# Fall 2012

```STA 6166 – Fall 2012 – Exam 4 –
PRINT Name __________________
Conduct all tests at  = 0.05 significance level
Q.1. A multiple regression equation was fit for n = 36 observations using 5 independent variables X1, X2,, X5 gave
SS(Residual) = 900. What is the residual standard deviation (standard error of estimate)?
Q.2. A multiple regression equation was fit for n = 21 observations using 5 independent variables X1, X2,, X5 gave
SS(Total) = 1500 and SS(Residual) = 375.
p.2.a. Calculate the value of the coefficient of determination.
p.2.b. Test the hypothesis that all the slopes are zero. H0: =0
Test Statistic ___________________________________ Rejection Region: _______________________________
Q.3. Write the multiple regression equations needed to be fit for determining if the linear relationship of Y = response
time as a function of X1 = strength of signal has the same slope for three groups (clearly define all independent
variables).
p.3.a. Complete (Full) Model:
p.3.b. Reduced Model:
Q.4. The ANOVA tables for fitting Y as a linear function of X are shown below. In the first table the “independent
variables” include X1, the continuous variable, X2, X3, and X4 as dummy variables to denote the four groups, and
X12, X13, and X14 representing the crossproducts of X1 and the dummy variables. The second table is the ANOVA
table for fitting Y as a linear function of X1, X2, X3, and X4.
Model:(X1,X2,X3,X4,X12,X13,X14)
Source
df
SS
Regression
28000
Error
Total
19
35000
Model:(X1,X2,X3,X4)
Source
df
Regression
Error
Total
19
SS
21000
35000
p.4.a. Complete the tables.
p.4.b. For the second model, test H0 = 0
Test Statistic _______________________________ Rejection Region ______________________________________
p.4.b. Is there significant evidence the slopes are not equal among the 4 groups?
H0: _____________________________________________
Test Statistic _______________________________ Rejection Region ______________________________________
Q.5. The medical records for a sample of patients in a local retirement center were analyzed to determine if there was
a relationship between an individual’s blood pressure and the probability of the individual having problems with
his/her circulation system. Fitting a logistic regression equation using X = blood pressure and Y = 1 if the individual
had problems with his/her circulation system gave as estimates
Parameter DF Estimate
Intercept
1 -7.4374
x
1 0.0455
Estimate the probability that an individual with blood pressure = 135 will have problems with his/her circulation
system.
^
Q.6. You obtain the following spreadsheet from a regression model. The fitted equation is Y  4.67  4.00 X
the F-test for Lack-of-Fit. n = ______________ c = _______________
X
2
2
4
4
6
6
Source
Lack-of-Fit
Pure Error
Y
3
5
8
12
18
22
df
Ybar_grp Y-hat_grp Pure Error
SS
MS
F
Conduct
Lack of Fit
F(0.05)
Q.7. A logistic regression model is fit, relating whether a soldier died during the civil war (Y=1 if he died, 0 if
not) to two independent variables: rank (X1=1 if private, 0 if of higher rank) and duty (X2=1 if infantry, 0 if not).
Consider the following models for log(:
log(
Fitted equation
-2 log L

-2.15
2868.6
X1
-2.58+0.46X1
2862.9
X1+2X2
-3.28+0.50X1+0.87X2
2812.3
p.6.a. Test whether the probability of death is associated with either rank or duty at the =0.05 significance
level.
Null hypothesis:
Alternative hypothesis:
Test Statistic _________________________ Rejection Region: _______________________________
p.6.b. Give the fitted values (in terms of probabilities) for each of the following two categories (based on the
full model):
Private/Infantry:
Nonprivate/Noninfantry:
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