Question 1

A(n) _____ refers to a measurable factor that defines a characteristic of a population, process, or system.

Accepted Answer

A)  random variable 
B)  expectation 
C)  parameter 
D)  residual 
A)  random variable 
B)  expectation 
C)  parameter 
D)  residual C

Question 2

The process of making estimates and drawing conclusions about one or more characteristics of a population through analysis of sample data drawn from the population is known as _____.

Accepted Answer

A)  inductive inference 
B)  deductive inference 
C)  statistical inference 
D)  Bayesian inference 
A)  inductive inference 
B)  deductive inference 
C)  statistical inference 
D)  Bayesian inference C

Question 3

A survey conducted by a research team was to investigate how the education level, tenure in current employment, and age, are related to annual income. A sample 20 employees is selected and the data is given below.
   a. Check if the F test leads to conclude that an overall regression relationship exists. If yes, use the t test to determine the significance of each independent variable. What is the conclusion for each test at the 0.05 level of significance?
b. Remove all independent variables that are not significant at the 0.05 level of significance from the estimated regression equation. What is your estimated regression equation in this case?

Accepted Answer

a. Using the following Excel output, we conclude that there is an overall regression relationship at the 0.05 level of significance.
   
The p-value associated with the estimated regression parameter b₁ is 0.0013. Because this p-value is less than the 0.05 level of significance, we reject the hypothesis that β₁ = 0. We conclude that there is a relationship between the annual income and the education level at the 0.05 level of significance. Our best estimate is that if we hold the length of tenure in current employment and the age constant, a one year increase in the education level corresponds to an increase of $10,011.92 in annual income.
The p-value associated with the estimated regression parameter b₂ is 0.3246. Because this p-value is greater than the 0.05 level of significance, we do not reject the hypothesis that β₂ = 0. We cannot conclude that there is a relationship between the length of tenure in current employment and the annual income at the 0.05 level of significance when controlling for education level and age.
The p-value associated with the estimated regression parameter b₃ is 0.0149. Because this p-value is less than the 0.05 level of significance, we reject the hypothesis that β₃ = 0. We conclude that there is a relationship between the age and the annual income at the 0.05 level of significance. Our best estimate is that if we hold the education level and length of tenure in current employment constant, an increase in age by a year corresponds to an increase of $2,689.24 in annual income.
b. The following Excel output is obtained by removing the independent variable, length of tenure in current employment (x₂), which is not significant at 0.05 significance level. Hence, this output provides the estimated multiple linear regression equation with education (x₁), age (x₃) as the independent variables.
   The estimated multiple linear regression equation is $ \hat{y}=-138671.68+9588.89 x_{1}+2234.56 x_{3} $. .

Question 4

A researcher wanted to study effect of two factors, x₁ and x₂, on yield (y). The observations are given below.
   a. Develop an estimated linear regression equation with the factor x₁ as the independent variable. Test for a significant relationship between factor x₁ and yield at the 0.05 level of significance. 
b. How much of the variation in the sample values of yield does the model in part (a) explain?

Accepted Answer

a. The following Excel output provides t

Question 5

_____ refers to the data set used to compare model forecasts and ultimately pick a model for predicting values of the dependent variable.

Accepted Answer

A)  Codomain 
B)  Training set 
C)  Validation set 
D)  Range 
A)  Codomain 
B)  Training set 
C)  Validation set 
D)  Range

Question 6

A production company is studying the relationship between the average cost/unit and number of units produced in a batch. A sample of 10 batches is selected and the data is given below.
   
   a. Develop an estimated quadratic regression equation for the data. How much variation in the sample values of cost/unit does this regression model explain? 
b. Is the overall regression relationship significant at a 0.05 level of significance? If so, then test the relationship between the independent variable and the dependent variable at a 0.05 level of significance.

Accepted Answer

a. The following Excel output provides t

Question 7

The principle of using the simplest meaningful model possible without sacrificing accuracy is referred to as_____.

Accepted Answer

A)  Engel's law 
B)  KISS principle 
C)  Murphy's law 
D)  Ockham's razor 
A)  Engel's law 
B)  KISS principle 
C)  Murphy's law 
D)  Ockham's razor

Question 8

The coefficient of determination:

Accepted Answer

A)  takes values between -1 to +1. 
B)  is equal to zero for a perfect fit. 
C)  is equal to one for the poorest fit. 
D)  is used to evaluate the goodness of fit. 
A)  takes values between -1 to +1. 
B)  is equal to zero for a perfect fit. 
C)  is equal to one for the poorest fit. 
D)  is used to evaluate the goodness of fit.

Question 9

The following scatter chart would help conclude that:

Accepted Answer

A)  the model is time-invariant. 
B)  the model captures the relationship between the variables accurately. 
C)  the residuals are interdependent. 
D)  the residuals are normally distribute
D)  
A)  the model is time-invariant. 
B)  the model captures the relationship between the variables accurately. 
C)  the residuals are interdependent. 
D)  the residuals are normally distribute
D)

Question 10

What would be the coefficient of determination if the total sum of squares (SST) is 23.29 and the sum of squares due to regression (SSR) is 10.03?

Accepted Answer

A)  2.32 
B)  0.43 
C)  13.26 
D)  0.89 
A)  2.32 
B)  0.43 
C)  13.26 
D)  0.89

Question 11

The _____ is a measure of the error in using the estimated regression equation to predict the values of the dependent variable in a sample.

Accepted Answer

A)  sum of squares due to regression (SSR) 
B)  error term 
C)  sum of squares due to error (SS
E)  
D)  residual 
A)  sum of squares due to regression (SSR) 
B)  error term 
C)  sum of squares due to error (SS
E)  
D)  residual

Question 12

A survey is conducted to determine whether the age of car influences the annual maintenance cost. A sample of 10 cars is selected and the data is shown below.
   a. Test whether each of the regression parameters β0 and β1 is equal to zero at a 0.05 level of significance. 
b. Interpret the estimated regression parameters? Are these interpretations reasonable?

Accepted Answer

a. First we check the conditions necessa

Question 13

The _____ is an indication of how frequently interval estimates based on samples of the same size taken from the same population using identical sampling techniques will contain the true value of the parameter we are estimating.

Accepted Answer

A)  residual 
B)  tolerance factor 
C)  confidence level 
D)  accuracy level 
A)  residual 
B)  tolerance factor 
C)  confidence level 
D)  accuracy level

Question 14

A student is interested in studying the impact of number of books referred by students on a statistics course and the number of lectures they attended on the final grade on the course. A sample of 25 students is selected and the data is given below.
   a. Develop an estimated regression equation using number of books referred and the number of lectures attended to predict the final grade on the course. 
b. Joseph referred 4 books and attended 19 lectures. What is his predicted final score on the course?

Accepted Answer

a. The following Excel output provides t

Question 15

Which of the following inferences can be drawn from the scatter chart given below?

Accepted Answer

A)  The residuals have a constant variance. 
B)  The model captures the relationship between the variables accurately. 
C)  The model underpredicts the value of the dependent variable for intermediate values of the independent variable. 
D)  The residual distribution is not normally distribute
D)  
A)  The residuals have a constant variance. 
B)  The model captures the relationship between the variables accurately. 
C)  The model underpredicts the value of the dependent variable for intermediate values of the independent variable. 
D)  The residual distribution is not normally distribute
D)

Question 16

When the mean value of the dependent variable is independent of variation in the independent variable, the slope of the regression line is _____.

Accepted Answer

A)  positive 
B)  zero 
C)  negative 
D)  infinite 
A)  positive 
B)  zero 
C)  negative 
D)  infinite

Question 17

A research team in at the Gonzaga University is interested in predicting a student's overall university GPA if his/her high school GPA is known. Assume that a random sample of 20 students is selected and the data is given below.
   a. Develop a scatter chart for these data with High School GPA as the independent variable. What does the scatter chart indicate about the relationship between high school GPAs and overall university GPA?
b. Develop an estimated regression equation showing how high school GPA is related to overall university GPA. What is the estimated regression model?
c. What is the predicted overall university GPA of Sophia, a student who has been admitted to Gonzaga University, with 3.40 high school GPA?

Accepted Answer

a. The scatter chart with high school GP

Question 18

Prediction of the value of the dependent variable outside the experimental region is called _____.

Accepted Answer

A)  interpolation 
B)  forecasting 
C)  averaging 
D)  extrapolation 
A)  interpolation 
B)  forecasting 
C)  averaging 
D)  extrapolation

Question 19

The graph of the simple linear regression equation is a(n) _____.

Accepted Answer

A)  ellipse 
B)  hyperbola 
C)  parabola 
D)  straight line 
A)  ellipse 
B)  hyperbola 
C)  parabola 
D)  straight line

Question 20

What would be the F test statistic in this case?

Accepted Answer

A)  396.46 
B)  400 
C)  350.32 
D)  298.55 
A)  396.46 
B)  400 
C)  350.32 
D)  298.55

A(n) _____ refers to a measurable factor that defines a characteristic of a population, process, or system.

The process of making estimates and drawing conclusions about one or more characteristics of a population through analysis of sample data drawn from the population is known as _____.

_____ refers to the data set used to compare model forecasts and ultimately pick a model for predicting values of the dependent variable.

The principle of using the simplest meaningful model possible without sacrificing accuracy is referred to as_____.

The coefficient of determination:

The following scatter chart would help conclude that:

What would be the coefficient of determination if the total sum of squares (SST) is 23.29 and the sum of squares due to regression (SSR) is 10.03?

The _____ is a measure of the error in using the estimated regression equation to predict the values of the dependent variable in a sample.

The _____ is an indication of how frequently interval estimates based on samples of the same size taken from the same population using identical sampling techniques will contain the true value of the parameter we are estimating.

Which of the following inferences can be drawn from the scatter chart given below?

When the mean value of the dependent variable is independent of variation in the independent variable, the slope of the regression line is _____.

Prediction of the value of the dependent variable outside the experimental region is called _____.

The graph of the simple linear regression equation is a(n) _____.

What would be the F test statistic in this case?

Introduction

Descriptive Statistics

Data Visualization

Time Series Analysis and Forecasting

Data Mining

Spreadsheet Models

Linear Optimization Models

Integer Linear Optimization Models

Nonlinear Optimization Models

Monte Carlo Simulation

Decision Analysis

Filters

Exam 4: Linear Regression

A(n) _____ refers to a measurable factor that defines a characteristic of a population, process, or system.

The process of making estimates and drawing conclusions about one or more characteristics of a population through analysis of sample data drawn from the population is known as _____.

_____ refers to the data set used to compare model forecasts and ultimately pick a model for predicting values of the dependent variable.

The principle of using the simplest meaningful model possible without sacrificing accuracy is referred to as_____.

The coefficient of determination:

The following scatter chart would help conclude that:

What would be the coefficient of determination if the total sum of squares (SST) is 23.29 and the sum of squares due to regression (SSR) is 10.03?

The _____ is a measure of the error in using the estimated regression equation to predict the values of the dependent variable in a sample.

The _____ is an indication of how frequently interval estimates based on samples of the same size taken from the same population using identical sampling techniques will contain the true value of the parameter we are estimating.

Which of the following inferences can be drawn from the scatter chart given below?

When the mean value of the dependent variable is independent of variation in the independent variable, the slope of the regression line is _____.

Prediction of the value of the dependent variable outside the experimental region is called _____.

The graph of the simple linear regression equation is a(n) _____.

What would be the F test statistic in this case?

Introduction

Descriptive Statistics

Data Visualization

Time Series Analysis and Forecasting

Data Mining

Spreadsheet Models

Linear Optimization Models

Integer Linear Optimization Models

Nonlinear Optimization Models

Monte Carlo Simulation

Decision Analysis

Filters