In a multiple regression model,the following statistics are given: SSE = 100,R2 = 0.995,k = 5,n = 15.The multiple coefficient of determination adjusted for degrees of freedom is:

A) 0.955. B) 0.992. C) 0.900. D) 0.855. A) 0.955. B) 0.992. C) 0.900. D) 0.855.

What is the relationship between: (A)the results of the hypothesis test examining whether b2 differs significantly from zero at the 0.05 level and (B)the 95% confidence interval for $\beta _ { 2 }$ .

Both of these tests will reach the same

For the multiple regression model $\hat{ Y }$ = 3 - 4x1 + 5x2 + 2x3,a unit increase in x1,holding x2 and x3 constant,results in:

A) an increase of 4 units in the value of y. B) a decrease of 4 units in the value of y. C) a decrease of 4 units,on average,in the value of y. D) an increase of 6 units in the value of y. A) an increase of 4 units in the value of y. B) a decrease of 4 units in the value of y. C) a decrease of 4 units,on average,in the value of y. D) an increase of 6 units in the value of y.

In reference to the equation: $\hat{ Y }$ = -0.25 + 0.08x1 + 0.10x2,the value 0.08 is the:

A) predicted value of y. B) estimated change in y when x1 increases by one unit. C) estimated change in y when x2 increases by one unit. D) predicted value of y when x1 = 0 and x2 = 0. E) predicted value of y when x1= 2 and x2 = 1. A) predicted value of y. B) estimated change in y when x1 increases by one unit. C) estimated change in y when x2 increases by one unit. D) predicted value of y when x1 = 0 and x2 = 0. E) predicted value of y when x1= 2 and x2 = 1.

In reference to the equation: $\hat { Y }$ = -0.25 + 0.08x1 + 0.10x2,the value -0.25 is the:

A) predicted value of y. B) partial regression coefficient for x1. C) partial regression coefficient for x2. D) predicted value of y when x1 = 0 and x2 = 0. E) predicted value of when x1 = 2 and x2 = 1. A) predicted value of y. B) partial regression coefficient for x1. C) partial regression coefficient for x2. D) predicted value of y when x1 = 0 and x2 = 0. E) predicted value of when x1 = 2 and x2 = 1.

A multiple regression model was developed to predict the grade point average (GPA)for MBA students based on two entrance exam scores,verbal (VGMAT)and math (MGMAT).The following table shows the actual GPA and predicted GPA for 7 students. \[\begin{array} { | c | c | c | } \hline \text { Student } & \text { Actural CPA } & \text { Predicted CPA } \\ \hline 1 & 3.5 & 3.7 \\ \hline 2 & 3.1 & 3.6 \\ \hline 3 & 3.2 & 2.8 \\ \hline 4 & 4.0 & 3.5 \\ \hline 5 & 3.6 & 3.6 \\ \hline 6 & 3.2 & 3.7 \\ \hline 7 & 3.7 & 3.6 \\ \hline \end{array}\] Calculate the multiple standard error of estimate.

The answer of A multiple regression model was developed to...

Exam 16: Multiple Regression and Correlation

In a multiple regression model,the following statistics are given: SSE = 100,R² = 0.995,k = 5,n = 15.The multiple coefficient of determination adjusted for degrees of freedom is:

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Question 41

The adjusted multiple coefficient of determination is adjusted for the:

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Question 42

Motor Vehicle In order to predict motor vehicle purchases for the U.S.,the coefficients of a multiple regression equation were estimated using 25 years of data.The variables were: y = motor vehicle purchases (billions of dollars) x₁ = disposable personal income (billions of dollars) x₂ = U.S.population (millions of persons) x₃ = automobile installment credit (billions of dollars) Part of the results using MINITAB was: The regression equation is $Y = - 61.3 - 0.0022 \times 1 + 0.368 \times 2 + 0.725 \times 3$ Predictor Coef Stdev t-ratio Constant -61.28 36.96 -1.66 X1 -0.00221 0.01504 -0.15 X2 0.3679 0.2001 1.84 X3 0.7254 0.2115 3.43 Analysis of Variance SOURCE DF SS Regression 3 32624 Error 21 591 Total 24 33215 -Use the values in the analysis of variance table to compute R² using the values for SST and SSE or SSR.

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Question 43

What is the relationship between: (A)the results of the hypothesis test examining whether b₂ differs significantly from zero at the 0.05 level and (B)the 95% confidence interval for $\beta _ { 2 }$ .

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Question 44

A multiple regression equation includes 3 independent variables,and the coefficient of multiple determination is 0.64.The percentage of the variation in y that is explained by the regression equation is:

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Question 45

For the multiple regression model $\hat{ Y }$ = 3 - 4x₁ + 5x₂ + 2x₃,a unit increase in x₁,holding x₂ and x₃ constant,results in:

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Question 46

In simple linear regression,the regression equation is a straight line.In multiple regression,what geometric form is taken by the regression equation when there are two independent variables? When there are three or more independent variables?

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Question 47

In reference to the equation: $\hat{ Y }$ = -0.25 + 0.08x₁ + 0.10x₂,the value 0.08 is the:

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Question 48

A health science-kinesiology program to lose weight collected data from ten students.Sex was coded as 1 = female and 0 = male.The regression equation obtained was given by: Pounds lost = 15.8 + 0.65 time + 6.00 sex.What is the estimated weight loss of a male who stayed in the program for 5 time periods?

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Question 49

A multiple regression analysis includes 25 data points and 4 independent variables results in SST = 200 and SSR = 150.The multiple standard error of estimate will be:

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Question 50

In a multiple regression problem,the regression equation is given by $\hat { Y }$ = 58.0 - 5.66x₁ + 0.61 x₂.Compute the point estimate for y when x₁ = 3 and x₂ = 4.

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Question 51

What is the multiple standard error estimate?

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Question 52

Nutritionist A nutritionist is analyzing the cost of an 8 oz.serving of pasta.The nutritionist anticipates that cost is related to: x₁ = Grams of protein/8 oz. x₂ = Grams of carbohydrates/8 oz. x₃ = Grams of fat/8 oz. Using MINITAB,the nutritionist obtained the following results: The regression equation is $Y = 1.39 + 0.0178 \times 1 - 0.0258 \times 2 - 0.00050 \times 3$ Predictor Coef Stdev t-ratio Constant 1.3928 0.1096 12.71 X1 0.017806 0.006600 2.70 X2 -0.025825 0.001613 -16.01 X3 -0.000501 0.002779 -0.18 $s=0.04805 \quad \mathrm{R}-\mathrm{sq}=97.5 \% \quad \mathrm{R}-\mathrm{sq}(\mathrm{adj})=96.6 \%$ Analysis of Variance SOURCE DF SS MS Regression 3 0.72562 0.24187 Error 8 0.01847 0.00231 Total 11 0.74409 -From these regression results,compute a 95% confidence interval for $\beta$ ₁, $\beta$ ₂,and $\beta$ ₃.

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Question 53

In reference to the equation: $\hat { Y }$ = -0.25 + 0.08x₁ + 0.10x₂,the value -0.25 is the:

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Question 54

States Concern over the number of car thefts grew into a project to determine the relationship between car thefts by state and these variables: x₁ = Police per 10,000 persons,by state x₂ = Expenditure by local government for police protection,in thousands,by state x₃ = New passenger car registrations,in thousands,by state. Data from 13 states were collected.The MINITAB regression results are: The regression equation is car-thf $= - 25.3 + 1.28$ police $+ 0.0188$ polexp $+ 0.0969$ registr Predictor Coef Stdev t-ratio p Constant -25.29 17.85 -1.42 0.190 police 1.2831 0.9275 1.38 0.200 polexp 0.018827 0.008460 2.23 0.053 registr 0.09686 0.03536 2.74 0.023 $s = ? ? \quad \mathrm { R } - s q = ? ? \% \quad \mathrm { R } - s q ( a d j ) = ? ? \%$ Analysis of Variance SOURCE DF SS MS F p Regression 3 33007 11002 107.14 0.000 Error 9 924 103 Total 12 33932 Correlation between the variables: car-thf police polexp registr car-thf 1.000 police 0.466 1.000 polexp 0.970 0.390 1.000 registr 0.976 0.406 0.958 1.000 -Test the significance of the regression equation at the 0.01 level of significance. Test statistic = Critical Value = Conclusion:

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Question 55

In a regression model involving 25 observations,the following estimated regression model was obtained: $\hat { Y }$ = 60 + 2.8x₁ + 1.2x₂ - x₃.For this model,SST = 600 and SSE = 150.Calculate the value of the F statistic for testing the significance of this model. F = ____________________

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Question 56

In a regression model involving 40 observations, the following estimated regression model was obtained $\hat{y}$ = 10 + 3x1 + 5x2 + 6x3. For this model, SSR = 300 and SSE = 75. Then, the value of MSR is:

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Question 57

Salary Data was collected from 40 employees to develop a regression model to predict the employee's annual salary using their years with the company (Years),their starting salary (Starting),and their Gender (Male = 0,Female = 1).The results from Excel regression analysis are shown below: RegresionSlalinlics Multiple R 0.719714957 R Square 0.516551199 Adjusted R Square 0.476253780 Standard Errar 10515.63461 Dbservations 40 $\text { ANOVA }$ of SS MS F Significance F Regression 3 4334682510 1444894170 12.82165585 7.48476-06 Residual 36 4056901131 112691698.1 Total 39 8391583641 Coefficients Standard Error t Stat P -value Intercept 27946.57894 4832.438706 5.783121245 1.35464-06 Years 1665.251558 425.0829092 3.917474737 0.000383313 Starting 0.266374185 0.12610443 2.112330112 0.041661598 Gender -3285.541043 5617.145392 -0.584912943 0.56225464 -In testing the significance of the partial regression coefficient associated with the Gender variable at the 0.05 significance level,what is the appropriate conclusion?

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Question 58

Equation The regression equation, $\hat{ Y }$ = 4 + 1.5x₁ + 2.5x₂ has been fitted to 25 data points.The means of x₁ and x₂ are 30 and 46,respectively.The sum of the squared differences between observed and predicted values of y has been calculated as SSE = 175,and the sum of the squared differences between y values and mean of y is SST = 525. -Determine the multiple standard error of estimate.

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Question 59

A multiple regression model was developed to predict the grade point average (GPA)for MBA students based on two entrance exam scores,verbal (VGMAT)and math (MGMAT).The following table shows the actual GPA and predicted GPA for 7 students. Student Actural CPA Predicted CPA 1 3.5 3.7 2 3.1 3.6 3 3.2 2.8 4 4.0 3.5 5 3.6 3.6 6 3.2 3.7 7 3.7 3.6 Calculate the multiple standard error of estimate.

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Question 60

In a multiple regression model,the following statistics are given: SSE = 100,R² = 0.995,k = 5,n = 15.The multiple coefficient of determination adjusted for degrees of freedom is:

The adjusted multiple coefficient of determination is adjusted for the:

What is the relationship between: (A)the results of the hypothesis test examining whether b₂ differs significantly from zero at the 0.05 level and (B)the 95% confidence interval for $\beta _ { 2 }$ .

A multiple regression equation includes 3 independent variables,and the coefficient of multiple determination is 0.64.The percentage of the variation in y that is explained by the regression equation is:

For the multiple regression model $\hat{ Y }$ = 3 - 4x₁ + 5x₂ + 2x₃,a unit increase in x₁,holding x₂ and x₃ constant,results in:

In simple linear regression,the regression equation is a straight line.In multiple regression,what geometric form is taken by the regression equation when there are two independent variables? When there are three or more independent variables?

In reference to the equation: $\hat{ Y }$ = -0.25 + 0.08x₁ + 0.10x₂,the value 0.08 is the:

A multiple regression analysis includes 25 data points and 4 independent variables results in SST = 200 and SSR = 150.The multiple standard error of estimate will be:

In a multiple regression problem,the regression equation is given by $\hat { Y }$ = 58.0 - 5.66x₁ + 0.61 x₂.Compute the point estimate for y when x₁ = 3 and x₂ = 4.

What is the multiple standard error estimate?

In reference to the equation: $\hat { Y }$ = -0.25 + 0.08x₁ + 0.10x₂,the value -0.25 is the:

In a regression model involving 25 observations,the following estimated regression model was obtained: $\hat { Y }$ = 60 + 2.8x₁ + 1.2x₂ - x₃.For this model,SST = 600 and SSE = 150.Calculate the value of the F statistic for testing the significance of this model. F = ____________________

In a regression model involving 40 observations, the following estimated regression model was obtained $\hat{y}$ = 10 + 3x1 + 5x2 + 6x3. For this model, SSR = 300 and SSE = 75. Then, the value of MSR is:

A Preview of Business Statistics

Visual Description of Data

Statistical Description of Data

Data Collection and Sampling Methods

Probability: Review of Basic Concepts

Discrete Probability Distributions

Continuous Probability Distributions

Sampling Distributions

Estimation From Sample Data

Hypothesis Tests Involving a Sample Mean or Proportion

Hypothesis Tests Involving Two Sample Means

Analysis of Variance Tests

Chi-Square Applications

Nonparametric Methods

Simple Linear Regression and Correlation

Model Building

Models for Time Series and Forecasting

Decision Theory

Total Quality Management

Filters

Exam 16: Multiple Regression and Correlation

In a multiple regression model,the following statistics are given: SSE = 100,R2 = 0.995,k = 5,n = 15.The multiple coefficient of determination adjusted for degrees of freedom is:

The adjusted multiple coefficient of determination is adjusted for the:

What is the relationship between: (A)the results of the hypothesis test examining whether b2 differs significantly from zero at the 0.05 level and (B)the 95% confidence interval for β2\beta _ { 2 }β2​ .

A multiple regression equation includes 3 independent variables,and the coefficient of multiple determination is 0.64.The percentage of the variation in y that is explained by the regression equation is:

For the multiple regression model Y^\hat{ Y }Y^ = 3 - 4x1 + 5x2 + 2x3,a unit increase in x1,holding x2 and x3 constant,results in:

In simple linear regression,the regression equation is a straight line.In multiple regression,what geometric form is taken by the regression equation when there are two independent variables? When there are three or more independent variables?

In reference to the equation: Y^\hat{ Y }Y^ = -0.25 + 0.08x1 + 0.10x2,the value 0.08 is the:

A multiple regression analysis includes 25 data points and 4 independent variables results in SST = 200 and SSR = 150.The multiple standard error of estimate will be:

In a multiple regression problem,the regression equation is given by Y^\hat { Y }Y^ = 58.0 - 5.66x1 + 0.61 x2.Compute the point estimate for y when x1 = 3 and x2 = 4.

What is the multiple standard error estimate?

In reference to the equation: Y^\hat { Y }Y^ = -0.25 + 0.08x1 + 0.10x2,the value -0.25 is the:

In a regression model involving 25 observations,the following estimated regression model was obtained: Y^\hat { Y }Y^ = 60 + 2.8x1 + 1.2x2 - x3.For this model,SST = 600 and SSE = 150.Calculate the value of the F statistic for testing the significance of this model. F = ____________________

In a regression model involving 40 observations, the following estimated regression model was obtained y^\hat{y}y^​ = 10 + 3x1 + 5x2 + 6x3. For this model, SSR = 300 and SSE = 75. Then, the value of MSR is:

A Preview of Business Statistics

Visual Description of Data

Statistical Description of Data

Data Collection and Sampling Methods

Probability: Review of Basic Concepts

Discrete Probability Distributions

Continuous Probability Distributions

Sampling Distributions

Estimation From Sample Data

Hypothesis Tests Involving a Sample Mean or Proportion

Hypothesis Tests Involving Two Sample Means

Analysis of Variance Tests

Chi-Square Applications

Nonparametric Methods

Simple Linear Regression and Correlation

Model Building

Models for Time Series and Forecasting

Decision Theory

Total Quality Management

Filters

In a multiple regression model,the following statistics are given: SSE = 100,R² = 0.995,k = 5,n = 15.The multiple coefficient of determination adjusted for degrees of freedom is:

What is the relationship between: (A)the results of the hypothesis test examining whether b₂ differs significantly from zero at the 0.05 level and (B)the 95% confidence interval for $\beta _ { 2 }$ .

For the multiple regression model $\hat{ Y }$ = 3 - 4x₁ + 5x₂ + 2x₃,a unit increase in x₁,holding x₂ and x₃ constant,results in:

In reference to the equation: $\hat{ Y }$ = -0.25 + 0.08x₁ + 0.10x₂,the value 0.08 is the:

In a multiple regression problem,the regression equation is given by $\hat { Y }$ = 58.0 - 5.66x₁ + 0.61 x₂.Compute the point estimate for y when x₁ = 3 and x₂ = 4.

In reference to the equation: $\hat { Y }$ = -0.25 + 0.08x₁ + 0.10x₂,the value -0.25 is the:

In a regression model involving 25 observations,the following estimated regression model was obtained: $\hat { Y }$ = 60 + 2.8x₁ + 1.2x₂ - x₃.For this model,SST = 600 and SSE = 150.Calculate the value of the F statistic for testing the significance of this model. F = ____________________

In a regression model involving 40 observations, the following estimated regression model was obtained $\hat{y}$ = 10 + 3x1 + 5x2 + 6x3. For this model, SSR = 300 and SSE = 75. Then, the value of MSR is: