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quiz-04
Q1 Directions
0 Points
You have 45 minutes to finish the quiz.
Please read each question carefully and answer what is asked.
Do not assume anything that is not explicitly stated.
Q2
2 Points
When is it absolutely acceptable to completely remove an outlier
point?
To get a better model fit.
When it is an outlier in X and Y.
When it is only an outlier in X.
When it is only an outlier in Y.
When it is clearly a data input error or mistake.
Q3 MC
2 Points
To compute the VIF (variance inflation factor), all we need are:
All the Y’s
All the X’s
All the Y’s and X’s
No Y’s or X’s
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Q4 MC
2 Points
To compute the MSE (mean squared error), all we need are:
All the Y’s
All the X’s
All the Y’s and X’s
No Y’s or X’s
Q5
2 Points
Leverage can be defined as a measure of how far away the
covariate values of an observation are from those of the other
observations.
In a sentence or two, explain why “leverage” has no useful
meaning when the only explanatory variable is a categorical yes/no
(1 or 0) variable.
Be clear in your explanation using the definition of leverage and
try to give an example.
Enter your answer here
Q6
6 Points
Use the following information for the next three (3) questions.
Say we have a dataset with n=50 observations, and the fitted
regression equation using these 50 observations is:
Y = 15 + 25.5X
The 50 observations have a sample mean of the X values being
ˉ = 200), and a sample standard deviation of 50, while the
200 (X
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ˉ = 5100), with a sample
sample mean of the Y values is 5100 (Y
standard deviation of 500.
Q6.1
2 Points
Now say a new observation is going to be added to the dataset,
the 51-st observation. This observation has X = 800 and Y =
45000. Which of the following is the most reasonable?
PICK ONLY ONE.
This 51-st observation does not have high leverage and will not
change the model substantially.
This 51-st observation does not have high leverage and will
change the model substantially.
This 51-st observation has high leverage but will not change the
model substantially.
This 51-st observation has high leverage and will change the
model substantially.
Q6.2
2 Points
Now say a new observation is going to be added to the dataset,
the 51-st observation. This observation has X = 800 and Y =
20500. Which of the following is the most reasonable?
PICK ONLY ONE.
This 51-st observation does not have high leverage and will not
change the model substantially.
This 51-st observation does not have high leverage and will
change the model substantially.
This 51-st observation has high leverage but will not change the
model substantially.
This 51-st observation has high leverage and will change the
model substantially.
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Q6.3
2 Points
Now say a new observation is going to be added to the dataset,
the 51-st observation. This observation has X = 210 and Y =
5400. Which of the following is the most reasonable?
PICK ONLY ONE.
This 51-st observation does not have high leverage and will not
change the model substantially.
This 51-st observation does not have high leverage and will
change the model substantially.
This 51-st observation has high leverage but will not change the
model substantially.
This 51-st observation has high leverage and will change the
model substantially.
Q7
2 Points
Say we have the following model (call this the old model):
Yi = β0 + β1 Xi + εi .
Now say we are going to add a new covariate, Z , that is highly
correlated with X (corr(X, Z) = 0.90). Call this the new model.
What will most likely happen to the slope coefficient β1 in this new
model compared to the old model?
Be equal to 0.
Be approximately the same (within a few percent of the old one).
Be substantially different (over a few percent different than the
old one).
Q8
2 Points
Say we have the following model (call this the old model):
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Yi = β0 + β1 Xi + εi .
Now say we are going to add a new covariate, Z , that is
completely uncorrelated with X (corr(X, Z) = 0). Call this the
new model. What will most likely happen to the estimated slope
coefficient on X , β1 , in this new model compared to the old
model?
Be equal to 0.
Be approximately the same (within a few percent of the old one).
Be substantially different (over a few percent different than the
old one).
Q9
2 Points
Say we have the following model:
Yi = β0 + β1 Xi + β2 Zi + εi .
The covariates X and Z are completely uncorrelated with one
another. What will the variance inflation factors (VIF) be for each of
these covariates?
Both will be large (greater than 5) and equal
Both will be large (greater than 5) and not equal
Both will be approximately equal to 0
Both will be approximately equal to 1
Q10
2 Points
Say we have the following model:
Yi = β0 + β1 Xi + β2 Zi + εi .
The covariates X and Z are highly correlated with one another.
What will the variance inflation factors (VIF) be for each of these
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covariates?
Both will be large (greater than 5) and equal
Both will be large (greater than 5) and not equal
Both will be approximately equal to 0
Both will be approximately equal to 1
Q11
2 Points
Say we have a model with p=5 covariates in it. What happens to
MSE (mean squared error) as our dataset gets infinitely large (n
goes to infinity)?
Goes to 5
Goes to negative values
Goes to infinity
Goes to 1
Goes to 0
Q12
9 Points
Use the following information to answer the next four (4)
questions.
Say we have a response variable Y , and 5 (five) potential
covariates X1 , X2 , X3 , X4 , and X5 .
Q12.1
3 Points
If we decide to go with the forward selection method, we must
start with the null model (or reduced) with only an intercept in it
(and no covariates).
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Need more information
False
True
Q12.2
2 Points
If we decide to go with the backward selection method, we will
eventually end up with a model with only one covariate in it if we
let the selection process to go on until it naturally stops.
Need more information
False
True
Q12.3
2 Points
If we decide to go with the forward selection method, we will
eventually end up with a model with all the covariates in it if we let
the selection process to go on until it naturally stops..
Need more information
False
True
Q12.4
2 Points
If we decide to go with the forward selection method, we will add
at least one covariate to the model.
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Need more information
False
True
Q13
6 Points
Use the following to answer the next three (3) questions.*
Say we have a response variable Y , and 4 (four) potential
covariates X1 , X2 , X3 , and X4 .
In the forward selection method, the following covariates are
added at each step:
Step 1: X2 is added.
Step 2: X3 is added.
Step 3: X1 is added.
Step 4: X4 is added.
A best subsets method is also ran for the best model with 1, 2, 3,
and 4 covariates.
Q13.1
2 Points
The best subsets model with only one (1) covariate in it will
definitely be with the X2 covariate.
False
True
Q13.2
2 Points
The best subsets model with four (4) covariate in it will definitely be
with X2 , X3 , X1 , and X4 covariates.
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False
True
Q13.3
2 Points
The best subsets model with three (3) covariate in it will definitely
be with X2 , X3 and X1 covariates.
False
True
Q14
13 Points
A study is conducted to assess the relationship between a vehicles
horsepower (hp) and it’s obtained miles per gallon (mpg). The
following simple linear model is fit:
mpgi = β0 + β1 hpi + εi .
Q14.1
3 Points
The following three (3) plots in order are the scatterplot with linear
line, scatterplot with quadratic term of hp2 added to the simple
linear model, and residual plot of the simple linear model with no
quadratic term.
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Based on the plots above, does it seem that we need to add a
transformed hp covariate?
No transformation needs to be added.
Yes, a quadratic term should be added.
Q14.2
2 Points
In a sentence or two, explain what the quadratic term will do to with
respect to how hp affects mpg.
Be very clear in your explanation. What happens to mpg as hp
increases (decreases, increases, or stays the same), while
considering the hp value ranges of 50 to 200 and 200 to 300+
separately.
Enter your answer here
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Q14.3
3 Points
If a quadratic term of hp2 is added to the model, what will be the
most reasonable values for the variance inflation factor (VIF) for hp
and hp2 . PICK ONLY ONE
small (below 5)
equal to 0
equal to 1
large (above 5)
Q14.4
3 Points
The output of the quadratic model, mpgi = β0 + β1 hpi +
β2 hp2i + ε, is below:
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 4.041e+01 2.741e+00 14.744 5.23e-15 ***
hp
-2.133e-01 3.488e-02 -6.115 1.16e-06 ***
I(hp^2)
4.208e-04 9.844e-05
4.275 0.000189 ***
–Signif. codes:
0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 3.077 on 29 degrees of freedom
Multiple R-squared: 0.7561,
Adjusted R-squared: 0.7393
F-statistic: 44.95 on 2 and 29 DF, p-value: 1.301e-09
What is the test statistic to test if we need to include the quadratic
term in the model? ROUND TO THE NEAREST 2nd DECIMAL
PLACE X.XX.
Enter your answer here
Q14.5
2 Points
Using the output in the previous question, what would be the test
statistic if we want to test if horsepower (hp) should be in the model
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in some form (regular term and/or quadratic) ? ROUND TO THE
NEAREST 2nd DECIMAL PLACE X.XX.
Enter your answer here
Q15
3 Points
Say we have a model with a single response variable Y and three
(3) covariates: X, W , and Z . We fit the following model:
Y = β0 + β1 Xi + β2 Wi + β3 Zi + εi .
The general linear F-test to test the null hypothesis of H0 : β1 =
β2 = β3 = 0 returns a p-value that is approximately equal to 0.50
(large p-value). Which of the following is most reasonable. PICK
ONLY ONE.
We need at least one of X, W, or Z but not all three.
We do need X, W, and Z in the model.
We do not need X, W, or Z in the model.
Q16
3 Points
Say we have a model with a single response variable Y and three
(3) covariates: X, W , and Z . We fit the following model:
Y = β0 + β1 Xi + β2 Wi + β3 Zi + εi .
The general linear F-test to test the null hypothesis of H0 : β1 =
β2 = β3 = 0 returns a p-value that is approximately equal to 0
(very small p-value) but the individual coefficient tests (H0 : βk =
0 for k=1,2,3) returns a p-value of approximately 0.5 (large p-value).
Which of the following is most reasonable. PICK ONLY ONE.
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We need at least one of X, W, or Z but not all three.
We do need X, W, and Z in the model.
We do not need X, W, or Z in the model.
Q17
2 Points
The form of the confidence interval for a parameter θ was of the
form:
θ^ ± c ∗ SE
Where θ^ is an estimate, SE is the estimates standard error and c
is the multiplier.
What happens to the multiplier c as the confidence level increases
(say from 90% to 99%)? PICK ONLY ONE.
Becomes 0
Stays the same
Gets smaller
Gets larger
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