Deck 16: Regression Analysis: Model Building

Question 1

A test to determine whether or not first-order autocorrelation is present is

A)a t test
B)an F test
C)a test of interaction
D)a chi-square test

Answer 1

D

Question 2

A variable such as Z,whose value is Z = X₁X₂ is added to a general linear model in order to account for potential effects of two variables X₁ and X₂ acting together.This type of effect is

A)impossible to occur
B)called interaction
C)called multicollinearity effect
D)called transformation effect

Answer 2

B

Question 3

Exhibit 16-1
In a regression analysis involving 25 observations,the following estimated regression equation was developed. Also,the following standard errors and the sum of squares were obtained.

Refer to Exhibit 16-1.The coefficient of X₁

A)is significant
B)is not significant
C)can not be tested,because not enough information is provided
D)None of these alternatives is correct.

Answer 3

A

Question 4

In multiple regression analysis,the general linear model

A)can not be used to accommodate curvilinear relationships between dependent variables and independent variables
B)can be used to accommodate curvilinear relationships between the independent variables and dependent variable
C)must contain more than 2 independent variables
D)None of these alternatives is correct.

Question 5

Exhibit 16-1
In a regression analysis involving 25 observations,the following estimated regression equation was developed. Also,the following standard errors and the sum of squares were obtained.

Refer to Exhibit 16-1.The coefficient of X₂

A)is significant
B)is not significant
C)can not be tested,because not enough information is provided
D)None of these alternatives is correct.

Question 6

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

A)a t test
B)a Z test
C)an F test
D)a chi-square test

Question 7

The following model
Is referred to as a

A)curvilinear model
B)curvilinear model with one predictor variable
C)simple second-order model with one predictor variable
D)simple first-order model with one predictor variable

Question 8

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

A)1
B)2
C)-2
D)0

Question 9

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

A)1/X as the independent variable instead of X
B)X² as the independent variable instead of X
C)Y² as the dependent variable instead of Y
D)1/Y as the dependent variable instead of Y

Question 10

The range of the Durbin-Watson statistic is between

A)-1 to 1
B)0 to 1
C)-infinity to + infinity
D)0 to 4

Question 11

Serial correlation is

A)the correlation between serial numbers of products
B)the same as autocorrelation
C)the same as leverage
D)None of these alternatives is correct.

Question 12

The parameters of nonlinear models have exponents

A)larger than zero
B)larger than 1
C)larger than 2
D)larger than 3

Question 13

In multiple regression analysis,the word linear in the term "general linear model" refers to the fact that

A) $\beta$ ₁, $\beta$ ₂,... $\beta$ _p,all have exponents of 0
B) $\beta$ ₁, $\beta$ ₂,... $\beta$ _p,all have exponents of 1
C) $\beta$ ₀ $\beta$ ₁,... $\beta$ _p,all have exponents of at least 1
D) $\beta$ ₀, $\beta$ ₁,... $\beta$ _p,all have exponents of less than 1

Question 14

A model in the form of y = $\beta$ ₀ + $\beta$ ₁z₁ + $\beta$ ₂z₂ + ...+ $\beta$ _pz_p + $\varepsilon$ where each independent variable z_j (for j = 1,2,... ,p)is a function of x_j .x_j is known as the

A)general linear model
B)general curvilinear model
C)multiplicative model
D)multiplicative curvilinear model

Question 15

All the variables in a multiple regression analysis

A)must be quantitative
B)must be either quantitative or qualitative but not a mix of both
C)must be positive
D)None of these alternatives is correct.

Question 16

The correlation in error terms that arises when the error terms at successive points in time are related is termed

A)leverage
B)multicorrelation
C)autocorrelation
D)parallel correlation

Question 17

The joint effect of two variables acting together is called

A)autocorrelation
B)interaction
C)serial correlation
D)joint regression

Question 18

Exhibit 16-1
In a regression analysis involving 25 observations,the following estimated regression equation was developed. Also,the following standard errors and the sum of squares were obtained.


-Refer to Exhibit 16-1.If you want to determine whether or not the coefficients of the independent variables are significant,the critical value of t statistic at $\alpha$ = 0.05 is

A)2.080
B)2.060
C)2.064
D)1.96

Question 19

The following regression model
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 alternatives is correct.

Question 20

A test used to determine whether or not first order autocorrelation is present is

A)z test
B)t test
C)Chi-square test
D)Durbin-Watson Test

Question 21

Exhibit 16-4
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. Also provided are SSR = 60 and SST = 180.
Refer to Exhibit 16-4.The life expectancy of a rat that was not given any protein and that did not take agent X₂ is

A)36.7
B)34.3
C)36
D)38.4

Question 22

Exhibit 16-2
In a regression model involving 30 observations,the following estimated regression equation was obtained. For this model,SSR = 1,740 and SST = 2,000.
Refer to Exhibit 16-2.The coefficient of determination for this model is

A)0.6923
B)0.1494
C)0.1300
D)0.8700

Question 23

Exhibit 16-4
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. Also provided are SSR = 60 and SST = 180.
Refer to Exhibit 16-4.The life expectancy of a rat that was given 3 units of protein daily,and who took agent X₂ is

A)36.7
B)36
C)49
D)38.4

Question 24

Exhibit 16-2
In a regression model involving 30 observations,the following estimated regression equation was obtained. For this model,SSR = 1,740 and SST = 2,000.
Refer to Exhibit 16-2.The degrees of freedom associated with SSE are

A)24
B)6
C)19
D)5

Question 25

Exhibit 16-3
Below you are given a partial computer output based on a sample of 25 observations.


-Refer to Exhibit 16-3.We want to test whether the parameter $\beta$ ₂ is significant.The test statistic equals

A)4
B)5
C)3
D)-3

Question 26

Exhibit 16-2
In a regression model involving 30 observations,the following estimated regression equation was obtained. For this model,SSR = 1,740 and SST = 2,000.
Refer to Exhibit 16-2.The test statistic F for testing the significance of the above model is

A)32.12
B)6.69
C)4.8
D)58

Question 27

Exhibit 16-3
Below you are given a partial computer output based on a sample of 25 observations.

Refer to Exhibit 16-3.The critical t value obtained from the table to test an individual parameter at the 5% level is

A)2.06
B)2.069
C)2.074
D)2.080

Question 28

Exhibit 16-1
In a regression analysis involving 25 observations,the following estimated regression equation was developed. Also,the following standard errors and the sum of squares were obtained.

Refer to Exhibit 16-1.The multiple coefficient of determination is

A)0.27
B)0.73
C)0.50
D)0.33

Question 29

Exhibit 16-2
In a regression model involving 30 observations,the following estimated regression equation was obtained. For this model,SSR = 1,740 and SST = 2,000.
Refer to Exhibit 16-2.The degrees of freedom associated with SST are

A)24
B)6
C)19
D)None of these alternatives is correct.

Question 30

Exhibit 16-1
In a regression analysis involving 25 observations,the following estimated regression equation was developed. Also,the following standard errors and the sum of squares were obtained.

Refer to Exhibit 16-1.The coefficient of X₃

A)is significant
B)is not significant
C)can not be tested,because not enough information is provided
D)None of these alternatives is correct.

Question 31

Exhibit 16-2
In a regression model involving 30 observations,the following estimated regression equation was obtained. For this model,SSR = 1,740 and SST = 2,000.
Refer to Exhibit 16-2.The value of SSE is

A)3,740
B)170
C)260
D)2000

Question 32

Exhibit 16-1
In a regression analysis involving 25 observations,the following estimated regression equation was developed. Also,the following standard errors and the sum of squares were obtained.

Refer to Exhibit 16-1.The test statistic for testing the significance of the model is

A)0.730
B)18.926
C)3.703
D)1.369

Question 33

Exhibit 16-2
In a regression model involving 30 observations,the following estimated regression equation was obtained. For this model,SSR = 1,740 and SST = 2,000.
Refer to Exhibit 16-2.The value of MSR is

A)10.40
B)348
C)10.83
D)52

Question 34

Exhibit 16-3
Below you are given a partial computer output based on a sample of 25 observations.

Refer to Exhibit 16-3.The estimated regression equation is

A)
B)
C)
D)

Question 35

Exhibit 16-4
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. Also provided are SSR = 60 and SST = 180.
Refer to Exhibit 16-4.From the above function,it can be said that the life expectancy of rats that were given agent X₂ is

A)1.7 months more than those who did not take agent X₂
B)1.7 months less than those who did not take agent X₂
C)0.8 months less than those who did not take agent X₂
D)0.8 months more than those who did not take agent X₂

Question 36

Exhibit 16-2
In a regression model involving 30 observations,the following estimated regression equation was obtained. For this model,SSR = 1,740 and SST = 2,000.
Refer to Exhibit 16-2.The degrees of freedom associated with SSR are

A)24
B)6
C)19
D)5

Question 37

Exhibit 16-1
In a regression analysis involving 25 observations,the following estimated regression equation was developed. Also,the following standard errors and the sum of squares were obtained.

Refer to Exhibit 16-1.The p-value for testing the significance of the regression model is

A)less than 0.01
B)between 0.01 and 0.025
C)between 0.025 and 0.05
D)between 0.05 and 0.1

Question 38

Exhibit 16-2
In a regression model involving 30 observations,the following estimated regression equation was obtained. For this model,SSR = 1,740 and SST = 2,000.
Refer to Exhibit 16-2.The value of MSE is

A)348
B)10.40
C)10.83
D)32.13

Question 39

Exhibit 16-1
In a regression analysis involving 25 observations,the following estimated regression equation was developed. Also,the following standard errors and the sum of squares were obtained.


-Refer to Exhibit 16-1.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 $\alpha$ = 0.05 is

A)2.76
B)2.78
C)3.10
D)3.07

Question 40

Exhibit 16-2
In a regression model involving 30 observations,the following estimated regression equation was obtained. For this model,SSR = 1,740 and SST = 2,000.
Refer to Exhibit 16-2.The p-value for testing the significance of the regression model is

A)less than 0.01
B)between 0.01 and 0.025
C)between 0.025 and 0.05
D)between 0.05 and 0.1

Question 41

Exhibit 16-4
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. Also provided are SSR = 60 and SST = 180.
Refer to Exhibit 16-4.The model

A)is significant
B)is not significant
C)Not enough information is provided to answer this question.
D)None of these alternatives is correct.

Question 42

Consider the following data for two variables x and y.

a.An estimated regression equation of the formwas developed for the above data and the results are shown below.Comment on the adequacy of this equation for predicting y.Let $\alpha$ = .05.
b.A regression equation of the formwas developed for the above data and results are shown below.Comment on the adequacy of this equation for predicting y.Let
$\alpha$ = .05.
c.Predict the value of y when x = 5.

Question 43

We want to test whether or not the addition of 3 variables to a model will be statistically significant.You are given the following information based on a sample of 25 observations.

The equation was also estimated including the 3 variables.The results are

a.State the null and alternative hypotheses.
b.Test the null hypothesis at the 5% level of significance.

Question 44

Exhibit 16-4
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. Also provided are SSR = 60 and SST = 180.
Refer to Exhibit 16-4.The life expectancy of a rat that was given 2 units of agent X₂ daily,but was not given any protein is

A)32.6
B)36
C)38
D)34.3

Question 45

Exhibit 16-4
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. Also provided are SSR = 60 and SST = 180.
Refer to Exhibit 16-4.The degrees of freedom associated with SSR are

A)2
B)33
C)32
D)30

Question 46

We are interested in determining what type of model best describes the relationship between two variables x and y.
a.For a given data set,an estimated regression equation relating x and y of the formwas developed,using Excel.The results are shown below.Comment on the adequacy of this equation for predicting y.Let $\alpha$ = .05.

b.An estimated regression equation for the same data set (as in part a)of the formwas developed.The Excel output is shown below.Comment on the adequacy of this equation for predicting y.Let $\alpha$ = .05.
c.Use the results of Part b and predict y when x = 4.

Question 47

The following estimated regression equation has been developed for the relationship between y,the dependent variable,and x,the independent variable.
The sample size for this regression model was 23,and SSR = 600 and SSE = 400.
a.Compute the coefficient of determination.
b.Using $\alpha$ = .05,test for a significant relationship.

Question 48

Consider the following data.

a.Draw a scatter diagram.Does the relationship between X and Y appear to be linear?
b.Assume the relationship between X and Y can best be given by
Estimate the parameters of this curvilinear function.

Question 49

In a regression analysis involving 21 observations and 4 independent variables,the following information was obtained.
= 0.80
S = 5.0
Based on the above information,fill in all the blanks in the following ANOVA.
Hint:
=
,but also
= 1-
.

Question 50

Exhibit 16-4
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. Also provided are SSR = 60 and SST = 180.
Refer to Exhibit 16-4.The multiple coefficient of determination is

A)0.2
B)0.5
C)0.333
D)5

Question 51

Multiple regression analysis was used to study the relationship between a dependent variable,Y,and four independent variables;X₁,X₂,X₃ and,X₄.The following is a partial result of the regression analysis involving 31 observations.

a.Compute the coefficient of determination.
b.Perform a t test and determine whether or not $\beta$ ₁ is significantly different from zero ( $\alpha$ = 0.05).
c.Perform a t test and determine whether or not $\beta$ ₄ is significantly different from zero ( $\alpha$ = 0.05).
d.At $\alpha$ = 0.05,perform an F test and determine whether or not the regression model is significant.

Question 52

Exhibit 16-4
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. Also provided are SSR = 60 and SST = 180.
Refer to Exhibit 16-4.If we want to test for the significance of the model,the critical value of F at 95% confidence is

A)4.17
B)3.32
C)2.92
D)1.96

Question 53

Exhibit 16-4
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. Also provided are SSR = 60 and SST = 180.
Refer to Exhibit 16-4.The test statistic for testing the significance of the model is

A)0.50
B)5.00
C)0.25
D)0.33

Question 54

Multiple regression analysis was used to study the relationship between a dependent variable,Y,and three independent variables X₁,X₂ and,X₃.The following is a partial result of the regression analysis involving 20 observations.

a.Compute the coefficient of determination.
b.Perform a t test and determine whether or not $\beta$ ₁is significantly different from zero ( $\alpha$ = 0.05).
c.Perform a t test and determine whether or not $\beta$ ₂ is significantly different from zero ( $\alpha$ = 0.05).
d.Perform a t test and determine whether or not $\beta$ ₃ is significantly different from zero ( $\alpha$ = 0.05).
e.At \9\alpha\) = 0.05,perform an F test and determine whether or not the regression model is significant.

Question 55

Exhibit 16-4
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. Also provided are SSR = 60 and SST = 180.
Refer to Exhibit 16-4.The degrees of freedom associated with SSE are

A)3
B)33
C)32
D)30

Question 56

In a regression analysis involving 20 observations and five independent variables,the following information was obtained.

Fill in all the blanks in the above ANOVA table.

Question 57

Monthly total production costs and the number of units produced at a local company over a period of 10 months are shown below.

a.Draw a scatter diagram for the above data.
b.Assume that a model in the form of
best describes the relationship between X and Y.Estimate the parameters of this curvilinear regression equation.

Question 58

Exhibit 16-4
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. Also provided are SSR = 60 and SST = 180.
Refer to Exhibit 16-4.The p-value for testing the significance of the regression model is

A)less than 0.01
B)between 0.01 and 0.025
C)between 0.025 and 0.05
D)between 0.05 and 0.10

Question 59

A data set consisting of 7 observations of a dependent variable y and two independent variables x₁ and x₂ was used in a regression analysis.Using (x₁)as the only independent variable,the following function is provided.
= 0.408 + 1.338x₁
The SSE for the above model is 39.535.
Using both x₁ and x₂ as independent variables yields the following function.
= 0.805 + 0.498x₁ - 0.477x₂
The SSE for this latter function is 1.015.
Use an F test and determine if x₂ contributes significantly to the model.Let $\alpha$ = 0.05.

Question 60

A researcher is trying to decide whether or not to add another variable to his model.He has estimated the following model from a sample of 28 observations.

He has also estimated the model with an additional variable X₃.The results are

What advice would you give this researcher? Use a .05 level of significance.

Question 61

A regression analysis was applied in order to determine the relationship between a dependent variable and 8 independent variables.The following information was obtained from the regression analysis.

a.Fill in the blanks in the following ANOVA table.
b.Is the model significant? Let $\alpha$ = 0.05.

Question 62

A regression analysis was applied in order to determine the relationship between a dependent variable and 4 independent variables.The following information was obtained from the regression analysis.

a.Fill in the blanks in the following ANOVA table.
b.At $\alpha$ = 0.05 level of significance,test to determine if the model is significant.

Question 63

A regression analysis relating a company's sales,their advertising expenditure,price,and time resulted in the following.

a.At 95% confidence,determine whether or not the regression model is significant.Fully explain how you arrived at your conclusion (give numerical reasoning)and what your answer indicates.
b.At 95% confidence determine which variables are significant and which are not.Explain how you arrived at your conclusion (Give numerical reasoning).
c.Fully explain the meaning of R-square,which is given in this model.Be very specific and give numerical explanation.

Question 64

A regression analysis was applied in order to determine the relationship between a dependent variable and 4 independent variables.The following information was obtained from the regression analysis.

a.Fill in the blanks in the following ANOVA table.
b.At $\alpha$ = 0.05 level of significance,test to determine if the model is significant.

Question 65

A regression model relating a dependent variable,Y,with one independent variable,X₁,resulted in an SSE of 400.Another regression model with the same dependent variable,Y,and two independent variables,X₁ and X₂,resulted in an SSE of 320.At $\alpha$ = .05,determine if X₂ contributed significantly to the model.The sample size for both models was 20.

Question 66

A regression model relating the yearly income (Y),age (X₁),and the gender of the faculty member of a university (X₂ = 1 if female and 0 if male)resulted in the following information.

a.Is gender a significant variable?
b.Determine the multiple coefficient of determination.

Question 67

Forty-eight observations of a dependent variable (Y)and five independent variables resulted in an SSE of 438.When two additional independent variables were added to the model,the SSE was reduced to 375.At 95% confidence,determine whether or not the two additional independent variables contribute significantly to the model.

Question 68

In a regression analysis involving 18 observations and four independent variables,the following information was obtained.

Based on the above information,fill in all the blanks in the following ANOVA table.

Question 69

Ziba,Inc.has provided the following information regarding their sales for January through December of 2009.(Part of the data file is shown below. )

The results of the regression analysis relating these variables are shown below.

a.The company is planning to increase their advertising by 5% per month for the months of January and February of 2010.What would be the advertising for January and February of 2010? Give your answers in dollars.
b.Use the regression model that is provided above and forecast sales for January and February of 2010,assuming the company increases their advertising by 5% per month for the months of January and February of 2010.Show your computations and write your answers in dollars below.

Question 70

A regression model relating units sold (Y),price (X₁),and whether or not promotion was used (X₂ = 1 if promotion was used and 0 if it was not)resulted in the following model.
and the following information is provided.

a.Is price a significant variable?
b.Is promotion significant?

Question 71

A regression model with one independent variable,X₁,resulted in an SSE of 50.When a second independent variable,X₂,was added to the model,the SSE was reduced to 40.At $\alpha$ = 0.05,determine if X₂ contributes significantly to the model.The sample size for both models was 30.

Question 72

A regression analysis (involving 45 observations)relating a dependent variable (Y)and two independent variables resulted in the following information.
The SSE for the above model is 49.
When two other independent variables were added to the model,the following information was provided.
This latter model's SSE is 40.
At 95% confidence test to determine if the two added independent variables contribute significantly to the model.

Question 73

When a regression model was developed relating sales (Y)of a company to its product's price (X₁),the SSE was determined to be 495.A second regression model relating sales (Y)to product's price (X₁)and competitor's product price (X₂)resulted in an SSE of 396.At $\alpha$ = 0.05,determine if the competitor's product's price contributed significantly to the model.The sample size for both models was 33.

Question 74

The following are partial results of a regression analysis involving sales (Y in millions of dollars),advertising expenditures (X₁ in thousands of dollars),and number of salespeople (X₂)for a corporation.The regression was performed on a sample of 10 observations.

a.At $\alpha$ = 0.05,test for the significance of the coefficient of advertising.
b.If the company uses $20,000 in advertisement and has 300 salespersons,what are the expected sales? (Give your answer in dollars. )

Question 75

Thirty-four observations of a dependent variable (Y)and two independent variables resulted in an SSE of 300.When a third independent variable was added to the model,the SSE was reduced to 250.At 95% confidence,determine whether or not the third independent variable contributes significantly to the model.