Question

4. The following output is taken from applying Backward elimination variable selection

procedure to fit a regression model to predict Y (Earnings) using Scoring Avg., Greens in

Reg., Putting Avg. and Sand Saves. (consider α to remove = 0.05)

Regression Analysis: Earnings Scoring Avg., Greens in Reg., Putting Avg. and Sand Saves

Candidate terms: Scoring Avg., Greens in Reg., Putting Avg., Sand Saves

----Step 1---- -----Step 2---- Coef P Coef P Coef P

-----Step 3----

31737
-440.3 0.000

1507 0.022

        262.749
         64.57%
         61.94%
         39.06%

5.78

Constant 19835 ScoringAvg. -248

0.050
0.056
0.211
0.007

22252
-344.9 0.001

  3726    0.092
  1622    0.012

        253.259
         68.30%
         64.64%
         44.93%

4.64

Greens in Reg.
Putting Avg.
Sand Saves

 4326
-2795
 1767

S 250.178 R-sq 70.26% R-sq(adj) 65.50% R-sq(pred) 40.91%Mallows’ Cp 5.00

1. a) What variables should be included in the model from the above variable selection procedure?

2. b) According to this output, write down the estimated regression equation to predict Earnings.

The following output is taken from applying Best Subsets Regression to fit a regression model to

predict RPG (runs/game) statistic.

Best Subsets Regression: Earnings vs Scoring Avg., Greens in Reg., Putting Avg. and Sand Saves

Response is Earnings ($1000)

R-Sq Vars R-Sq (adj) 1 56.8 55.3 1 32.0 29.6 2 64.6 61.9 2 59.5 56.5

R-Sq Mallows (pred) Cp 28.1 10.3 0.4 31.1 39.1 5.8 29.8 10.1

G

r SeP ceu

ontS rsta iin nind gng

S ARAa vevv ggge S ...s

284.75  X
357.41    X
262.75  X     X
281.05  X X

3 68.364.644.9 3 65.561.532.6 4 70.3 65.5 40.9

4.6253.26XXX 7.0264.35XXX 5.0 250.18 XXXX

c) Using R-Square adjusted as the criteria, what variables should be included in the best two- variable estimated regression equation?

Answer 1

A) What variables should be included in the model from the above variable selection procedure is given as below :

Of the output, p-value as X1=0.000 also as X4=0.022. Both from which do smaller than alpha=0.005. X1 including X4 do notable.

Therefore, X1 & X4 should do involved in the design i.e. Scoring avg. also Sand Saves should be held in the design.

B)According to this output, write down the estimated regression equation to predict Earnings are given below :

The equalization is as develops:

Of step 3, we notice, beta0=31737, beta1=-440.3, beta4=1507

y=31737-440.3*X1+1507*X4

hence, Earnings=31737-440.3*(Scoring Avg.)+1507*(Sand Saves) .

C) Utilizing R-Square set being the standards, what variables should be included in the best two-variable estimated regression equation is given as below :

Reminder: The more prominent the R-Square adjusted value, the greater is the design.

Of the output,

**** this largest R-square fixed value of 65.5 is achieved during all some variables are existing in the design.

**** Yet, specific topic questions as two-variables in the design.

Two-variables design are:

design 1': Variables-- X1 (Scoring Avg.) and X4 (Sand Saves) and R-square adjusted=61.9

design 2': Variables-- X1 (Scoring Avg.) and X2 (Greens in Reg.) and R-square adjusted=56.5

finally, 61.9 > 56.5

design1' is best than design2'.

Variables X1 (Scoring Avg.) & X4 (Sand Saves) should do involved in the ablest two-variable measured regression equation.