INDUSTRIAL IEE 578-Adding more regressors to a regression model
Subject: Mathematics / Statistics
Question
Regression Analysis
QUESTION 1
Adding more regressors to a regression model is always desirable because it may increase the .
True
False
4 points
QUESTION 2
A prediction interval of a future response of y at an observation x is always wider than a confidence interval for the same observation of x.
True
False
4 points
QUESTION 3
Adjusted will not necessarily increase when adding more regressors to a regression model.
True
False
4 points
QUESTION 4
In a multiple regression, if the t-tests for individual regression coefficients show none of the coefficients are significant, then no regressors are useful.
True
False
4 points
QUESTION 5
A variance inflation factor greater than 10 for a regressor implies that is linearly related to the other regressors.
True
False
4 points
QUESTION 6
Normal probability plot of the observed y’s is used to check the normality assumption of the errors.
True
False
4 points
QUESTION 7
A lack-of-fit test requires that we have replicate observations on the response y for at least one level of x.
True
False
4 points
QUESTION 8
Data transformation can be used when some of the model assumptions are violated.
True
False
4 points
QUESTION 9
A predicted residual or prediction error is calculated for a row when the corresponding row is not used to estimate the coefficients of the model.
True
False
4 points
QUESTION 10
A large implies that a point has high leverage.
True
False
4 points
QUESTION 11
What are the units of the slope estimate 1 hat?
miles per gallon
cubic inches
miles per gallon per cubic inch
1/(cubic inches)
4 points
QUESTION 12
A one-unit change in x1 changes the estimated mean of y by how much?
an increase of 0.0761
a decrease of 0.0761
an increase of 19.4
cannot be determined from the output
4 points
QUESTION 13
What is the estimated ?
3.146
9.895
9.752
95.11
4 points
QUESTION 14
Calculate a 95% confidence interval for 1.
(-0.13236, -0.0199)
(-0.1938, 0.0416)
(-0.24482, 0.09256)
Not available
4 points
QUESTION 15
In the output, no t-tests are significant at
=0.05, but the F-test for regression has a p-value of approximately 0. The best explanation of these results is:
These regressors are not useful predictors
Multicollinearity is present
All these regressors are useful predictors
Only first variable x1 is a useful predictor
4 points
QUESTION 16
Four assumptions for the multiple linear regression equation are: linearity, errors with constant variance, means zero, and normally distributed. To obtain estimates of the parameters, which assumptions are needed?
Linearity, errors with means zero, and normally distributed
Errors with constant variance, means zero, and normally distributed
Linearity, errors with constant variance and normally distributed
Linearity, errors with constant variance, means zero
4 points
QUESTION 17
A failure of the linearity assumption is best detected by what plot?
Normal probability plots of the residuals
Residuals versus predicted
y versus each x separately
Plot of residuals in time sequence
4 points
QUESTION 18
A failure of the nonconstant variance assumption is best detected by what plots?
Normal probability plot
Residuals versus predicted
Residuals versus independent variables
Both b and c
4 points
QUESTION 19
If a row of data affects the prediction of its own y, but does not change other predictors very much, what influence measure would be most sensitive?
COOK’S D
DFFITS
DFBETAS
Both b and c
4 points
QUESTION 20
Given that the following is the covariance matrix for the parameters in a multiple regression model with 3 parameters (one intercept and two slopes), what is the estimated standard error of
1 hat?
B0 B1 B2
2 1.7 .09
1.7 9 5
.9 5 3
a- 1.41
b- 3
c- 1.75
d- 0.9
4 points
QUESTION 21
To calculate the Variance Inflation Factor for x3 in the regression model y on x1, x2, x3, one can use the R-squared obtained from the regression model of x3 on x1 and x2 and the VIF is VIF = 1/(1-R2j)
True
False
4 points
QUESTION 22
In a regression problem whit n = 40 observations, and 4 parameters (including the intercept), what is the distribution of a deleted residual?
Normal distribution
t-distribution with 35 degrees of freedom
t-distribution with 36 degrees of freedom
none of the above
4 points
QUESTION 23
Given a multiple regression problem with n = 30 rows and 3 predictors and an intercept, calculate the mean square for pure error. There are only 3 points with replicated y’s and the y’s are shown below.
Point x y
1
3.5 10
2 3.5 8
3 3.5 12
4 7 14
5 7 16
6 9 2
7 9 4
8 9 6
a- 18.25
b- 21
c- 2.25
d- 3.6
4 points
QUESTION 24
If the x’s are considered to be fixed numbers, in the 95% statement in the confidence interval what is assumed about the x’s in hypothetical future sample?
Observations of y are obtained at the same x values
Observations of y are obtained at random x values
Observations of y are obtained at a subset of the same x values
Does not matter
4 points
QUESTION 25
By adding any new regressors to a regression model, the R2 of the new model
will not change
will not decrease
will not increase
depends on which regressors are added