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Due January 3, 2022

Week 5: Knowledge Check Chapter 16

Which of the following statements about the backward elimination procedure is false?

a. It is a one-variable-at-a-time procedure.

b. It does not permit an independent variable to be reentered once it has been removed.

c. It does not guarantee that the best regression model will be found.

d. It begins with the regression model found using the forward selection procedure.

Excel’s Regression tool can be used to perform the ____ procedure.

a. best-subsets

b. forward selection

c. stepwise regression

d. backward elimination

In a laboratory experiment, data were gathered on the life span (y in months) of 33 rats, units of daily protein intake (x1), and whether or not agent x2 (a proposed life-extending agent) was added to the rats’ diet (x2 = 0 if agent x2 was not added, and x2 = 1 if agent was added). From the results of the experiment, the following regression model was developed:

ŷ = 36 + .8×1 − 1.7×2

Also provided are SSR = 60 and SST = 180.

The degrees of freedom associated with SSE are _____.

a. 3

b. 30

c. 33

d. 32

In a laboratory experiment, data were gathered on the life span (y in months) of 33 rats, units of daily protein intake (x1), and whether or not agent x2 (a proposed life-extending agent) was added to the rats’ diet (x2 = 0 if agent x2 was not added, and x2 = 1 if agent was added). From the results of the experiment, the following regression model was developed:

ŷ = 36 + .8×1 − 1.7×2

Also provided are SSR = 60 and SST = 180.

The multiple coefficient of determination is _____.

a. .333

b. 5

c. .5

d. .2

The null hypothesis in the Durbin–Watson test is always that there is _____.

a. no autocorrelation

b. negative autocorrelation

c. positive autocorrelation

d. either positive or negative autocorrelation

Week 5: Chapter 16 Homework

In a regression analysis involving 25 observations, the following estimated regression equation was developed.

ŷ = 10 – 18×1 + 3×2 + 14×3

Also, the following standard errors and the sum of squares were obtained.

Sb1 = 3 Sb1 = 6 Sb1 = 7

SST = 4,800 SSE = 1,296

The coefficient of x3 _____.

a. is significant

b. is not significant

c. Cannot be tested, because not enough information is provided

d. None of these answers are correct.

In a regression model involving 30 observations, the following estimated regression equation was obtained.

ŷ = 170 + 34×1 – 3×2 + 8×3 + 58×4 + 3×5

For this model, SSR = 1,740 and SST = 2,000.

The value of MSE is _____.

a. 10.40

b. 32.13

c. 10.83

d. 348

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In a laboratory experiment, data were gathered on the life span (y in months) of 33 rats, units of daily protein intake (x1), and whether or not agent x2 (a proposed life-extending agent) was added to the rats’ diet (x2 = 0 if agent x2 was not added, and x2 = 1 if agent was added). From the results of the experiment, the following regression model was developed:

ŷ = 36 + .8×1 − 1.7×2

Also provided are SSR = 60 and SST = 180.

The life expectancy of a rat that was given two units of agent x2 daily, but was not given any protein, is _____.

a. 36

b. 38

c. 34.3

d. 32.6

Which of the following tests is used to determine whether an additional variable makes a significant contribution to a multiple regression model?

a. an F test

b. a t test

c. a z test

d. a chi-square test

Excel’s Regression tool can be used to perform the ____ procedure.

a. stepwise regression

b. forward selection

c. best-subsets

d. backward elimination

The null hypothesis in the Durbin–Watson test is always that there is _____.
a. positive autocorrelation
b. no autocorrelation
c. negative autocorrelation
d. either positive or negative autocorrelation

In a regression analysis involving 25 observations, the following estimated regression equation was developed.

ŷ = 10 – 18×1 + 3×2 + 14×3

Also, the following standard errors and the sum of squares were obtained.

Sb1 = 3 Sb1 = 6 Sb1 = 7

SST = 4,800 SSE = 1,296

If we are interested in testing for the significance of the relationship among the variables (i.e., significance of the model), the critical value of F at α = .05 is _____.
a. 3.10
b. 2.78
c. 2.76
d. 3.07

In a laboratory experiment, data were gathered on the life span (y in months) of 33 rats, units of daily protein intake (x1), and whether or not agent x2 (a proposed life-extending agent) was added to the rats’ diet (x2 = 0 if agent x2 was not added, and x2 = 1 if agent was added). From the results of the experiment, the following regression model was developed:

ŷ = 36 + .8×1 − 1.7×2

Also provided are SSR = 60 and SST = 180.

If we want to test for the significance of the model, the critical value of F at 95% confidence is _____.

a. 8.62

b. 2.92

c. 2.96

d. 3.35

In a laboratory experiment, data were gathered on the life span (y in months) of 33 rats, units of daily protein intake (x1), and whether or not agent x2 (a proposed life-extending agent) was added to the rats’ diet (x2 = 0 if agent x2 was not added, and x2 = 1 if agent was added). From the results of the experiment, the following regression model was developed:

ŷ = 36 + .8×1 − 1.7×2

Also provided are SSR = 60 and SST = 180.

The model _____.

a. is significant

b. Not enough information is provided to answer this question.

c. is not significant

d. None of these answers are correct.

The joint effect of two variables acting together is called _____.

a. autocorrelation

b. joint regression

c. interaction

d. serial correlation

Week 5: Chapter 16 Quiz

In a regression model involving 30 observations, the following estimated regression equation was obtained.

ŷ = 170 + 34×1 – 3×2 + 8×3 + 58×4 + 3×5

For this model, SSR = 1,740 and SST = 2,000.

The degrees of freedom associated with SSR are _____.

a. 24

b. 19

c. 6

d. 5

Below you are given a partial Excel output based on a sample of 25 observations.

Coefficients

Standard Error

Intercept

145

29

x1

20

5

x2

–18

6

x3

4

4

We want to test whether the parameter β2 is significant. The test statistic equals _____.

a. 4

b. 3

c. 5

d. –3

Top of Form

In a regression analysis involving 25 observations, the following estimated regression equation was developed.

ŷ = 10 – 18×1 + 3×2 + 14×3

Also, the following standard errors and the sum of squares were obtained.

Sb1 = 3 Sb1 = 6 Sb1 = 7

SST = 4,800 SSE = 1,296

The coefficient of x2 _____.

a. is not significant

b. is significant

c. Cannot be tested, because not enough information is provided

d. None of these answers are correct.

Bottom of Form
The correlation in error terms that arises when the error terms at successive points in time are related is termed _____.

a. parallel correlation

b. leverage

c. autocorrelation

d. multicorrelation

When dealing with the problem of non-constant variance, the reciprocal transformation means using _____.

a. x2 as the independent variable instead of x

b. y2 as the dependent variable instead of y

c. 1/x as the independent variable instead of x

d. 1/y as the dependent variable instead of y

Which of the following tests is used to determine whether an additional variable makes a significant contribution to a multiple regression model?

a. a chi-square test

b. a z test

c. a t test

d. an F test

Top of Form
In a laboratory experiment, data were gathered on the life span (y in months) of 33 rats, units of daily protein intake (x1), and whether or not agent x2 (a proposed life-extending agent) was added to the rats’ diet (x2 = 0 if agent x2 was not added, and x2 = 1 if agent was added). From the results of the experiment, the following regression model was developed:

ŷ = 36 + .8×1 − 1.7×2

Also provided are SSR = 60 and SST = 180.

From the given function, it can be said that the life expectancy of rats that were given agent x2 is _____.

a. .8 month more than those who did not take agent x2

b. 1.7 months more than those who did not take agent x2

c. .8 month less than those who did not take agent x2

d. 1.7 months less than those who did not take agent x2

Serial correlation is_____.

a. the correlation between serial numbers of products

b. the same as leverage

c. the same as autocorrelation

d. None of these answers are correct.

Bottom of Form

The parameters of nonlinear models have exponents _____.

a. only equal to 2

b. larger than 3

c. larger than 0

d. other than 1

In a laboratory experiment, data were gathered on the life span (y in months) of 33 rats, units of daily protein intake (x1), and whether or not agent x2 (a proposed life-extending agent) was added to the rats’ diet (x2 = 0 if agent x2 was not added, and x2 = 1 if agent was added). From the results of the experiment, the following regression model was developed:

ŷ = 36 + .8×1 − 1.7×2

Also provided are SSR = 60 and SST = 180.

The model _____.

a. is significant

b. Not enough information is provided to answer this question.

c. is not significant

d. None of these answers are correct.

What value of Durbin–Watson statistic indicates no autocorrelation is present?

a. 1

b. –2

c. 0

d. 2

he following model y = β0 + β1×1 + ε is referred to as a _____.

a. simple second-order model with one predictor variable

b. simple first-order model with one predictor variable

c. curvilinear model with one predictor variable

d. curvilinear model

The following regression model y = β0 + β1×1 + β2×2 + ε is known as _____.

a. first-order model with one predictor variable

b. second-order model with two predictor variables

c. second-order model with one predictor variable

d. None of these answers are correct.

In a regression model involving 30 observations, the following estimated regression equation was obtained.

ŷ = 170 + 34×1 – 3×2 + 8×3 + 58×4 + 3×5

For this model, SSR = 1,740 and SST = 2,000.

The degrees of freedom associated with SST are _____.

a. 19

b. 24

c. 6

d. None of these answers are correct

The forward selection procedure starts with how many independent variable(s) in the multiple regression model?

a. 0

b. 2

c. 1

d. All of these answers are correct.

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