INDUSTRIAL IEE 578-Adding more regressors to a regression model

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