Deck 16: Regression Analysis: Model Building

Question 1

The following regression model y = $\beta$ ₀ + $\beta$ ₁x₁ + $\beta$ ₂x² + $\varepsilon$
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.

Answer 1

second-order model with one predictor variable

Question 2

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

A)a t test
B)the Durbin-Watson test
C)an F test
D)a chi-square test

Answer 2

B

Question 3

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

Answer 3

D

Question 4

In multiple regression analysis, the general linear model

A)cannot 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. = 10 - 18x₁ + 3x₂ + 14x₃
Also, the following standard errors and the sum of squares were obtained.S_b1 = 3 S_b2 = 6 S_b3 = 7
SST = 4,800 SSE = 1,296
Refer to Exhibit 16-1. The coefficient of x₁

A)is significant
B)is not significant
C)cannot 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 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 8

The joint effect of two variables acting together is called

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

Question 9

The following model y = $\beta$ ₀ + $\beta$ ₁x₁ + $\varepsilon$
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 10

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

Question 11

The parameters of nonlinear models have exponents

A)larger than zero
B)other than 1
C)only equal to 2
D)larger than 3

Question 12

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

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

Question 13

Exhibit 16-1
In a regression analysis involving 25 observations, the following estimated regression equation was developed. = 10 - 18x₁ + 3x₂ + 14x₃
Also, the following standard errors and the sum of squares were obtained.S_b1 = 3 S_b2 = 6 S_b3 = 7
SST = 4,800 SSE = 1,296

-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 14

Exhibit 16-1
In a regression analysis involving 25 observations, the following estimated regression equation was developed. = 10 - 18x₁ + 3x₂ + 14x₃
Also, the following standard errors and the sum of squares were obtained.S_b1 = 3 S_b2 = 6 S_b3 = 7
SST = 4,800 SSE = 1,296
Refer to Exhibit 16-1. The multiple coefficient of determination is

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

Question 15

Exhibit 16-1
In a regression analysis involving 25 observations, the following estimated regression equation was developed. = 10 - 18x₁ + 3x₂ + 14x₃
Also, the following standard errors and the sum of squares were obtained.S_b1 = 3 S_b2 = 6 S_b3 = 7
SST = 4,800 SSE = 1,296
Refer to Exhibit 16-1. The coefficient of x₂

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

Question 16

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 17

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

A) $\beta$ ₀, $\beta$ ₁, . . . $\beta$ _p, all have exponents of 0
B) $\beta$ ₀, $\beta$ ₁, . . . $\beta$ _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 18

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 19

Exhibit 16-1
In a regression analysis involving 25 observations, the following estimated regression equation was developed. = 10 - 18x₁ + 3x₂ + 14x₃
Also, the following standard errors and the sum of squares were obtained.S_b1 = 3 S_b2 = 6 S_b3 = 7
SST = 4,800 SSE = 1,296
Refer to Exhibit 16-1. 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 alternatives is correct.

Question 20

Exhibit 16-1
In a regression analysis involving 25 observations, the following estimated regression equation was developed. = 10 - 18x₁ + 3x₂ + 14x₃
Also, the following standard errors and the sum of squares were obtained.S_b1 = 3 S_b2 = 6 S_b3 = 7
SST = 4,800 SSE = 1,296

-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 21

Exhibit 16-2
In a regression model involving 30 observations, the following estimated regression equation was obtained. = 170 + 34x₁ - 3x₂ + 8x₃ + 58x₄ + 3x₅
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 22

Exhibit 16-1
In a regression analysis involving 25 observations, the following estimated regression equation was developed. = 10 - 18x₁ + 3x₂ + 14x₃
Also, the following standard errors and the sum of squares were obtained.S_b1 = 3 S_b2 = 6 S_b3 = 7
SST = 4,800 SSE = 1,296
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 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. = 36 + 0.8x₁ - 1.7x₂
Also provided are SSR = 60 and SST = 180.
Refer to Exhibit 16-4. The degrees of freedom associated with SSR are

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

Question 24

Exhibit 16-2
In a regression model involving 30 observations, the following estimated regression equation was obtained. = 170 + 34x₁ - 3x₂ + 8x₃ + 58x₄ + 3x₅
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 25

Exhibit 16-2
In a regression model involving 30 observations, the following estimated regression equation was obtained. = 170 + 34x₁ - 3x₂ + 8x₃ + 58x₄ + 3x₅
For this model, SSR = 1,740 and SST = 2,000.
Refer to Exhibit 16-2. The computed F value for testing the significance of the above model is

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

Question 26

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. = 36 + 0.8x₁ - 1.7x₂
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 27

Exhibit 16-2
In a regression model involving 30 observations, the following estimated regression equation was obtained. = 170 + 34x₁ - 3x₂ + 8x₃ + 58x₄ + 3x₅
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 28

Exhibit 16-2
In a regression model involving 30 observations, the following estimated regression equation was obtained. = 170 + 34x₁ - 3x₂ + 8x₃ + 58x₄ + 3x₅
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 29

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

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

A)y = $\beta$ ₀ + $\beta$ ₁x₁ + $\beta$ ₂x₂ + $\beta$ ₃x₃ + $\varepsilon$
B)E(y) = $\beta$ ₀ + $\beta$ ₁x₁ + $\beta$ ₂x₂ + $\beta$ ₃x₃
C)= 29 + 5x₁ + 6x₂ + 4x₃
D)= 145 + 20x₁ - 18x₂ + 4x₃
E)None of the above answers are correct.

Question 30

Exhibit 16-2
In a regression model involving 30 observations, the following estimated regression equation was obtained. = 170 + 34x₁ - 3x₂ + 8x₃ + 58x₄ + 3x₅
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 31

Exhibit 16-2
In a regression model involving 30 observations, the following estimated regression equation was obtained. = 170 + 34x₁ - 3x₂ + 8x₃ + 58x₄ + 3x₅
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 32

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. = 36 + 0.8x₁ - 1.7x₂
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 33

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. = 36 + 0.8x₁ - 1.7x₂
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 34

Exhibit 16-1
In a regression analysis involving 25 observations, the following estimated regression equation was developed. = 10 - 18x₁ + 3x₂ + 14x₃
Also, the following standard errors and the sum of squares were obtained.S_b1 = 3 S_b2 = 6 S_b3 = 7
SST = 4,800 SSE = 1,296
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 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. = 36 + 0.8x₁ - 1.7x₂
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 36

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. = 36 + 0.8x₁ - 1.7x₂
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 37

Exhibit 16-3
Below you are given a partial Excel 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 38

Exhibit 16-2
In a regression model involving 30 observations, the following estimated regression equation was obtained. = 170 + 34x₁ - 3x₂ + 8x₃ + 58x₄ + 3x₅
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 39

Exhibit 16-1
In a regression analysis involving 25 observations, the following estimated regression equation was developed. = 10 - 18x₁ + 3x₂ + 14x₃
Also, the following standard errors and the sum of squares were obtained.S_b1 = 3 S_b2 = 6 S_b3 = 7
SST = 4,800 SSE = 1,296
Refer to Exhibit 16-1. The model

A)is significant
B)is not significant
C)may or may not be significant
D)None of these alternatives is correct.

Question 40

Exhibit 16-3
Below you are given a partial Excel 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 41

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

A)stepwise regression
B)forward selection
C)backward elimination
D)best-subsets

Question 42

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. = 36 + 0.8x₁ - 1.7x₂
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 43

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. = 36 + 0.8x₁ - 1.7x₂
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)8.62
B)3.35
C)2.92
D)2.96

Question 44

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 45

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

A)It is a one-variable-at-a-time procedure.
B)It begins with the regression model found using the forward selection procedure.
C)It does not permit an independent variable to be reentered once it has been removed.
D)It does not guarantee that the best regression model will be found.

Question 46

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

A)none
B)one
C)two
D)all of them

Question 47

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. = 62.42 - 1.836x₁ + 25.62x₂
SSE = 725 SSR = 526
The equation was also estimated including the 3 variables. The results are = 59.23 - 1.762x₁ + 25.638x₂ + 16.237x₃ + 15.297x₄ - 18.723x₅
SSE = 520 SSR = 731
a.State the null and alternative hypotheses.
b.Test the null hypothesis at the 5% level of significance.

Question 48

The variable selection procedure that identifies the best regression equation, given a specified number of independent variables, is

A)stepwise regression
B)forward selection
C)backward elimination
D)best-subsets regression

Question 49

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 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. = 36 + 0.8x₁ - 1.7x₂
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 51

When autocorrelation is present, one of the assumptions of the regression model is violated and that assumption is:

A)the expected value of the error term $\varepsilon$ is zero
B)the variance of the error term $\varepsilon$ is the same for all values of x
C)the values of the error term $\varepsilon$ are independent
D)the values of the error term $\varepsilon$ are normally distributed for all values of x

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. = 36 + 0.8x₁ - 1.7x₂
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 53

The null hypothesis in the Durbin-Watson test is always that there is

A)positive autocorrelation
B)negative autocorrelation
C)either positive or negative autocorrelation
D)no autocorrelation

Question 54

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

Question 55

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 56

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. = 23.62 + 18.86x₁ + 24.72x₂
SSE = 1,425 SSR = 1,326
He has also estimated the model with an additional variable x₃. The results are = 25.32 + 15.29x₁ + 7.63x₂ + 12.72x₃
SSE = 1,300 SSR = 1,451
What advice would you give this researcher? Use a .05 level of significance.

Question 57

Part of an Excel output relating y (dependent variable) and 4 independent variables, x₁ through x₄, is shown below.
a.Fill in all the blanks marked with "?"
b.At a 5% significance level, which independent variables are significant and which ones are not? Fully explain how you arrived at your answers.

Question 58

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
y = $\beta$ ₀ + $\beta$ ₁+ $\varepsilon$
best describes the relationship between x and y. Estimate the parameters of this curvilinear regression equation.

Question 59

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
y = $\beta$ ₀ + $\beta$ ₁+ $\varepsilon$
Estimate the parameters of this curvilinear function.

Question 60

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 $\beta$ ₁ is 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 $\alpha$ = 0.05, perform an F test and determine whether or not the regression model is significant.

Question 61

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. = 5,000 + 1.2x₁ + 0.9x₂
n = 20 SSE = 500 SSR = 1,500
S_b1 = 0.2 S_b2 = 0.1
a.Is gender a significant variable?
b.Determine the multiple coefficient of determination.

Question 62

Consider the following data. Use Excel's Regression Tool to estimate a general linear model of the form

Question 63

Monthly total production costs and the number of units produced at a local company over a period of 10 months are shown below. Use Excel's Regression Tool to estimate a second-order model of the form

Question 64

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 65

Consider the following data. Use Excel's Regression Tool to estimate a general linear model that uses a reciprocal transformation on the dependent variable.

Question 66

A sample of 6 recent college graduates shows their current annual income (in $1000), years of education, and current age (in years). The data follow: Use Excel's Regression Tool to estimate a general linear model of the form that predicts annual income.

Question 67

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 a 5% level of significance, determine if the third independent variable contributes significantly to the model.

Question 68

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 69

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.R Square = 0.60
SSR = 4,800
Total number of observations n = 35
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 70

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 a 5% level of significance, determine if the two additional independent variables contribute significantly to the model.

Question 71

In a regression analysis involving 18 observations and four independent variables, the following information was obtained.Multiple R = 0.6000
R Square = 0.3600
Standard Error = 4.8000
Based on the above information, fill in all the blanks in the following ANOVA table.

Question 72

A regression analysis (involving 45 observations) relating a dependent variable (y) and two independent variables resulted in the following information. = 0.408 + 1.3387x₁ + 2x₂
The SSE for the above model is 49.When two other independent variables were added to the model, the following information was provided. = 1.2 + 3.0x₁ + 12x₂ + 4.0x₃ + 8x₄
This latter model's SSE is 40.At a 5% significance level, test to determine if the two added independent variables contribute significantly to the model.

Question 73

Consider the following data. Use Excel's Regression Tool to estimate a general linear model of the form

Question 74

A regression analysis was applied in order to determine the relationship between a dependent variable and 14 independent variables. The following information was obtained from the regression analysis.R Square = 0.70
SSR = 7,000
Total number of observations n = 45
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 75

Consider the following data. Use Excel's Regression Tool to estimate a second-order model of the form

Question 76

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.R Square = 0.80
SSR = 4,280
Total number of observations n = 56
a.Fill in the blanks in the following ANOVA table.
b.Is the model significant? Let $\alpha$ = 0.05.

Question 77

Consider the following data. Use Excel's Regression Tool to estimate a general linear model of the form

Question 78

Consider the following data. Use Excel's Regression Tool to estimate a general linear model that uses a reciprocal transformation on the dependent variable.

Question 79

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. = 120 - 0.03x₁ + 0.7x₂
and the following information is provided.n = 15 S_b1 = .01 S_b2 = 0.1
a.Is price a significant variable?
b.Is promotion significant?

Question 80

A soft drink manufacturer has developed a regression model relating sales (y in $10,000) with four independent variables. The four independent variables are price per unit (x₁, in dollars), competitor's price (x₂, in dollars), advertising (x₃, in $1000) and type of container used (x₄; 1 = Cans and 0 = Bottles). Part of the regression results are shown below. (Assume n = 25)
a.If the manufacturer uses can containers and if his price is $1.25, his advertising expenditure is $200,000, and his competitor's price is $1.50, what is your estimate of his sales? (Give your answer in dollars.)
b.Test to see if there is a significant relationship between sales and unit price. Let $\alpha$ = 0.05.
c.Test to see if there is a significant relationship between sales and advertising. Let $\alpha$ = 0.05.
d.Is the type of container a significant variable? Let $\alpha$ = 0.05 = 0.05.
e.Test to see if there is a significant relationship between sales and competitor's price. Let $\alpha$ = 0.05.