The questions involves the data set for Richmond townhouses obtained on 2014.11.03.
You will get a different subset than in the preceding WebWork question.
For your subset, the response variable is:
asking price divided by 10000:
askpr=c(53.9, 77.8, 73.9, 62.8888, 58.68, 60.8, 53.8, 41.99, 59.8, 47.8, 57.5, 74.8, 51.99, 65.99, 50.8, 25.9, 48.5, 50.8, 58.39, 71.99, 68.5, 79.8, 55.8, 61.5, 54.8, 44.8, 73.8, 26.99, 40.8, 33.7, 54.98, 81.9, 55.2, 53.8, 65.8, 46.8, 68.5, 40.8, 56.8, 78.8, 48.8, 47.9, 40.9, 56.88, 79.99, 50.5, 62.9, 51.68, 57.8, 52.4)
The explanatory variables are:
(i) finished floor area divided by 100
ffarea=c(11.84, 16.5, 15.15, 15.77, 13.96, 13.2, 10.95, 12.9, 17.63, 13.34, 13.46, 17.48, 12.09, 22.78, 16.6, 6.1, 14.8, 12.27, 15.09, 15.05, 13.59, 15.25, 13.06, 14.5, 15.46, 9.4, 17.54, 10.5, 12.26, 12, 13.06, 20.95, 15.3, 12.22, 13.45, 16.2, 15.76, 14, 15.5, 19.48, 14.8, 12.1, 16.06, 15.78, 22, 12.26, 14, 15.1, 13.84, 16.22)
(ii) age
age=c(15, 3, 0, 6, 9, 3, 18, 44, 26, 32, 10, 5, 7, 35, 23, 11, 24, 17, 8, 8, 2, 3, 0, 7, 41, 14, 9, 37, 29, 28, 1, 19, 9, 9, 1, 30, 4, 38, 23, 11, 50, 7, 25, 17, 20, 3, 5, 20, 10, 25)
(iii) monthly maintenance fee divided by 10
mfee=c(21, 25.4, 22.2, 35.7, 22, 18.9, 24.7, 23.2, 32, 24.5, 22.1, 29.7, 18.1, 57.4, 19.9, 17.1, 16.1, 25.2, 20.3, 22.3, 17, 35, 18.6, 18.7, 31, 23.3, 18.2, 28, 19.8, 25.9, 19.6, 34.8, 16.9, 18.5, 18.2, 16, 22.1, 23, 17.4, 20.4, 25, 18, 24.4, 17.3, 26.7, 18, 19.6, 24.5, 16, 36.4)
(iv) number of bedrooms
beds=c(2, 4, 4, 3, 3, 3, 2, 3, 5, 3, 3, 4, 3, 2, 4, 1, 3, 2, 4, 3, 3, 2, 3, 3, 3, 2, 4, 2, 3, 2, 3, 1, 3, 3, 3, 4, 4, 3, 3, 3, 3, 3, 2, 4, 3, 3, 3, 3, 3, 3)
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)

The corresponding vectors for the holdout set are:
askpr.ho=c(54.8, 108.8, 86.8, 49.9, 45.99, 58.8, 57.8, 68.8, 68.8)
ffarea.ho=c(11.26, 23.98, 15.08, 15.6, 16.01, 17.37, 12.01, 16.9, 15.95)
age.ho=c(0, 16, 1, 20, 25, 26, 0, 8, 18)
mfee.ho=c(24.8, 36.9, 48.8, 27, 33.7, 31, 14.2, 19.4, 23.6)
beds.ho=c(2, 3, 3, 3, 3, 3, 3, 4, 3)

Create a second data frame:
holdout=data.frame(askpr.ho,ffarea.ho,age.ho,mfee.ho,beds.ho)
names(holdout)=names(richmondtownh) [to make variables names the same as before]


Use the ls.cvrmse() function from the course web site with 3 and 4 explanatory variables, when askpr is the response variable.
For 4 explanatory variables, all of the above are included.
For 3 explanatory variables, all of the above are included except beds .

Please use 3 decimal places for the answers below which are not integer-valued

Part a)
The values of residual SD or residual SE for the regressions with 3 and 4 explanatory variables are respectively:
3 explanatory:
4 explanatory:

Part b)
The values of the leave-one-out cross-validation RMS prediction error for the regressions with 3 and 4 explanatory variables are respectively:
3 explanatory:
4 explanatory:

Part c)
The values of the holdout RMS prediction error for the regressions with 3 and 4 explanatory variables are respectively:
3 explanatory:
4 explanatory:

Part d)
Do you get the same conclusion on which is better between the 3-explanatory versus 4-explanatory models from the summaries in (a), (b), (c).
(enter either Yes or No).

Part e)
Compare the three values for the models with 3 explanatory variables (respectively 4 explanatory); that is, values of residual SE, leave-one out root mean square error and holdout subset root mean square error for 3 explanatory (respectively, 4 explanatory).
What is the best explanation for the root mean square prediction errors to be larger for parts (b) and (c)?

A. sampling variability
B. sample size is small
C. the linear approximation to a non-linear function of the explanatory variables
D. out-of-sample variability is always larger
E. the RMS prediction error values were not always larger for my data set

Hint: