2020/11/13Submit quiz-03 | Gradescope
0/25 Questions Answered
TIME REMAINING
mins
quiz-03
Q1
15 Points
You have 45 minutes to complete the quiz.
When needed, set α = 0.05 (assume a 5% significance level).
Below is the R output of a model where the response is resting
heart rate (Rest) and the predictors are Weight (Wgt, in pounds) and
Gender (0 for female and 1 for male), with an interaction term
between Weight and Gender.
Our population model is: Resti = β0 + β1 W gti +
β2 Genderi + β3 W gti Genderi + ε
Q1.1
3 Points
Test whether the model is significant. In other words, conduct a test
via the general linear test of all the slope coefficients equaling 0.
The null hypothesis is H0 : β1 = β2 = β3 = 0
What would be the correct alternative hypothesis? Pick only one.
https://www.gradescope.com/courses/191654/assignments/826238/submissions/new
1/14
2020/11/13
Submit quiz-03 | Gradescope
= 0 for i=1,2,3
HA : All βi
HA : β1
= β2
= β3
=0
= 0 for i=1,2,3
HA : at most one βi
= 0 for i=1,2,3
HA : at least one βi
HA : β1
= β2
= β3
Q1.2
2 Points
What is the general linear test presented in the previous question
Q1.1 doing with respect to the full model fitted in Q1 description?
Pick only one
Testing to see if your fitted model is the best model.
Testing to see if your fitted model is better than a model with all
the covariates in it.
Testing to see if your fitted model is better than a model with
only a single covariate in it.
Testing to see if your fitted model is better than a model with
only an intercept in it.
Q1.3
2 Points
Continuing from Q1.1, what is the correct test statistic? Round to 3
decimal places, X.XXX.
Enter your answer here
Q1.4
2 Points
Continuing from Q1.1, what is the correct p-value? Round to 3
decimal places, X.XXX.
https://www.gradescope.com/courses/191654/assignments/826238/submissions/new
2/14
2020/11/13
Submit quiz-03 | Gradescope
Enter your answer here
Q1.5 Interpretation I
3 Points
For males, as weight increases one unit, the predicted/estimated
average resting heart rate changes by ____ units. Round to 5
decimal places, X.XXXXX, and provide correct sign (+/-). If
answer is negative, then would input -X.XXXXX
Enter your answer here
Q1.6
3 Points
Do we have enough information in the R output above to test if the
coefficients for Wgt and Gender*Wgt are both zero? Yes or no.
If you answered yes, provide the test statistic, p-value, and
conclusion. If you answered no, what model would you need to fit
in order to get enough information to conduct the test? Explain in a
sentence or two.
Enter your answer here
Q2 MC
2 Points
^ , we need:
To compute the predicted value of Y , Y
All the Y’s
All the X’s
All the Y’s and X’s
No Y’s or X’s
https://www.gradescope.com/courses/191654/assignments/826238/submissions/new
3/14
2020/11/13
Submit quiz-03 | Gradescope
Q3 MC
2 Points
What can we do to help ensure that our errors in a linear
regression model are independent of one another?
Take a small sample
Take a large sample.
Take a sample from the target population.
Take a random sample.
Q4
3 Points
What is the QQ (quantile-quantile) plot used for? Pick only one.
Assessing the constant variance assumption of the errors in the
linear regression model.
Assessing the independence assumption of the errors in the
linear regression model.
Assessing the linearity assumption of the errors in the linear
regression model.
Assessing the normality assumption of the errors in the linear
regression model.
Q5 MC
3 Points
https://www.gradescope.com/courses/191654/assignments/826238/submissions/new
4/14
2020/11/13
Submit quiz-03 | Gradescope
Based on the scatterplot of X and Y above, what would you
suggest to improve the validity of the model in terms of
assumptions of the linear regression model? Pick only one.
Transform the Y’s
Transform the X’s
Transform both X’s and Y’s
No need to transform anything
Q6 MC
2 Points
You have a model with a single response Y and two categorical
explanatory variables, each with 3 groups. Say one is A, B, C
categories and the other is Left, Right, Center categories.
In a multiple linear regression setting, how many coefficients (not
including the intercept, thus only talking about slope coefficients)
would there be in a model that has these two categorical variables
as explanatory variables (main effects) and interaction terms
between them (added effects)?
https://www.gradescope.com/courses/191654/assignments/826238/submissions/new
5/14
2020/11/13
Submit quiz-03 | Gradescope
15
13
9
8
Cannot be determined.
Q7 T/F
3 Points
The regular unadjusted R2 (multiple R-squared in R) will naturally
increase as more predictors are added to the model.
True
False
Need more information
Q8 T/F
3 Points
The adjusted R2 will naturally increase as more predictors are
added to the model.
True
False
Need more information
Q9
3 Points
Use the following fitted values against residuals plot for the
following question.
https://www.gradescope.com/courses/191654/assignments/826238/submissions/new
6/14
2020/11/13
Submit quiz-03 | Gradescope
Q9.1
3 Points
Does there seem to be any issue with respect to the non-constant
variance assumption? Explain in a sentence or two.
Enter your answer here
Q10
4 Points
Use the following scatterplot of X and Y to answer the following
two (2) questions.
https://www.gradescope.com/courses/191654/assignments/826238/submissions/new
7/14
2020/11/13
Submit quiz-03 | Gradescope
Q10.1
2 Points
Is there any issue with the constant variance of Y given X in this
scatterplot? Pick only one.
No, there appears to be a curved shape to the points.
There does not seem to be any issue with the constant variance
assumption.
Yes, there appears to be a curved shape to the points.
Yes, the Y points seem to scatter more and more as we move
left to right along the X axis.
Q10.2
2 Points
Based on the fitted values against residuals plot above, what would
you suggest to improve the validity of the model in terms of
assumptions? Pick only one.
https://www.gradescope.com/courses/191654/assignments/826238/submissions/new
8/14
2020/11/13
Submit quiz-03 | Gradescope
Transform the Y’s
Transform the X’s
Transform both X’s and Y’s
No need to transform anything
Q11
4 Points
The following graphs is from an observational study on people with
PhDs where the response variable is yearly salary and the
explanatory variable is the number of years since obtaining a PhD.
The first graph is the scatterplot with years since PhD on the X-axis
and yearly salary on the Y-axis.
The second graph is the fitted values against the residuals plot.
https://www.gradescope.com/courses/191654/assignments/826238/submissions/new
9/14
2020/11/13
Submit quiz-03 | Gradescope
Q11.1
2 Points
Is there any issue with the linearity assumption for the relationship
between years since PhD (X) and yearly salary (Y)? Pick only one.
No, points have no pattern as we move left to right in the plots.
No, points have equal scatter as we move left to right in the
plots.
Yes, the points exhibit more scatter as we move left to right in
the plots.
Yes, the points exhibit a pattern as we move left to right in the
plots.
Q11.2
2 Points
What would be an appropriate transformation for this model to deal
with the linearity assumption issue, if any ? Pick only one.
https://www.gradescope.com/courses/191654/assignments/826238/submissions/new
10/14
2020/11/13
Submit quiz-03 | Gradescope
No transformations needed
Transform X to X 2
Transform X to
X
Transform Y to
Y
Transform Y to log(Y )
Q12
2 Points
We have a model where the response variable, Y, is the systolic
blood pressure of a subject, and the covariate is their weight in
kilograms, X. Call this model 1. Now say we convert weight to
pounds, set this covariate to be Z (that is to say we take kilograms
and multiply by a factor of 2.2, Z=2.2X). Call this model 2. Which of
the following is true? Pick only one.
The F-test statistic for testing the coefficient on X is not the
same as the t-test statistic for testing the coefficient on Z.
Need more information.
The t-test statistic for testing the coefficient on X is not the
same as the t-test statistic for testing the coefficient on Z.
The t-test statistic for testing the coefficient on X is the same as
the t-test statistic for testing the coefficient on Z.
Q13
9 Points
Use the following ANOVA sequential sum of regression table for
the model:
Resti = β0 + β1 Activei + β2 Genderi + β3 Activei ∗
Genderi + εi
where Rest is the resting heart rate of an individual, Active is the
active heart rate, and Gender is equal to 0 for female and equal to 1
for male.
https://www.gradescope.com/courses/191654/assignments/826238/submissions/new
11/14
2020/11/13
Submit quiz-03 | Gradescope
Analysis of Variance Table
Response: Rest
Df
Active
1
Gender
1
Active:Gender
1
Residuals
228
Sum Sq Mean Sq
8347
8347
82
82
161
161
14275
63
Q13.1
3 Points
Given that Active and Gender are already in the model, how much
does an interaction term between them add to the sum of squared
regressions? Put a whole integer number.
Enter your answer here
Q13.2
2 Points
What is the sum of square total for the model? Put a whole integer
number.
Enter your answer here
Q13.3
2 Points
What is the following output from R doing? Write out the null and
alternative hypothesis based on the model in the description of
Q13, and explain in a sentence while making a conclusion.
Analysis of Variance Table
Model 1: Rest ~ Active
Model 2: Rest ~ Active + Gender + Active * Gender
Res.Df
RSS Df Sum of Sq
F Pr(>F)
1
230 14519
2
228 14276 2
243.54 1.9448 0.1454
https://www.gradescope.com/courses/191654/assignments/826238/submissions/new
12/14
2020/11/13
Submit quiz-03 | Gradescope
Enter your answer here
Q13.4
2 Points
Now say we replace the covariate Active in the model with the
covariate Smoker status (0 for non-smoker and 1 for smoker) but
keep Rest as the response variable.
What happens to the SSTO of this model compared to the original
one? Pick only one.
Need more information
Decreases
Increases
Stays the same
Q14
5 Points
Use the following for the next 2 questions, 14.1 and 14.2.
Say we have a single response variable Y, and two explanatory
variables, X and W. We fit a model as follows:
Y = β0 + β1 X + β2 W + ε
Q14.1
3 Points
The general linear test to test the null hypothesis that H0 : β1 =
β2 = 0 returns a p-value that is 0.01, but the individual t-tests of
H0 : β1 = 0 and H0 : β2 = 0 both have p-values of about 0.50.
Which of the following best explains what is going on with the
information provided? Pick only one.
https://www.gradescope.com/courses/191654/assignments/826238/submissions/new
13/14
2020/11/13
Submit quiz-03 | Gradescope
W should be in the model, but not X.
X should be in the model, but not W.
Both X and W should not be in the model.
Both X and W should be in the model.
X or W (but not both) should be in the model.
Q14.2
2 Points
Now say we fit the model described in Q14 (with both X and W), call
this model 1. Next, we fit a model with only X as covariate (no W).
Call this model with only X as covariate model 2.
The intercept estimate of model 1 is most likely to be different
(even by the smallest of margins) than the intercept estimate of
model 2. True or false?
False
True
Submit & View Submission
https://www.gradescope.com/courses/191654/assignments/826238/submissions/new
14/14
Essay Writing Service Features
Our Experience
No matter how complex your assignment is, we can find the right professional for your specific task. Achiever Papers is an essay writing company that hires only the smartest minds to help you with your projects. Our expertise allows us to provide students with high-quality academic writing, editing & proofreading services.
Free Features
Free revision policy
$10Free bibliography & reference
$8Free title page
$8Free formatting
$8How Our Dissertation Writing Service Works
First, you will need to complete an order form. It's not difficult but, if anything is unclear, you may always chat with us so that we can guide you through it. On the order form, you will need to include some basic information concerning your order: subject, topic, number of pages, etc. We also encourage our clients to upload any relevant information or sources that will help.
Complete the order form
Once we have all the information and instructions that we need, we select the most suitable writer for your assignment. While everything seems to be clear, the writer, who has complete knowledge of the subject, may need clarification from you. It is at that point that you would receive a call or email from us.
Writer’s assignment
As soon as the writer has finished, it will be delivered both to the website and to your email address so that you will not miss it. If your deadline is close at hand, we will place a call to you to make sure that you receive the paper on time.
Completing the order and download