Question 1

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

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Question 2

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.

Accepted Answer

F = 6.75;p-value is between .0

Question 3

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

Accepted Answer

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

Question 4

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

Accepted Answer

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

Question 5

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 (XS1U1B11S1U1B0),and whether or not agent XS1U1B12S1U1B0 (a proposed life extending agent)was added to the rats diet (XS1U1B12S1U1B0 = 0 if agent XS1U1B12S1U1B0 was not added,and XS1U1B12S1U1B0 = 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

Accepted Answer

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

Question 6

In multiple regression analysis,the general linear model

Accepted Answer

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. 
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 7

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

Accepted Answer

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

Question 8

Serial correlation is

Accepted Answer

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. 
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 9

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.

Accepted Answer

a.Source of
Variation
Degrees
of Freedom

Question 10

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

Accepted Answer

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 
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 11

The joint effect of two variables acting together is called

Accepted Answer

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

Question 12

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.

Accepted Answer

F = 2.308;p-value is

Question 13

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.

Accepted Answer

a.H₀: @#LAT-DLM&₃= @#LAT-DLM&₂

Question 14

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

Accepted Answer

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

Question 15

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 (XS1U1B11S1U1B0),and whether or not agent XS1U1B12S1U1B0 (a proposed life extending agent)was added to the rats diet (XS1U1B12S1U1B0 = 0 if agent XS1U1B12S1U1B0 was not added,and XS1U1B12S1U1B0 = 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

Accepted Answer

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

Question 16

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

Accepted Answer

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

Question 17

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.

Accepted Answer

a.= 2.7857 + 0.4643 x,r² = 0.

Question 18

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.

Accepted Answer

F = 7.5;p-value is between .01

Question 19

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.

Accepted Answer

a.r<sup>2</sup> = 0.

Question 20

The range of the Durbin-Watson statistic is between

Accepted Answer

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

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 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.

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

In multiple regression analysis,the general linear model

Serial correlation is

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

The joint effect of two variables acting together is called

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

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

The range of the Durbin-Watson statistic is between

Data and Statistics

Descriptive Statistics: Tabular and Graphical Presentations

Descriptive Statistics: Numerical Measures

Introduction to Probability

Discrete Probability Distributions

Continuous Probability Distributions

Sampling and Sampling Distributions

Interval Estimation

Hypothesis Tests

Statistical Inference About Means and Proportions With Two Populations

Inferences About Population Variances

Tests of Goodness of Fit and Independence

Analysis of Variance and Experimental Design

Simple Linear Regression

Multiple Regression

Index Numbers

Forecasting

Nonparametric Methods

Statistical Methods for Quality Control

Decision Analysis

Sample Survey

Filters

Exam 16: Regression Analysis: Model Building

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 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 α\alphaα = 0.05,determine if X2 contributes significantly to the model.The sample size for both models was 30.

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 β\betaβ 2 is significant.The test statistic equals

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

In multiple regression analysis,the general linear model

Serial correlation is

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

The joint effect of two variables acting together is called

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

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

The range of the Durbin-Watson statistic is between

Data and Statistics

Descriptive Statistics: Tabular and Graphical Presentations

Descriptive Statistics: Numerical Measures

Introduction to Probability

Discrete Probability Distributions

Continuous Probability Distributions

Sampling and Sampling Distributions

Interval Estimation

Hypothesis Tests

Statistical Inference About Means and Proportions With Two Populations

Inferences About Population Variances

Tests of Goodness of Fit and Independence

Analysis of Variance and Experimental Design

Simple Linear Regression

Multiple Regression

Index Numbers

Forecasting

Nonparametric Methods

Statistical Methods for Quality Control

Decision Analysis

Sample Survey

Filters

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.