Supplementary Exercise 11.17 of IPS7e:
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Minitab commands and output:

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 WOpen "R:\Chapter 11\ex11_015.mtw".

 Regress 'GPA' 3 'IQ' 'C1' 'C5';
 GNormalplot;
 GFits;
 RType 2;
  Constant;
  Brief 2.

The regression equation is
GPA = - 4.94 + 0.0815 IQ + 0.183 C1 + 0.142 C5

Predictor        Coef     SE Coef          T        P
Constant       -4.937       1.491      -3.31    0.001
IQ            0.08145     0.01367       5.96    0.000
C1            0.18308     0.06475       2.83    0.006
C5            0.14205     0.06663       2.13    0.036

S = 1.475       R-Sq = 52.5%     R-Sq(adj) = 50.6%

Analysis of Variance

Source            DF          SS          MS         F        P
Regression         3     178.340      59.447     27.31    0.000
Residual Error    74     161.087       2.177
Total             77     339.427

Source       DF      Seq SS
IQ            1     136.319
C1            1      32.129
C5            1       9.893

Unusual Observations
Obs         IQ        GPA         Fit      SE Fit    Residual    St Resid
  8         97      2.412       5.504       0.282      -3.092       -2.14R 
 22        109      1.760       5.140       0.555      -3.380       -2.47R 
 48        102      3.936       7.395       0.241      -3.459       -2.38R 
 51        103      0.530       6.542       0.252      -6.012       -4.14R 
 54         72      7.295       5.378       0.662       1.917        1.45 X
 72         90      3.820       4.546       0.710      -0.726       -0.56 X

R denotes an observation with a large standardized residual
X denotes an observation whose X value gives it large influence.

Normplot of Residuals for GPA
Residuals vs Fits for GPA

Comments and answers to questions:
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The fitted regression model is:  GPAhat = -4.94 + 0.0815*IQ + 0.183*C1 + 0.142*C5,
and R^2=52.5%. The standard deviation about the fitted model is s=1.475. For a
student with IQ=109, C1=13 and C5=8, the predicted value is
  GPAhat = -4.94 + 0.0815*109 + 0.183*13 + 0.142*8 = 7.46.


(b)
For constant C1 and C5, the GPA increases by 0.0815 for each unit increase in
IQ - the regression coefficient for IQ. A 95% confidence for this parameter is
  beta for IQ: 0.0815 +- t(.975,74)*0.0137 = 0.0815 +- 0.0273.
using t(.975,74)=1.99.


(c)
The most extreme residual is for observation 51. A standardized residual of -
4.08 in a model with 74 observations can be considered seriously outlying. More
advanced methods for outlier detection than covered in VHM 801 show that it is
strongly significant as an outlier. It seems that the observation is for the
only student of age 15. This would in itself be a good reason to consider this
student to be outside the target population. Also, the GPA score is the lowest
in the dataset.


(d) Minitab command and output:

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 Copy c2 c14
 Name c14 'GPA-1'
 Let c14(51)='*'
 Regress 'GPA-1' 3 'IQ' 'C1' 'C5';
 GNormalplot;
 GFits;
 RType 2;
  Constant;
  Brief 2.
Regression Analysis: GPA-1 versus IQ, C1, C5

The regression equation is
GPA-1 = - 4.68 + 0.0805 IQ + 0.197 C1 + 0.109 C5

77 cases used 1 cases contain missing values

Predictor        Coef     SE Coef          T        P
Constant       -4.678       1.318      -3.55    0.001
IQ            0.08050     0.01207       6.67    0.000
C1            0.19707     0.05724       3.44    0.001
C5            0.10950     0.05923       1.85    0.069

S = 1.303       R-Sq = 57.4%     R-Sq(adj) = 55.7%

Analysis of Variance

Source            DF          SS          MS         F        P
Regression         3     167.112      55.704     32.83    0.000
Residual Error    73     123.855       1.697
Total             76     290.967

Source       DF      Seq SS
IQ            1     128.405
C1            1      32.910
C5            1       5.798

Unusual Observations
Obs         IQ      GPA-1         Fit      SE Fit    Residual    St Resid
  8         97      2.412       5.648       0.250      -3.236       -2.53R 
 22        109      1.760       5.301       0.491      -3.541       -2.93R 
 46         97      3.647       6.371       0.212      -2.724       -2.12R 
 48        102      3.936       7.474       0.213      -3.538       -2.75R 
 54         72      7.295       5.388       0.585       1.907        1.64 X
 72         90      3.820       4.450       0.627      -0.630       -0.55 X

R denotes an observation with a large standardized residual
X denotes an observation whose X value gives it large influence.

Normplot of Residuals for GPA-1
Residuals vs Fits for GPA-1

Comments and answers to questions:
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The regression equation for the reduced dataset is
  GPAhat = -4.68 + 0.0805*IQ + 0.197*C1 + 0.109*C5
The regression coefficients for IQ and C1 are only little changed, but the
coefficient for C5 has dropped from 0.142 to 0.109, and it is no longer
significant in the model (P=0.069). The R^2 is 57.4%, a fair bit up from the
previous analysis, and the standard deviation about the fitted model is s=1.303,
about 10% down from the previous analysis. The prediction for a specific student
is
    GPAhat = -4.68 + 0.0805*109 + 0.197*13 + 0.109*8 = 7.53,
a little bit up from 7.46 of the previous model. In conclusion, the outlying
observation affected the regression equation only moderately, but it changed the
significance for the predictor C5.

We note that the residual plot still does not look good. There is some
indication of a larger variation at small values, and the distribution of
residuals is quite asymmetrical (left-skewed). Further improvement of the model
seems necessary before we can make precise inferences about the effects of
variables.