Deck 9: Regression Analysis

Question 1

The regression function indicates the

A)average value the dependent variable assumes for a given value of the independent variable.
B)actual value the independent variable assumes for a given value of the dependent variable
C)average value the dependent variable assumes for a given value of the dependent variable
D)actual value the dependent variable assumes for a given value of the independent variable

Answer 1

A

Question 2

The regression line denotes the ____ between the dependent and independent variables.

A)unsystematic variation
B)systematic variation
C)random variation
D)average variation

Answer 2

B

Question 3

The term $\varepsilon$ in the regression model represents

A)the slope of the regression model.
B)a random error term.
C)a correction for mistakes in measuring X.
D)a correction for the fact that we are taking a sample.

Answer 3

a random error term.

Question 4

The terms $\beta$ ₀ and $\beta$ ₁ are referred to as

A)sample statistics
B)random variables
C)population variables
D)population parameters

Question 5

The estimated value of Y₁ is given by

A)
B)
C)
D)

Question 6

The terms b₀ and b₁ are

A)estimated population parameters.
B)estimated intercept and slope values, respectively.
C)random variables.
D)all of these.

Question 7

Why do we create a scatter plot of the data in regression analysis?

A)To compute the error terms.
B)Because Excel calculates the function from the scatter plot.
C)To visually check for a relationship between X and Y.
D)To estimate predicted values.

Question 8

In the equation Y = $\beta$ ₀ + $\beta$ ₁ X_1i + $\varepsilon$
, $\beta$ 0₁ is

A)the Y intercept
B)the slope of the regression line
C)the mean of the dependent data.
D)the X intercept

Question 9

The total sum of squares (TSS) is best defined as

A)the sums of squares of the dependent variables.
B)the total variation of Y around its mean.
C)the sums of squares of the predicted values.
D)the variation of Y around its mean plus the variation of Y around the predicted values.

Question 10

Which of the following represents a regression model?

A)= f(X₁, X₂, ..., X_k)
B)= f(X₁, X₂, ..., X_k) + $\varepsilon$
C)Y = f(X₁, X₂, ..., X_k)
D)Y = f(X₁, X₂, ..., X_k) + $\varepsilon$

Question 11

The actual value of a dependent variable will generally differ from the regression equation estimate due to

A)unaccounted for random variation.
B)the inability of the nonlinear Solver to find optimal values.
C)not building the regression model with enough data.
D)the model R² not equal to 1.

Question 12

The terms b₀ and b₁ are referred to as

A)population variables.
B)population parameters.
C)estimated population variables.
D)estimated population parameters.

Question 13

On average, the differences between the actual and predicted values of Y

A)are equal to b₀.
B)sum to an unknown value.
C)are distributed uniformly.
D)sum to zero.

Question 14

Estimation errors are often referred to as

A)mistakes.
B)constant errors.
C)residuals.
D)squared errors.

Question 15

The error term $\varepsilon$ in a regression model represents

A)a random error in the data.
B)unsystematic variation in the dependent variable.
C)variation not explained by the independent variables.
D)all of these.

Question 16

The reason an analyst creates a regression model is

A)to determine the errors in the data collected.
B)to predict a dependent variable value given specific independent variable values.
C)to predict an independent variable value given specific dependent variable values.
D)to verify the errors are normally distributed.

Question 17

Error sum of squares (ESS) is computed as

A)
B)
C)
D)

Question 18

Regression analysis is a modeling technique

A)that assumes all data is normally distributed.
B)for analyzing the relationship between dependent and independent variables.
C)for examining linear trend data only.
D)for capturing uncertainty in predicted values of Y.

Question 19

The regression residuals are computed as

A)
B)
C)
D)

Question 20

The $\beta$ ₁ term indicates

A)the average change in Y for a unit change in X.
B)the Y value for a given value of X.
C)the change in observed X for a given change in Y.
D)the Y value when X equals zero.

Question 21

When using the Regression tool in Excel the dependent variable is entered as the

A)X-range.
B)Y-range.
C)dependent-range.
D)independent-range.

Question 22

Based on the following regression output, what conclusion can you reach about $\beta$ ₀?

A) $\beta$ ₀ = 0, with P-value = 0.016353
B) $\beta$ ₀ $\neq$ 0, with P-value = 0.016353
C) $\beta$ ₀ = 0, with P-value = 0.000186
D) $\beta$ ₀ $\neq$ 0, with P-value = 0.000186

Question 23

R² is calculated as

A)ESS/TSS
B)1 - (RSS/TSS)
C)RSS/ESS
D)RSS/TSS

Question 24

In regression terms what does "best fit" mean?

A)The estimated parameters, b₀ and b₁, are minimized.
B)The estimated parameters, b₀ and b₁, are linear.
C)The error terms are as small as possible.
D)The largest error term is as small as possible.

Question 25

What is the correct range for R² values?

A)( $\le$ 1 $\le$ R² $\le$ 0)
B)( $\le$ 1 $\le$ R² $\le$ 1)
C)(0 $\le$ R² $\le$ 1)
D)(0 $\le$ R² $\le$ .5)

Question 26

Based on the following regression output, what is the equation of the regression line?

A) _i = 1.131661 + 31.62378 X_1i
B)11ef0f86_6b3d_a1b9_8c09_172087681a6b_TB5443_11 _i = 31.62378 + 1.131661 X_1i
C)11ef0f86_6b3d_a1b9_8c09_172087681a6b_TB5443_11_i = 3.028236 + 6.511819 X_1i

Question 27

Which of the following is an advantage of using the TREND() function versus the regression tool?

A)The TREND() function provides more statistical information.
B)The TREND() function handles multiple dependent variable data.
C)The TREND() function is dynamically updated when input to the function changes.
D)The TREND() function does not use a least squares regression line.

Question 28

R² is also referred to as

A)coefficient of determination.
B)correlation coefficient.
C)total sum of squares.
D)regression sum of squares.

Question 29

Based on the following regression output, what proportion of the total variation in Y is explained by X?

A)0.917214
B)0.841282
C)0.821442
D)9.385572

Question 30

When using the Regression tool in Excel the independent variable is entered as the

A)X-range.
B)Y-range.
C)dependent-range.
D)independent-range.

Question 31

The method of least squares finds parameter values that

A)minimizes TSS.
B)minimizes RSS.
C)minimizes ESS.
D)minimizes ESS + RSS.

Question 32

What is the formula for total sum of squares (TSS)

A)
B)
C)
D)

Question 33

The standard error measures the

A)variability in the X values.
B)variability in the actual data around the fitted regression function.
C)variability in the independent variable around the fitted regression function.
D)variability in the dependent variable around the fitted regression function.

Question 34

The problem of finding the optimal values of b₀ and b₁ is

A)a linear programming problem.
B)an unconstrained nonlinear optimization problem.
C)a goal programming problem.
D)a constrained nonlinear optimization problem.

Question 35

The objective function in regression analysis is

A)
B)
C)
D)

Question 36

For a simple linear regression model, a 100(1 - $\alpha$ )% prediction interval for a new value of Y when X = X_h is computed as

A)
B)
C)
D)

Question 37

The error sum of squares term is used as a criterion for determining b₀ and b₁ because

A)the sum of errors will always equal zero.
B)the term can be solved for exact values of b₀ and b₁.
C)both b₀ and b₁ can be easily calculated using the sum of squares term.
D)all of these.

Question 38

Based on the following regression output, what conclusion can you reach about $\beta$ ₁?

A) $\beta$ ₁ = 0, with P-value = 0.016353
B) $\beta$ ₁ $\neq$ 0, with P-value = 0.016353
C) $\beta$ ₁ = 0, with P-value = 0.000186
D) $\beta$ ₁ $\neq$ 0, with P-value = 0.000186

Question 39

The standard prediction error is

A)always smaller than the standard error.
B)used to construct confidence intervals for predicted values.
C)measures the variability in the predicted values.
D)all of these.

Question 40

Residuals are assumed to be

A)dependent, uniformly distributed random variables.
B)independent, uniformly distributed random variables.
C)dependent, normally distributed random variables.
D)independent, normally distributed random variables.

Question 41

Polynomial regression is used when

A)the independent variables are non-linear.
B)there is a non-linear relationship between the dependent and independent variables.
C)there is a non-linear relationship between the independent variables.
D)there is a curvilinear change in the dependent variables.

Question 42

The following questions are based on the problem description and spreadsheet below.
A company has built a regression model to predict the number of labor hours (Y_i) required to process a batch of parts (X_i). It has developed the following Excel spreadsheet of the results.


-Refer to Exhibit 9.1. Test the significance of the model and explain which values you used to reach your conclusions.

Question 43

The following questions are based on the problem description and spreadsheet below.
A paint manufacturer is interested in knowing how much pressure (in pounds per square inch, PSI) builds up inside aerosol cans at various temperatures (degrees Fahrenheit). It has developed the following Excel spreadsheet of the results.


-Refer to Exhibit 9.2. Test the significance of the model and explain which values you used to reach your conclusions.

Question 44

The following questions are based on the problem description and spreadsheet below.
A paint manufacturer is interested in knowing how much pressure (in pounds per square inch, PSI) builds up inside aerosol cans at various temperatures (degrees Fahrenheit). It has developed the following Excel spreadsheet of the results.


-Refer to Exhibit 9.2. Interpret the meaning of the "Lower 95%" and "Upper 95%" terms in cells F16:G16 of the spreadsheet.

Question 45

The company would like to build a prediction interval on the pressure for a can with a temperature of 125 degrees. What formula should be entered in cells B17:F21 of the following spreadsheet to compute this prediction interval? Partial results of the Regression analysis of the data are provided below.

Question 46

An analyst has identified 3 independent variables (X₁, X₂, X₃) which might be used to predict Y. He has computed the regression equations using all combinations of the variables and the results are summarized in the following table. Why is the R² value for the X₃ model the same as the R² value for the X₁ and X₃ model, but the Adjusted R² values differ?

A)The standard error for X₁ is greater than the standard error for X₃.
B)X₁ does not reduce ESS enough to compensate for its addition to the model.
C)X₁ does not reduce TSS enough to compensate for its addition to the model.
D)X₁ and X₃ represent similar factors so multicollinearity exists.

Question 47

The following questions are based on the problem description and spreadsheet below.
A paint manufacturer is interested in knowing how much pressure (in pounds per square inch, PSI) builds up inside aerosol cans at various temperatures (degrees Fahrenheit). It has developed the following Excel spreadsheet of the results.


-Refer to Exhibit 9.2. Interpret the meaning of R Square in cell B3 of the spreadsheet.

Question 48

A variable which takes on m discrete values would be modeled using

A)(m - 1) binary variables.
B)m binary variables.
C)(m - 1) integer variables.
D)m non-linear variables.

Question 49

What is a clear indicator of non-constant variance in a plot of regression model residuals?

A)A non-linear trend in the residual plot.
B)An intercept standard error larger that the estimated intercept coefficient.
C)A funnel shaped trend in the residual plot.
D)The standard errors from each independent variable differ.

Question 50

The following questions are based on the problem description and spreadsheet below.
A company has built a regression model to predict the number of labor hours (Y_i) required to process a batch of parts (X_i). It has developed the following Excel spreadsheet of the results.


-Refer to Exhibit 9.1. Predict the mean number of labor hours for a batch of 5 parts.

Question 51

The company would like to build a prediction interval on the time for a new batch of 8 parts. What formula should be entered in cells B17:F21 of the following spreadsheet to compute this prediction interval? Partial results of the Regression analysis of the data are provided below.

Question 52

The following questions are based on the problem description and spreadsheet below.
A paint manufacturer is interested in knowing how much pressure (in pounds per square inch, PSI) builds up inside aerosol cans at various temperatures (degrees Fahrenheit). It has developed the following Excel spreadsheet of the results.


-Refer to Exhibit 9.2. What is the estimated regression function for this problem? Explain what the terms in your equation mean.

Question 53

The R² statistic

A)varies between -1 and 1.
B)compares the regression sum of squares to the total sum of squares.
C)accounts for the number of parameters in the regression model.
D)is the ratio of the error sum of squares to the regression sum of squares.

Question 54

The following questions are based on the problem description and spreadsheet below.
A company has built a regression model to predict the number of labor hours (Y_i) required to process a batch of parts (X_i). It has developed the following Excel spreadsheet of the results.


-Refer to Exhibit 9.1. Provide a rough 95% confidence interval on the number of labor hours for a batch of 5 parts.

Question 55

The following questions are based on the problem description and spreadsheet below.
A paint manufacturer is interested in knowing how much pressure (in pounds per square inch, PSI) builds up inside aerosol cans at various temperatures (degrees Fahrenheit). It has developed the following Excel spreadsheet of the results.


-Refer to Exhibit 9.2. Predict the mean pressure for a temperature of 120 degrees.

Question 56

The following questions are based on the problem description and spreadsheet below.
A company has built a regression model to predict the number of labor hours (Y_i) required to process a batch of parts (X_i). It has developed the following Excel spreadsheet of the results.


-Refer to Exhibit 9.1. What is the estimated regression function for this problem? Explain what the terms in your equation mean.

Question 57

The following questions are based on the problem description and spreadsheet below.
A company has built a regression model to predict the number of labor hours (Y_i) required to process a batch of parts (X_i). It has developed the following Excel spreadsheet of the results.


-Refer to Exhibit 9.1. Interpret the meaning of R Square in cell B3 of the spreadsheet.

Question 58

The following questions are based on the problem description and spreadsheet below.
A company has built a regression model to predict the number of labor hours (Y_i) required to process a batch of parts (X_i). It has developed the following Excel spreadsheet of the results.


-Refer to Exhibit 9.1. Interpret the meaning of the "Lower 95%" and "Upper 95%" terms in cells F16:G16 of the spreadsheet.

Question 59

Based on the following regression output, what is the equation of the regression line?

A)_i = 14.169 + 0.985 X_1i + 0.995 X_2i
B)11ef0f88_27fc_278e_8c09_6ff059a56c10_TB5443_11_i = 14.169 + 0.995 X_1i + 0.985 X_2i
C)11ef0f88_27fc_278e_8c09_6ff059a56c10_TB5443_11_i = 0.995 + 14.169 X_1i + 0.985 X_2i

Question 60

What goodness-of-fit measure is commonly used to evaluate a multiple regression function?

A)R²
B)adjusted R²
C)partial R²
D)total R²

Question 61

The following questions are based on the problem description and spreadsheet below.
A charitable organization wants to determine what type of people donate to charities like itself. The charity felt that a person's education (in years), annual income, ($1,000) and the number of children the person had were important variables to consider. The charity developed regression models for all of the possible combinations of these three variables but does not know what to do with the results.


-Refer to Exhibit 9.4. Predict the mean donation by a person with 16 years of education, $90,000 annual income and 2 children. Use a full model based on data from the table.

Question 62

The partial regression output below applies to the following questions.


-Refer to Exhibit 9.6. What is the F-statistic value?

Question 63

The following questions are based on the problem description and spreadsheet below.
A charitable organization wants to determine what type of people donate to charities like itself. The charity felt that a person's education (in years), annual income, ($1,000) and the number of children the person had were important variables to consider. The charity developed regression models for all of the possible combinations of these three variables but does not know what to do with the results.


-Refer to Exhibit 9.4. Based on the data in the table which is the best model for the charity to use? Explain which values you used to reach your conclusion.

Question 64

The following questions are based on the problem description and spreadsheet below.
A researcher is interested in determining how many calories young men consume. She measured the age of the individuals and recorded how much food they ate each day for a month. The average daily consumption was recorded as the dependent variable. She has developed the following Excel spreadsheet of the results.


-Refer to Exhibit 9.3. Interpret the meaning of R square in cell B3 of the spreadsheet.

Question 65

Exhibit 9.5
The following questions are based on the description and spreadsheet below.
An analyst has identified 3 independent variables (X₁, X₂,X₃) which might be used to predict Y. He has computed the regression equations using all of the variables and the results are summarized in the following table.
Refer to Exhibit 9.5. Predict the mean value based on (X₁, X₂, X₃) = (3, 32, 50). Use the best predictive model based on data from the table.

Question 66

The following questions are based on the problem description and spreadsheet below.
A researcher is interested in determining how many calories young men consume. She measured the age of the individuals and recorded how much food they ate each day for a month. The average daily consumption was recorded as the dependent variable. She has developed the following Excel spreadsheet of the results.


-Refer to Exhibit 9.3. Test the significance of the model and explain which values you used to reach your conclusions.

Question 67

Handel Manufacturing produces test stands for various maintenance functions ranging from automobile to jet airline testing stations. For years, their cost estimating function was based on a myriad of historical data fed into a cost analysis model that produced very accurate estimates of both development and support costs for various proposed test stands. James Mudd was a recent hire into the cost analysis shop. Unfortunately, during his first week on the job, James deleted the cost analysis database and failed to maintain a backup of the model. Fortunately, all is not lost. The computer support personnel can come in Monday and retrieve the model using their system backup tapes. Unfortunately, the cost proposals for three new test stand development and deployment projects are due first thing Monday morning. Since James recently left the company, you have been tasked to complete the cost estimate portion of the proposals.
After much gnashing of your teeth, you settle down to make the best of what you initially believe is a losing situation. While studying James' files you find historical records on 25 recent test stand development and deployment projects. Rejuvenated, you realize you can succeed in this prematurely perceived doomed situation. All you need to do is analyze this historical data, develop some cost estimating functions using regression, and then use your regression models to develop estimates for the three projects due Monday. The historical data in the files is the following. The data estimates for the three cost proposal due Monday is the following:
One thing unclear from reading the files was on the form of the cost estimating relationships contained within the lost cost analysis model. You are somewhat sure the regression models were not polynomial in form, but you are not certain of this fact. You are not even sure which variables were included in the model for development cost and which variables were included in the model for support costs. However, you are undaunted because you know you can develop accurate models and produce good cost estimates for each of the proposed projects.
Develop appropriate models for development and for support costs. Use these models to develop cost estimates for each of the new lines of test stands. For each of these cost estimates provide 95% confidence intervals for the predicted values.

Question 68

The following questions are based on the problem description and spreadsheet below.
A researcher is interested in determining how many calories young men consume. She measured the age of the individuals and recorded how much food they ate each day for a month. The average daily consumption was recorded as the dependent variable. She has developed the following Excel spreadsheet of the results.


-Refer to Exhibit 9.3. Interpret the meaning of the "Lower 95%" and "Upper 95%" terms in cells F16:G16 of the spreadsheet.

Question 69

The following questions are based on the problem description and spreadsheet below.
A researcher is interested in determining how many calories young men consume. She measured the age of the individuals and recorded how much food they ate each day for a month. The average daily consumption was recorded as the dependent variable. She has developed the following Excel spreadsheet of the results.


-Refer to Exhibit 9.3. What is the estimated regression function for this problem? Explain what the terms in your equation mean

Question 70

How many binary variables are required to encode a persons age group as being either young, middle-age or old? What are the variables and what are the meanings of their 0, 1 values?

Question 71

The researcher would like to build a prediction interval on the calories consumed by an 18 year old man. What formula should be entered in cells B17:F21 of the following spreadsheet to compute this prediction interval? Partial results of the Regression analysis of the data are provided below.

Question 72

The partial regression output below applies to the following questions.


-Refer to Exhibit 9.7. What is the SS for Total?

Question 73

The partial regression output below applies to the following questions.


-Refer to Exhibit 9.6. What is the MS for Residual?

Question 74

Exhibit 9.5
The following questions are based on the description and spreadsheet below.
An analyst has identified 3 independent variables (X₁, X₂,X₃) which might be used to predict Y. He has computed the regression equations using all of the variables and the results are summarized in the following table.
Refer to Exhibit 9.5. Based on the data in the table which is the best model for the charity to use? Explain which values you used to reach your conclusion.

Question 75

The partial regression output below applies to the following questions.


-Refer to Exhibit 9.7. What is the SS for Residual and MS for Residual?

Question 76

The following questions are based on the problem description and spreadsheet below.
A researcher is interested in determining how many calories young men consume. She measured the age of the individuals and recorded how much food they ate each day for a month. The average daily consumption was recorded as the dependent variable. She has developed the following Excel spreadsheet of the results.


-Refer to Exhibit 9.3. Predict the mean number of calories consumed by a 19 year old man.

Question 77

Assume you have chosen to use all three variables in your model. Test the significance of the model and explain which values you used to reach your conclusion.