The questions here involve the data set for Richmond townhouses obtained on 2014

Question

The questions here involve the data set for Richmond townhouses obtained on 2014.11.03.
You are to apply the regsubsets() function in the leaps R package.
For your subset, the response variable is:
asking price divided by 10000:
askpr=c(44.8, 40.8, 33.7, 108.8, 51.68, 62.9, 50.8, 53.8, 62.8888, 79.99, 58.8, 50.5, 57.8, 68.8, 68.5, 73.8, 47.8, 65.99, 77.8, 57.8, 50.8, 58.39, 81.9, 56.88, 54.98, 49.9, 54.8, 48.8, 53.9, 40.8, 25.9, 52.4, 46.8, 41.99, 55.8, 65.8, 48.5, 59.8, 45.99, 86.8, 53.8, 26.99, 57.5, 58.68, 79.8, 56.8, 73.9, 40.9, 68.5, 54.8)
The explanatory variables are:
(i) finished floor area divided by 100
ffarea=c(9.4, 12.26, 12, 23.98, 15.1, 14, 12.27, 12.22, 15.77, 22, 17.37, 12.26, 12.01, 16.9, 15.76, 17.54, 13.34, 22.78, 16.5, 13.84, 16.6, 15.09, 20.95, 15.78, 13.06, 15.6, 11.26, 14.8, 11.84, 14, 6.1, 16.22, 16.2, 12.9, 13.06, 13.45, 14.8, 17.63, 16.01, 15.08, 10.95, 10.5, 13.46, 13.96, 15.25, 15.5, 15.15, 16.06, 13.59, 15.46)
(ii) age
age=c(14, 29, 28, 16, 20, 5, 17, 9, 6, 20, 26, 3, 0, 8, 4, 9, 32, 35, 3, 10, 23, 8, 19, 17, 1, 20, 0, 50, 15, 38, 11, 25, 30, 44, 0, 1, 24, 26, 25, 1, 18, 37, 10, 9, 3, 23, 0, 25, 2, 41)
(iii) monthly maintenance fee divided by 10
mfee=c(23.3, 19.8, 25.9, 36.9, 24.5, 19.6, 25.2, 18.5, 35.7, 26.7, 31, 18, 14.2, 19.4, 22.1, 18.2, 24.5, 57.4, 25.4, 16, 19.9, 20.3, 34.8, 17.3, 19.6, 27, 24.8, 25, 21, 23, 17.1, 36.4, 16, 23.2, 18.6, 18.2, 16.1, 32, 33.7, 48.8, 24.7, 28, 22.1, 22, 35, 17.4, 22.2, 24.4, 17, 31)
(iv) number of bedrooms
beds=c(2, 3, 2, 3, 3, 3, 2, 3, 3, 3, 3, 3, 3, 4, 4, 4, 3, 2, 4, 3, 4, 4, 1, 4, 3, 3, 2, 3, 2, 3, 1, 3, 4, 3, 3, 3, 3, 5, 3, 3, 2, 2, 3, 3, 2, 3, 4, 2, 3, 3)
(v) number of bathrooms
baths=c(2.5, 2.5, 2.5, 3.5, 2.5, 3.5, 2.5, 3.5, 3.5, 4.5, 3.5, 3.5, 3.5, 4.5, 3.5, 3.5, 3.5, 3.5, 4.5, 3.5, 3.5, 3.5, 3.5, 3.5, 3.5, 3.5, 3.5, 2.5, 2.5, 2.5, 1.5, 2.5, 4.5, 2.5, 3.5, 3.5, 3.5, 2.5, 3.5, 3.5, 2.5, 1.5, 3.5, 3.5, 3.5, 3.5, 3.5, 3.5, 3.5, 3.5)
After you have copied the above R vectors into your R session, you can get a dataframe with
richmondtownh=data.frame(askpr,ffarea,age,mfee,beds,baths)



Use regsubsets (with default method="exhaustive") in the leaps R package to find the best subsets with 1, 2, 3, 4, 5 explanatory variables, when askpr is the response variable.
Please use 3 decimal places for the answers below which are not integer-valued

Part a) The values of adjusted R2 for the best models with 2, 3 and 4 explanatory variables are respectively: 2 explanatory 0.772 3 explanatory: 0.779 4 explanatory: 0.775 Part b) The values of the Cp statistics for the best models with 2, 3 and 4 explanatory variables are respectively: 2 explanatory: 200.4 3 explanatory: 199.731 4 explanatory: 201.539 Part c) For the best model based on adjusted R2, the number of explanatory variables is Part d) For the best model based on Cp, the number of explanatory variables is: 4

Explanation / Answer

Use the code,

a=regsubsets(askpr~.,data=richmondtownh,nvmax=2)
summ1=summary(a)
max(summ1$adjr2)
min(summ1$cp)

b=regsubsets(askpr~.,data=richmondtownh,nvmax=3)
summ2=summary(b)
max(summ2$adjr2)
min(summ2$cp)

The best model based on Cp, the number of explanatory variable is 3. (Minimum among the Cp)

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