Deck 16: Multiple Regression and Correlation

Question 1

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.

Answer 1

estimated change in y when x₁ increases by one unit.

Question 2

The adjusted multiple coefficient of determination is adjusted for the:

A) number of regression parameters including the y-intercept.
B) number of dependent variables and the sample size.
C) number of independent variables and the sample size.
D) coefficient of correlation and the significance level.

Answer 2

number of independent variables and the sample size.

Question 3

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:

A) 64%.
B) 80%.
C) 36%.
D) 21%.

Answer 3

64%.

Question 4

For the multiple regression model $\hat { Y }$ = 50 + 25x₁ - 10x₂ + 8x₃,if x₂ were to increase by 5,holding x₁ and x₃ constant,the value of y would:

A) increase by 5.
B) increase by 50.
C) decrease on average by 5.
D) decrease on average by 50.

Question 5

True or False The purpose of the multiple correlation analysis is to measure the strength of the relationship between the dependent (y)and the set of independent (x)variables.

Question 6

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:

A) 1.333.
B) 6.124.
C) 2.500.
D) 1.581.

Question 7

True or False A dummy variable is used to incorporate qualitative data into the analysis.

Question 8

True or False Multicollinearity is a situation in which two or more of the independent variables are highly correlated with each other.

Question 9

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.

Question 10

True or False It is a good idea to make point estimates based on x values that lie beyond the range of the underlying data.

Question 11

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.

Question 12

In reference to the equation: $\hat { y }$ = -0.25 + 0.08x₁ + 0.10x₂,the value 0.01 is the:

A) predicted value of y.
B) partial regression coefficient for x_1.
C) partial regression coefficient for x_2.
D) predicted value y when x₁ = 0 and x₂ = 0.
E) predicted value of y when x₁ = 2 and x₂ = 1.

Question 13

In a multiple regression analysis involving 40 observations and 4 independent variables,SST = 375 and SSE = 75.The multiple coefficient of determination is:

A) 0.8333.
B) 0.8000.
C) 0.1875.
D) 0.9375.

Question 14

A multiple regression model has the form: $\hat { Y }$ = 5.25 + 2.5x₁ + 4x₂.As x₂ increases by 1 unit,holding x₁ constant,then the value of y will increase by:

A) 2.5 units.
B) 7.75 units.
C) 4 units on average.
D) 11.75 units on average.

Question 15

True or False In interpreting the multiple regression equation,it can be a mistake to conclude that one independent variable is more important than another just because its partial regression coefficient happens to be large.

Question 16

A multiple regression model has the form $\hat { Y }$ = b₀ + b₁x₁ + b₂x₂.The coefficient b₁ is interpreted as the:

A) estimated change in y per unit change in x₁.
B) estimated change in y per unit change in x₁,holding x₂constant.
C) estimated change in y per unit change in x₁,when x₁ and x₂ values are correlated.
D) estimated change in y per unit change in x₂,holding x₁ constant.

Question 17

True or False Multiple regression analysis examines the linear relationship between a dependent variable (y)and two or more independent variables (x₁,x₂,and so on).

Question 18

For each y term in the multiple regression equation,the corresponding $\beta$ is referred to as the partial regression coefficient.

Question 19

The amount of variation in the dependent variable that is not explained by the multiple regression equation is known as:

A) total sum of squares.
B) residual sum of squares.
C) regression sum of squares.
D) treatment sum of squares.

Question 20

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.

Question 21

A dummy variable will have a value of either ____________________ or ____________________,depending on whether a given characteristic is present or absent.

Question 22

A multiple regression model has three independent variables.The following values of y are given: Compute the total sum of squares (SST).
SST = ____________________

Question 23

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 female who stayed in the program for 5 time periods?

Question 24

Consider the multiple regression equation, = 80 + 15x₁ - 5 x₂ + 100x₃.If x₁ = 10,x₂ = 4,x₃ = 12,what is the estimated value of y?

Question 25

For a multiple regression model the following statistics are given: SSE = 40,SST = 200,k = 4,n = 20.Calculate the coefficient of determination adjusted for degrees of freedom.

Question 26

In a regression model involving 50 observations,the following estimated regression model was obtained. $\hat { Y }$ = 51.4 + 0.70x₁ + 0.679x₂ - 0.378x₃.For this model SST = 120,524 and SSR = 85,400.Then,the value of MSE is:

A) 763.565.
B) 702.480.
C) 1708.0.
D) 2410.48.

Question 27

In testing the significance of a multiple regression model in which there are three independent variables,the null hypothesis is:

A) $H _ { 0 } : \beta _ { 1 } = \beta _ { 2 } = \beta _ { 3 } = 1$
B) $H _ { 0 } : \beta _ { 0 } = \beta _ { 1 } = \beta _ { 2 } = \beta _ { 3 }$
C) $H _ { 0 } : \beta _ { 1 } = \beta _ { 2 } = \beta _ { 3 } = 0$
D) $H _ { 0 } : \beta _ { 0 } = \beta _ { 1 } = \beta _ { 2 } = \beta _ { 3 } \neq 0$

Question 28

With four or more variables,the regression equation becomes a mathematical entity called a ____________________.

Question 29

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

Question 30

NARRBEGIN: 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:
How much of the variation in thefts is explained by the model?

Question 31

NARRBEGIN: 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:
Compute the multiple standard error of estimate (s_e)from the regression results.

Question 32

In a regression model involving 25 observations,the following estimated regression model was obtained: = 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 = ____________________

Question 33

In a multiple regression analysis involving k independent variables and n data points,the degrees of freedom associated with the error sum of squares is:

A) k - 1.
B) n - k - 1.
C) n - 1.
D) n - k.

Question 34

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.For the same length of time in the program,compare the weight loss of a female to a male.What is your conclusion?

Question 35

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

A) 100.
B) 225.
C) 25.
D) 75.

Question 36

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?

Question 37

The ____________________ is the proportion of the variation in y that is explained by the multiple regression equation.

Question 38

In order to test the significance of a multiple regression model involving 4 independent variables and 30 observations,the numerator and denominator degrees of freedom (respectively)for the critical value of F are:

A) 4 and 30.
B) 3 and 29.
C) 4 and 25.
D) 5 and 31.

Question 39

NARRBEGIN: 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:
Use the values in the analysis of variance table to compute R² using the values for SST and SSE or SSR.

Question 40

NARRBEGIN: 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:
Use the values in the analysis of variance table to compute the multiple standard error of the estimate.

Question 41

NARRBEGIN: Equation
The regression equation, = 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.
What is the approximate 95% confidence interval for the mean of y whenever x₁ = 20 and x₂ = 25.

Question 42

Consider the multiple regression equation, = 80 + 15x₁ - 5 x₂ + 100x₃.Identify the y-intercept and partial regression coefficients:
y-intercept: ____________________
x₁: ____________________
x₂: ____________________
x₃: ____________________

Question 43

NARRBEGIN: Grade
A statistics teacher collected the following data to determine if the number of hours a student studied during the semester and the number of classes missed could be used to predict the final grade for the course.The following table shows the results of the model being applied to 8 students.

Calculate the multiple standard error of estimate.

Question 44

NARRBEGIN: Equation
The regression equation, = 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.

Question 45

NARRBEGIN: 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:

In testing the significance of the partial regression coefficient associated with the Starting variable at the 0.05 significance level,what is the appropriate conclusion?

Question 46

NARRBEGIN: Regression Model
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.

Calculate the residual sum of squares.

Question 47

NARRBEGIN: 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:

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?

Question 48

Explain each of the terms in the multiple regression model: .

Question 49

NARRBEGIN: Equation
The regression equation, = 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.
What is the approximate 95% prediction interval for an individual y whenever x₁ = 20 and x₂ = 25?

Question 50

A multiple regression model has three independent variables.The following values of y and are given: Compute the multiple standard error of the estimate.

Question 51

NARRBEGIN: Grade
A statistics teacher collected the following data to determine if the number of hours a student studied during the semester and the number of classes missed could be used to predict the final grade for the course.The following table shows the results of the model being applied to 8 students.

Calculate the coefficient of multiple determination.

Question 52

NARRBEGIN: 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:

In testing the null hypothesis that the regression equation is not significant at the 0.05 level,what is the appropriate conclusion?

Question 53

NARRBEGIN: Regression Model
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.

Calculate the coefficient of multiple determination.

Question 54

Consider the multiple regression equation, = 80 + 15x₁ - 5x₂ + 100x₃.If x₃ were to increase by 5,what change would be necessary in x₂ in order for the estimated value of y to remain unchanged?
x₂ would ____________________ by ____________________.

Question 55

NARRBEGIN: 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:

In testing the significance of the partial regression coefficient associated with the Years variable at the 0.05 significance level,what is the appropriate conclusion?

Question 56

NARRBEGIN: Grade
A statistics teacher collected the following data to determine if the number of hours a student studied during the semester and the number of classes missed could be used to predict the final grade for the course.The following table shows the results of the model being applied to 8 students.

Calculate the residual sum of squares.

Question 57

NARRBEGIN: 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:

What is the regression equation?

Question 58

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.
Calculate the multiple standard error of estimate.

Question 59

NARRBEGIN: Grade
A statistics teacher collected the following data to determine if the number of hours a student studied during the semester and the number of classes missed could be used to predict the final grade for the course.The following table shows the results of the model being applied to 8 students.

Calculate the total sum of squares.

Question 60

NARRBEGIN: Regression Model
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.

Calculate the total sum of squares.

Question 61

NARRBEGIN: 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:
From these regression results,compute a 95% prediction interval for y when x₁ = 4,x₂ = 5,and x₃ = 3.

Question 62

NARRBEGIN: Marketing Analyst
A marketing analyst is interested in predicting prospective buyer's knowledge about compact disc players.A random sample of 36 buyers was taken,a questionnaire about compact disc players completed,and information about education,income and age was obtained.In estimating the equation,the variables were:
y = knowledge about compact disc players
x₁ = education (years)
x₂ = age
x₃ = income (thousands of dollars)
The resulting output using MINITAB was:
Identify the coefficient of multiple determination,R².
Interpret the value.

Question 63

NARRBEGIN: Professor
A statistics professor investigated some of the factors that affect an individual student's final grade in his course.He proposed the multiple regression model where:
y = final mark (out of 100)
x₁ = number of lectures skipped
x₂ = number of late assignments
x₃ = mid-term test mark (out of 100)
The professor recorded the data for 50 randomly selected students.The computer output is shown below.
Do these data provide enough evidence at the 1% significance level to conclude that the final mark and the mid-term mark are positively linearly related?
Test statistic = ____________________
Critical Value = ____________________
Conclusion: ____________________

Question 64

NARRBEGIN: 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:
Test the significance of the regression equation at the 0.01 level of significance.
Test statistic = ____________________
Critical Value = ____________________
Conclusion: ____________________

Question 65

NARRBEGIN: 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:

For a male employee with 5 years of experience and a starting salary of $30,000,what is the approximate 95% confidence interval for his annual salary?

Question 66

NARRBEGIN: 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:
What,if any,multicollinearity do you detect?

Question 67

The computer output for the multiple regression model is shown below.However,because of a printer malfunction some of the results are not shown.These are indicated by the boldface letters a to i.Fill in the missing results (up to three decimal places). a = ____________________
b = ____________________
c = ____________________
d = ____________________
e = ____________________
f = ____________________
g = ____________________
h = ____________________
i = ____________________

Question 68

NARRBEGIN: 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:
Use the values in the analysis of variance table to find MSR and MSE.
MSR = ____________________
MSE = ____________________

Question 69

NARRBEGIN: Professor
A statistics professor investigated some of the factors that affect an individual student's final grade in his course.He proposed the multiple regression model where:
y = final mark (out of 100)
x₁ = number of lectures skipped
x₂ = number of late assignments
x₃ = mid-term test mark (out of 100)
The professor recorded the data for 50 randomly selected students.The computer output is shown below.
What is the coefficient of determination?
What does this statistic tell you?

Question 70

NARRBEGIN: 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:
Do the partial regression coefficients have the algebraic sign you might expect?

Question 71

NARRBEGIN: Marketing Analyst
A marketing analyst is interested in predicting prospective buyer's knowledge about compact disc players.A random sample of 36 buyers was taken,a questionnaire about compact disc players completed,and information about education,income and age was obtained.In estimating the equation,the variables were:
y = knowledge about compact disc players
x₁ = education (years)
x₂ = age
x₃ = income (thousands of dollars)
The resulting output using MINITAB was:
Identify b₀,b₁,and b₃.
b₀ = ____________________
b₁ = ____________________
b₃ = ____________________

Question 72

NARRBEGIN: Professor
A statistics professor investigated some of the factors that affect an individual student's final grade in his course.He proposed the multiple regression model where:
y = final mark (out of 100)
x₁ = number of lectures skipped
x₂ = number of late assignments
x₃ = mid-term test mark (out of 100)
The professor recorded the data for 50 randomly selected students.The computer output is shown below.
Interpret the coefficients b₁ and b₃.
b₁ = ____________________
Interpretation: _____________________________________________________
b₃ = ____________________
Interpretation: _____________________________________________________

Question 73

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
$$Y = 1.39 + 0.0178 \times 1 - 0.0258 \times 2 - 0.00050 \times 3$$
$\begin{array}{lcll}\text { Predictor } & \text { Coef } & \text { Stdev } &{\text { t-ratio }} \\\text { Constant } & 1.3928 & 0.1096 & 12.71 \\\text { X1 } & 0.017806 & 0.006600 & 2.70 \\\text { X2 } & -0.025825 & 0.001613 & -16.01 \\X 3 & -0.000501 & 0.002779 & -0.18\end{array}$
$s=0.04805 \quad \mathrm{R}-\mathrm{sq}=97.5 \% \quad \mathrm{R}-\mathrm{sq}(\mathrm{adj})=96.6 \%$
Analysis of Variance
$\begin{array}{lllcc}\text { SOURCE } & \text { DF } & & \text { SS } & \text { MS } \\\text { Regression } & & 3 & 0.72562 & 0.24187 \\\text { Error } & 8 & {0.01847} && 0.00231 \\\text { Total } & 11 &&{0.74409} &\end{array}$

-Test the significance of the regression equation at $\alpha$ = 0.01.
Test statistic = ____________________
Critical Value = ____________________
Conclusion: ____________________

Question 74

NARRBEGIN: Marketing Analyst
A marketing analyst is interested in predicting prospective buyer's knowledge about compact disc players.A random sample of 36 buyers was taken,a questionnaire about compact disc players completed,and information about education,income and age was obtained.In estimating the equation,the variables were:
y = knowledge about compact disc players
x₁ = education (years)
x₂ = age
x₃ = income (thousands of dollars)
The resulting output using MINITAB was:
Predict the questionnaire score for a buyer who is 41 years of age,has 13 years of education,and $39,000 income.

Question 75

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
$$Y = 1.39 + 0.0178 \times 1 - 0.0258 \times 2 - 0.00050 \times 3$$
$\begin{array}{lcll}\text { Predictor } & \text { Coef } & \text { Stdev } &{\text { t-ratio }} \\\text { Constant } & 1.3928 & 0.1096 & 12.71 \\\text { X1 } & 0.017806 & 0.006600 & 2.70 \\\text { X2 } & -0.025825 & 0.001613 & -16.01 \\X 3 & -0.000501 & 0.002779 & -0.18\end{array}$
$s=0.04805 \quad \mathrm{R}-\mathrm{sq}=97.5 \% \quad \mathrm{R}-\mathrm{sq}(\mathrm{adj})=96.6 \%$
Analysis of Variance
$\begin{array}{lllcc}\text { SOURCE } & \text { DF } & & \text { SS } & \text { MS } \\\text { Regression } & & 3 & 0.72562 & 0.24187 \\\text { Error } & 8 & {0.01847} && 0.00231 \\\text { Total } & 11 &&{0.74409} &\end{array}$

-From these regression results,compute a 95% confidence interval for $\beta$ ₁, $\beta$ ₂,and $\beta$ ₃.

Question 76

NARRBEGIN: Professor
A statistics professor investigated some of the factors that affect an individual student's final grade in his course.He proposed the multiple regression model where:
y = final mark (out of 100)
x₁ = number of lectures skipped
x₂ = number of late assignments
x₃ = mid-term test mark (out of 100)
The professor recorded the data for 50 randomly selected students.The computer output is shown below.
Do these data provide enough evidence to conclude at the 5% significance level that the model is useful in predicting the final mark?
Test statistic = ____________________
Critical Value = ____________________
Conclusion: ____________________

Question 77

NARRBEGIN: Professor
A statistics professor investigated some of the factors that affect an individual student's final grade in his course.He proposed the multiple regression model where:
y = final mark (out of 100)
x₁ = number of lectures skipped
x₂ = number of late assignments
x₃ = mid-term test mark (out of 100)
The professor recorded the data for 50 randomly selected students.The computer output is shown below.
Do these data provide enough evidence at the 5% significance level to conclude that the final mark and the number of late assignments are negatively linearly related?
Test statistic = ____________________
Critical Value = ____________________
Conclusion: ____________________

Question 78

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
$\begin{array} { l l l c l } \text { Predictor } & \text { Coef } & \text { Stdev } & \text { t-ratio } & p \\ \text { Constant } & - 25.29 & 17.85 & - 1.42 & 0.190 \\ \text { police } & 1.2831 & 0.9275 & 1.38 & 0.200 \\ \text { polexp } & 0.018827 & 0.008460 & 2.23 & 0.053 \\ \text { registr } & 0.09686 & 0.03536 & 2.74 & 0.023 \end{array}$
$$s = ? ? \quad \mathrm { R } - s q = ? ? \% \quad \mathrm { R } - s q ( a d j ) = ? ? \%$$
Analysis of Variance
$\begin{array} { l l l l c l } \text { SOURCE } & \text { DF } & \text { SS } & \text { MS } & F & p \\ \text { Regression } & 3 & 33007 & 11002 & 107.14 & 0.000 \\ \text { Error } & 9 & 924 & 103 & & \\ \text { Total } & 12 & 33932 & & & \end{array}$
Correlation between the variables:
$\begin{array} { l c c c c } & \text { car-thf } & \text { police } & \text { polexp } & \text { registr } \\ \text { car-thf } & 1.000 & & & \\ \text { police } & 0.466 & 1.000 & & \\ \text { polexp } & 0.970 & 0.390 & 1.000 & \\ \text { registr } & 0.976 & 0.406 & 0.958 & 1.000 \end{array}$

-Perform a test for each partial regression coefficient using a 0.05 significance level.Results:
Conclusion: _________________________________________________________

Question 79

NARRBEGIN: Professor
A statistics professor investigated some of the factors that affect an individual student's final grade in his course.He proposed the multiple regression model where:
y = final mark (out of 100)
x₁ = number of lectures skipped
x₂ = number of late assignments
x₃ = mid-term test mark (out of 100)
The professor recorded the data for 50 randomly selected students.The computer output is shown below.
Do these data provide enough evidence to conclude at the 5% significance level that the final mark and the number of skipped lectures are linearly related?
Test statistic = ____________________
Critical Value = ____________________
Conclusion: ____________________

Question 80

NARRBEGIN: 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:
From these regression results,compute a 95% confidence interval for y when x₁ = 4,x₂ = 5,and x₃ = 3.