The accompanying data file contains salary data $($in $$1,000$ s$)$ for $30$ college$-$educated men with their respective BMI and a dummy variable that represents $1$ for a white man and $0$ otherwise. Model $1$ predicts Salary using BMI and White as predictor variables. Model $2$ includes BMI and White along with an interaction between the two.

Click here for the Excel Data File

a$-1.$ Use the holdout method to compare the predictability of the models using the first $20$ observations for training and the remaining $10$ observations for validation. Report the estimates of Models $1$ and $2$ derived from the training set.

Note: Negatlve values should be Indlcated by a minus sign. Round your answers to $2$ declmal places.

$\backslash$table$[[$Predictor Variable,Model $1($No interaction$),$Model $2($Interaction$)],[$Constant$,,],[$BMI$,-0\mathrm{.}96,],[$White$,,],[$BMI $$ White,,$-0\mathrm{.}73]]$

Q$-2.$ Calculate the RMSE of the two models in the validation set. Note: Do not round Intermedlate calculations and round your final answers to $2$ decimal places.

$\backslash$table$[[,$Model $1($No interaction$),$Model $2($Interaction$)],[$RMSE$,,]]$

a$-3.$ Which model is better for making predictions?

$\backslash$table$[[$Model $1,$because its RMSE is$,$lower$]]$

b$-1.$ Use the $k-$fold method, with $k=3,$ to calculate the average RMSE of the two models.

Note: Do not round Intermedlate calculations and round your final answers to $2$ decimal places.

$\backslash$table$[[,$Model $1($No interaction$),$Model $2($Interaction$)],[$Average RMSE,,$]]$

A$1$

$2$

$1$

Salary

B

:

$fx$

Salary

$2$

$3$

$43$

$4,44$

$534$

$6,34$

$7,53$

$8,42$

$9,37$

$10,35$

$1146$

$1246$

$13,34$

$1445$

$15,33$

$16,25$

$17,32$

$1846$

$\backslash$table$[[19,31],[20,54]]$

$21,37$

$22,42$

$23,38$

$24,45$

$2538$

$26,41$

$27,39$

$28,50$

$2941$

$30$

$38$

$45$

$32$

$33$

$34$

$35$

$36$

$37$

$$