Statistics 530
Name:__________________________
Final Exam
In-class Part (Total Points: 50)
1.
Be calm. 2. Good luck!
Write TRUE or FALSE for the following with reasons: ( 3 points each)
a. Robust regression with Huber weights is a special case of weighted regression.
b.
The number of parameters is proportional to the number of predictors for a non-linear regression
model.
c.
For Pairwise comparison of treatment means the Tukey’s procedure is always the exact method for
controlling Family-wise error rate.
d.
Since we are interested in a two-sided hypothesis in any general linear model the F test under
consideration should be two-sided.
e.
For a multiple regression model of form:
Yi = xi1 + xi2  xi3 + i
The Error degrees of freedom is (n - 3).
f.
If the concomitant (numerical) variable (covariate) is itself related to the treatment, one way
Analysis of Covariance (ANCOVA) is still valid.
g.
Since Logistic regression is essentially a transformation of the data, we could use yi=ln(Pi/(1-Pi))
transform on the data and then perform Simple Linear regression for the data relating Yi=b0+b1Xi
+I
h.
Measurement errors in Y are NOT as problematic as measurement errors in X.
i.
Consider the inverse prediction problem, i.e. predicting X given Y. Since our choice of X and Y
is arbitrary, we can switch the X and Y and perform simple regression.
j.
The standardized residuals are always smaller than the ordinary residuals.
Problems: (20 points)
1. You are interested in testing whether two simple regression lines are parallel.
Regression line 1: y = 1 +1 x + 
Regression line 2: y = 2 +2 x + 
What is the model, your hypothesis of interest, and testing procedure? Discuss this briefly. Hint: you may
want to use General Linear Testing techniques. (5 points)
2.
Is the following non-linear regression equation intrinsically linearizable? Why or why not? (6
points)
a.
f(x, ) = log(x)+2x
b.
Indicate how you would find starting values for (a), if you were to use non-linear methods.
3.
Mention 4 classic signs that would make you suspect that you may have a problem with
multicollinearity.
4.
You are given the following table on rotated factor scores on nine variables Var1-Var9 using
Varimax rotation. Based on the Table which variables would you consider relate to which factors?
Varimax Rotated Factor Pattern
Factor1
Factor2
Factor3
Factor4
Var1
-0.80065
0.03997
0.03137
0.05297
Var2
0.62302
0.30694
-0.27930
0.01978
Var3
0.07459
0.83236
0.03234
0.31625
Var4
0.03707
0.91395
-0.01210
-0.03861
Var5
0.27700
0.17264
0.28842
0.63901
Var6
0.07319
0.17414
0.80168
-0.11119
Var7
-0.07329
-0.15822
0.74358
0.11082
Var8
0.80224
0.00936
0.20642
0.05008
Var9
-0.18573
0.06387
-0.17869
0.82574
Have a great summer – I enjoyed teaching you!