Please go to documents for Appendix:MINITABoutput. Use the Minitab output for the gasoline mileage data to answer questions that refer to output. You do not need the data, but it appears in Table B.3 in the 4th edition textbook.

QUESTION 1

Adding more regressors to a regression model is always desirable because it may increase the .

True

False

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

QUESTION 3

Adjusted will not necessarily increase when adding more regressors to a regression model.

True

False

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

QUESTION 5

A variance inflation factor greater than 10 for a regressor x1 implies that x1 is linearly related to the other regressors.

True

False

QUESTION 6

Normal probability plot of the observed ys is used to check the normality assumption of the errors.

True

False

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

QUESTION 8

Data transformation can be used when some of the model assumptions are violated.

True

False

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

QUESTION 10

A large implies that a point has high leverage.

True

False

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)

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

QUESTION 13

What is the estimated ?

3.146

9.895

9.752

95.11

QUESTION 14

Calculate a 95% confidence interval for 1.

(-0.13236, -0.0199)

(-0.1938, 0.0416)

(-0.24482, 0.09256)

Not available

QUESTION 15

In the output, no t-tests are significant at

.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

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

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

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

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?

COOKS D

DFFITS

DFBETAS

Both b and c

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?

1.41

3

1.75

0.9

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

QUESTION 22

In a regression problem with 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

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 ys and the ys are shown below.

18.25

21

2.25

3.6

QUESTION 24

If the xs are considered to be fixed numbers, in the 95% statement in the confidence interval what is assumed about the xs 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

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