This quiz covers the generalized linear models and basic logistic regression.

Assessment #8
Started: Nov 2 at 11:35am
Quiz Instructions
This quiz covers the generalized linear models and basic logistic regression.
Question 1 0.1 pts
log(pi) = a + bx + e
Log(pi/(1-pi) = a + b*x + e
Log(pi/(1-pi) = a + b*x
log(pi) = a + bx
The logistic regression function is given as
Question 2 0.1 pts
In running a logistic regression, a statistician decided to include decade of life (20s,
30s, 40s, 50s, 60s) as a categorical variable in the systematic component because
they didn’t believe the relationship between the log-odds and age was linear. Using
dummy variables to create the systematic component, how many dummy variables
would be needed to represented age?
Question 3 0.1 pts
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11/2/22, 10:36 AM Quiz: Assessment #8
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I performing a Wald chi-square test for whether there was an effect of age in the
model described above, how many degrees of freedom would be associated with the
sampling distribution of the test statistic?
Question 4 0.1 pts
If they used a Wald chi-square test to assess whether age (entered as a continuous
variable in the model above) was significant. How many degrees of freedom would
the chi-square sampling distribution of that test statistic have?
Question 5 0.1 pts
An investigator modeled the log-odds of getting stomach cancer as a function of
number of servings of vegetables per week and the number of servings of red mean
per week using logistic regression. The odds that a person gets stomach cancer if
they have 4 servings of red meat a week are 1.2 times the odds of cancer for
someone who has 3 servings of red meat a week. What is the odds ratio for stomach
cancer for someone who has 5 servings as opposed to someone who has 3
servings? Enter your answer to 3 digits beyond the decimal point.
Question 6 0.1 pts
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11/2/22, 10:36 AM Quiz: Assessment #8
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In the example above, suppose the fitted regression model is given as
log-odds = -6 + 0.182 M – 0.105 V,
where M = #servings of red meat per week and V = #servings of vegetables per
week. What is the odds ratio representing the change in odds for an increase in one
serving of vegetables? Give the answer to three decimal places.
Question 7 0.1 pts
Suppose in the example, above, where the regression coefficient for servings of
vegetables is -0.105, we have also obtained from the SAS output a Standard Error
from the output of 0.097. Since our estimates are maximum likelihood estimates, we
can assume that they follow a normal distribution. As such we can create confidence
intervals for the regression coefficients using standard practices for estimates that
have normal sampling distributions. Calculate a 95% confidence interval for the
ODDS RATIO given above (odds ratio representing change in odds of stomach
cancer for a one serving increase in vegetables. Give the lower endpoint below to
three numbers beyond the decimal place.
Question 8 0.1 pts
The apparent association of stomach cancer and servings of vegetables is not impacted by
servings of meat
There is no evidence for an association between stomach cancer and number of servings of
vegetables
Based on the confidence interval calculated above, we would conclude that
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11/2/22, 10:36 AM Quiz: Assessment #8
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There is a significant association between stomach cancer and number of servings of
vegetables
We can not make a conclusion about evidence for an association because we did not do a
hypothesis test
Question 9 0.1 pts
Logit (i.e., g(mu)=ln(mu/(1-mu))
Identity (i.e., g(mu)=mu)
Log (e.g., g(mu)=ln(mu))
The link function for a standard linear regression model is
Question 10 0.1 pts
Log (e.g., g(mu)=ln(mu))
Logit (i.e., g(mu)=ln(mu/(1-mu))
Identity (i.e., g(mu)=mu)