 13 degrees of freedom
Multiple R-squared: 0.8861, Adjusted R-squared: 0.8599
F-statistic: 33.72 on 3 and 13 DF, p-value: 2.122e-06
From the above R output, it can be seen that
(a) The adjusted r2 value of model 4 is _59.6%__. [Answer format: one decimal place]
(b) The adjusted r2 value of model 5 is _86.93%__. [Answer format: two decimal places]
(c) The adjusted r2 value of model 6 is _79.7%_. [Answer format: one decimal place]
(d) The adjusted r2 value of model 7 is _85.99% __. [Answer format: two decimal places]
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