Additional HW Exercise 9.3

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Homework 24 Score____________
/ 25 Name ______________
Additional HW Exercise 9.3 (a)
Predicting whether or not nonsmokers will develop
cardiovascular problems within two years from
age, percent body fat, weight, and hours of
aerobic exercise weekly is being studied. A 0.05
significance level is chosen for a logistic
regression. Data from a random sample of
nonsmokers is recorded and entered into the SPSS
data file cardio.
Define a dummy variable cvp which matches the way
the variable cvp is coded in the SPSS data file
cardio. Write a logistic regression model to
predict whether or not a nonsmoker will develop
cardiovascular problems within two years from
age, percent body fat, weight, and hours of
aerobic exercise weekly.
1 for cardiovascular problems within two
years cvp 0 for no cardiovascular problems
within two years
prcft percent body fat wght weight exc
weekly hours of aerobic exercise
Log(odds) ?0 ?1(age) ?2(prcft) ?3(wght)
?4(exc)
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(b)
Using the SPSS data file cardio, select the
Analyze gt Regression gt Binary Logistic options to
display the Logistic Regression dialog box. From
the list of the variables on the left, select
cvp, and click on the arrow button pointing
toward the Dependent slot. Then select the
variables age, prcft, wght, and exc, and click on
the arrow button pointing toward the Covariates
section. Click on the OK button, after which
results are displayed as SPSS output. Title the
output to identify the homework exercise
(Additional HW Exercise 9.3 - part (b)), your
name, todays date, and the course number (Math
214). Use the File gt Print Preview options to see
if any editing is needed before printing the
output. Attach the printed copy to this
assignment before submission.
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Additional HW Exercise 9.3.-continued
(c) (d)
Based on the SPSS output in part (b), explain why
one predictor should be eliminated from the
model, and identify which predictor should be
eliminated.
Since neither weight or age is statistically
significant at the 0.05 level with predictors
percent body fat and aerobic exercise in the
model, then we choose to eliminate the predictor
corresponding to the larger P-value, which is
weight.
Repeat part (b) with all predictors in the
Covariates section except the one selected to be
eliminated in part (c). Title the output to
identify the homework exercise (Additional HW
Exercise 9.3 - part (d)), your name, todays
date, and the course number (Math 214). Use the
File gt Print Preview options to see if any
editing is needed before printing the output.
Attach the printed copy to this assignment before
submission.
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(e) (f)
Based on the SPSS output in part (d), explain why
one more predictor should be eliminated from the
model, and identify which predictor should be
eliminated.
Since age is not statistically significant at the
0.05 level with predictors percent body fat and
aerobic exercise in the model, then we choose to
eliminate age.
Repeat part (b) with all predictors in the
Covariates section except the two selected to be
eliminated in parts (c) and (e). Title the output
to identify the homework exercise (Additional HW
Exercise 9.3 - part (f)), your name, todays
date, and the course number (Math 214). Use the
File gt Print Preview options to see if any
editing is needed before printing the output.
Attach the printed copy to this assignment before
submission.
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Additional HW Exercise 9.3.-continued
(g) (h) (i)
Based on the SPSS output in part (f), explain why
no predictor should be eliminated from the model.
Since each of the two predictors is statistically
significant at the 0.05 level with the other
predictor in the model, then we choose to keep
both predictors in the model.
Write the estimated logistic equation for
predicting whether or not cardiovascular problems
will occur within two years.
Log(odds) 4.318 0.179(prcft) 0.063(exc)
Use the estimated logistic equation to predict
whether or not cardiovascular problems will occur
within two years for a nonsmoker whose percent
body fat is 20 and whose weekly aerobic exercise
time is 50 hours.
Log(odds) 4.318 0.179(20) 0.063(50)
3.888
Since Log(odds) is negative, we predict that
cardiovascular problems will not occur within two
years.
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(j) (k)
Use the estimated logistic equation to predict
whether or not cardiovascular problems will occur
within two years for a nonsmoker whose percent
body fat is 35 and whose weekly aerobic exercise
time is 30 hours.
Log(odds) 4.318 0.179(35) 0.063(30)
0.057
Since Log(odds) is positive, we predict that
cardiovascular problems will occur within two
years.
What does the classification table tell us about
the reliability of predictions with the estimated
logistic equation?
Among those with no cardiovascular problems,
12.5 of the predictions were incorrect. Among
those with cardiovascular problems, 18.7 of the
predictions were incorrect.
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Additional HW Exercise 9.4 (a)
Randomly selected customers of a car dealership
are polled in order to collect data concerning
area of residence and preferred color of a
certain type of sports car. For each customer,
an area of residence is recorded as rural,
suburban, or urban, and color preference is
recorded chosen from red, green, yellow, and
white. The data are stored in the SPSS data file
sportscar.
The data are to be used with a 0.05 significance
level to see if there is any evidence against the
claim that 40 of the customers prefer red, 30
prefer green, 20 prefer yellow, and 10 prefer
the white. Do this by completing the
following (i)
With the SPSS data file sportscar, use Additional
HW Exercise 9.2(b)(i) as a guide to obtaining the
SPSS output displaying the chi-square
goodness-of-fit test statistic needed for the
hypothesis test. Title the output to identify the
homework exercise (Additional HW Exercise 9.4 -
part (a)), your name, todays date, and the
course number (Math 214). Use the File gt Print
Preview options to see if any editing is needed
before printing the output. Attach the printed
copy to this assignment before submission.
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(ii)
Summarize the results (Step 4) of the chi-square
test to see if there is sufficient evidence at
the ? 0.05 level against the claim that 40 of
the customers prefer red, 30 prefer green, 20
prefer yellow, and 10 prefer the white.
Since ?23
15.262 and ?230.05
7.81473, we
have sufficient evidence to reject H0 .
We conclude that
at least one of the hypothesized proportions is
not correct
(P lt 0.005).
OR (P 0.002)