Directions

For your first computer project you are to reproduce Exhibits 8.8 and 8.9 on pages 180-181 in Judd & McClelland. However, to keep it interesting, you must use the School Referrals data set, and substitute AGGRESS for HSRANK and VIQ for SATV and PIQ for SATM in each of the models and each of the questions. Instead of predicting GPA, you will substitute ARITH scores.

These answers were generated using 200 cases. Using Statlets, you can only use the first 100 cases, so your answers won't be exact, but will probably be close.

Exhibit 8.8

Model 1 Last Year's Equation

ARITH = 30.00 + .4VIQ + .2PIQ + .1AGGRESS
no Parameter Estimates
SSE = 17153.410

Model 2 Simple (Mean) Model

ARITH = ß_o + ei
bo = 81.525
SSE = 27693.875

Model 3 AGGRESS only

ARITH = ß_o + ß₁AGGRESS + ei
bo = 81.255 b1 = 0.064
SSE= 27677.025

Model 4 AGGRESS and VIQ

ARITH = ß_o + ß₁AGGRESS ß₂VIQ + ei
bo = 39.885 b1 = 0.078 b2 = 0.481
SSE = 17366.615

Model 5 AGGRESS and Total IQ (IQ = VIQ + PIQ)

ARITH = ß_o + ß₁AGGRESS ß₂IQ + ei
bo = 34.508 b1 = 0.098 b2 = 0.264
SSE = 16968.641

Model 6 Complex Constraint [ b1 = (b2+b3)/2]

This is a compact model checking to see if the weight for AGGRESS should be equal to the average of the weights given to VIQ and PIQ.
ARITH = ß_o + ß₂(VIQ = .5AGGRESS) ß₃(PIQ +.5AGGRESS) + ei
bo = 34.578 b2 = 0.364 b3 =0.162
SSE = 16755.337

Model 7 Full Regression Model

ARITH = ß_o + ß₁AGGRESS + ß₂VIQ + ß₃PIQ + ei
bo = 34.595 b1 = 0.091 b2 = 0.370 b3 = 0.164
SSE = 16632.229

Exhibit 8.9

Is AGGRESS by itself, a good predictor of ARITH (simple regression)

Ho: ß₁=0
Model 2 vs Model 3

                            Analysis of Variance

   Source   Sum-of-squares    DF  Mean-square     F-ratio       P	PRE

 Regression         16.850     1       16.850       0.121       0.729	.001
   Residual      27677.025   198      139.783

Of course, we would fail to reject the null hypothesis

Is it worth adding the set of IQ scores to the model of ARITH which includes AGGRESS?

(addition of a set)
Ho: ß₂=ß₃=0
Model 3 versus Model 7
PRE = 0.399
F _2,196 = 65.078 Of course we would reject the null hypothesis. Adding this set is valuable.

Should VIQ and PIQ be weighted equally.

Note, while it is not stated, AGGRESS is in both the compact and augmented models. I'd rather it said should VIQ and PIQ be weighted equally when added to AGGRESS in a model?
Ho: ß₂=ß₃
Model 5 versus Model 7
PRE = 0.020
F_1,196 = 3.964

Compared to the mean, are AGGRESS, VIQ, and PIQ useful predictors of ARITH.

Overall regression
Ho: ß₁=ß₂=ß₃=0
PRE = .399

                            Analysis of Variance

   Source   Sum-of-squares    DF  Mean-square     F-ratio       P

 Regression      11061.646     3     3687.215      43.451       0.000
   Residual      16632.229   196       84.858

Of course we reject the null hypothesis.

Is it useful to add PIQ to a model predicting ARITH which already includes AGGRESS and VIQ?

(Adding the pth predictor)
Ho: ß₃=0
Model 4 vs Model 7. or you could just use the t in the full regression model for PIQ
PRE = .0423
F _1,196 = 8.655 Of course you reject the null hypothesis the p = .004

Does last years model aply to the current ARITH data?

Ho: ß₀= 30.00 ß₁= .4 ß₂= .2 ß₃= .1 If the variables are in this order VIQ, PIQ, AGGRESS
Model 1 versus Model 7
PRE = .03
F_4,196 = 1.535
Of course, we would fail to reject the null hypothesis

Is the weight for AGGRESS equal to the average of the two intelligence scores (VIQ & PIQ)?

Ho: ß₁ - (ß₂ + ß₃)/2 = 0
Model 6 versus Model 7
PRE = 0.007
F _1,196 = 1.451 Of course we fail to reject the null.