STAT 501 Mid-Term Exam 2 Spring 2015
A mid-term exam assessing statistical analysis and hypothesis testing.
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STAT 501 – Mid-Term Exam 2 – Spring 2015 – Due April 12
Instructions: Use Word to type your answers within this document. Then, submit your
answers in the appropriate dropbox in ANGEL by the due date and within 3 hours of
downloading the exam. The point distribution is located next to each question.
1. (4x2 = 8 points) State which of the following statements is TRUE and which is
FALSE. For the statements that are false, explain why they are false.
a. Removing an outlier in a regression analysis will result in narrower
confidence intervals.
b. In a simple linear regression (SLR) model, if a log transformation is
performed on X to remedy some non-linearity, the mean value of Y is bound
to change.
c. In model selection, the highest adjusted R2-value and the smallest S-value
criteria always yield the same "best" models.
d. Regression models with different responses, but the same predictor X
matrix, will have the same leverage values.
2. (3+3+4+4+3+3 = 20 points) Open the “Salary Data.” The dataset consists of current
salaries (Salary in thousands of dollars) for 63 individuals with information about
their years of work experience (YrsExp) and highest degree attained (Degree). Your
goal is to fit a regression model to express the dependence of Y (Salary) on X
(YrsExp) and Degree.
a. Clearly define a set of indicator variables that could be used in a regression
model to represent the qualitative variable Degree. [Hint: Think carefully
about the number of indicator variables needed given the number of levels of
Degree and use “Bachelor” as the reference level.]
b. Write a population multiple linear regression equation for predicting the
current salary in terms of YrsExp and Degree. Since education level could
impact the dependence of Y on X, the model should contain an interaction
effect between YrsExp and Degree, together with their main effects. [Hint:
Your equation should include Y, X, the indicator variables you defined in part
(a), interaction terms, and population regression coefficients (β’s).]
c. Conduct a hypothesis test for whether the average annual salary increase
per year of experience differs by level of education (i.e., test if the slopes for
two or more Degree categories differ). Write out the null and alternative
hypotheses, the test statistic, the p-value, and the conclusion. [Minitab v17:
Select Salary as the Response, YrsExp as the Continuous predictor, Degree
as the categorical predictor, click “Model,” select both YrsExp and Degree
together in the Predictors box and click the Add button next to “Interactions
through order 2.” Minitab v16: Create interaction terms using Calc >
Calculator before fitting the regression model.]
d. Write a new population regression equation based on your conclusion to part
(c). Fit this model and conduct two separate hypothesis tests for whether the
mean salary for a fixed number of years’ experience differs by education
level. For each test, write out the null and alternative hypotheses, the test
statistic, the p-value, and the conclusion.
Instructions: Use Word to type your answers within this document. Then, submit your
answers in the appropriate dropbox in ANGEL by the due date and within 3 hours of
downloading the exam. The point distribution is located next to each question.
1. (4x2 = 8 points) State which of the following statements is TRUE and which is
FALSE. For the statements that are false, explain why they are false.
a. Removing an outlier in a regression analysis will result in narrower
confidence intervals.
b. In a simple linear regression (SLR) model, if a log transformation is
performed on X to remedy some non-linearity, the mean value of Y is bound
to change.
c. In model selection, the highest adjusted R2-value and the smallest S-value
criteria always yield the same "best" models.
d. Regression models with different responses, but the same predictor X
matrix, will have the same leverage values.
2. (3+3+4+4+3+3 = 20 points) Open the “Salary Data.” The dataset consists of current
salaries (Salary in thousands of dollars) for 63 individuals with information about
their years of work experience (YrsExp) and highest degree attained (Degree). Your
goal is to fit a regression model to express the dependence of Y (Salary) on X
(YrsExp) and Degree.
a. Clearly define a set of indicator variables that could be used in a regression
model to represent the qualitative variable Degree. [Hint: Think carefully
about the number of indicator variables needed given the number of levels of
Degree and use “Bachelor” as the reference level.]
b. Write a population multiple linear regression equation for predicting the
current salary in terms of YrsExp and Degree. Since education level could
impact the dependence of Y on X, the model should contain an interaction
effect between YrsExp and Degree, together with their main effects. [Hint:
Your equation should include Y, X, the indicator variables you defined in part
(a), interaction terms, and population regression coefficients (β’s).]
c. Conduct a hypothesis test for whether the average annual salary increase
per year of experience differs by level of education (i.e., test if the slopes for
two or more Degree categories differ). Write out the null and alternative
hypotheses, the test statistic, the p-value, and the conclusion. [Minitab v17:
Select Salary as the Response, YrsExp as the Continuous predictor, Degree
as the categorical predictor, click “Model,” select both YrsExp and Degree
together in the Predictors box and click the Add button next to “Interactions
through order 2.” Minitab v16: Create interaction terms using Calc >
Calculator before fitting the regression model.]
d. Write a new population regression equation based on your conclusion to part
(c). Fit this model and conduct two separate hypothesis tests for whether the
mean salary for a fixed number of years’ experience differs by education
level. For each test, write out the null and alternative hypotheses, the test
statistic, the p-value, and the conclusion.
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Document Details
University
Pennsylvania State University
Subject
Statistics