Deck 14: Regression Analysis

Question 1

The value 0.35 of a sample correlation coefficient indicates a weaker linear relationship than that of -0.40.

Answer 1

True

Question 2

A scatterplot can help determine if two variables are related in some systematic way.

Answer 2

True

Question 3

Compared to the sample correlation coefficient,the sample covariance is a better measure to gauge the strength of the linear relationship between two variables.

Answer 3

False

Question 4

The value 0.75 of a sample correlation coefficient indicates a stronger linear relationship than that of 0.60.

Question 5

Each point in the scatterplot represents one observed value for one variable.

Question 6

The value -0.75 of a sample correlation coefficient indicates a stronger linear relationship than that of 0.60.

Question 7

In the simple linear regression model,β₀ is the y-intercept of the line .

Question 8

In testing the population correlation coefficient,the alternative hypothesis is .

Question 9

Which of the following identifies the range for a correlation coefficient?

A)Any value less than 1
B)Any value greater than 0
C)Any value between 0 and 1
D)None of the above

Question 10

The positive square root of the coefficient of determination in simple linear regression is always equal to the correlation coefficient.

Question 11

The correlation coefficient could be considered as a "standardized covariance."

Question 12

The sample correlation coefficient cannot equal zero.

Question 13

A correlation coefficient r = -0.85 could indicate a:

A)Very weak positive linear relationship.
B)Very strong negative linear relationship.
C)Very weak negative linear relationship.
D)Very strong positive linear relationship.

Question 14

The following scatterplot implies that the relationship between the two variables x and y is:

A)Strong and positive.
B)Strong and negative.
C)Weak and negative.
D)No relationship.

Question 15

If two linear regression models have the same number of explanatory variables,a model with an R² value of 0.45 is a better prediction model than a model with an R² value of 0.65.

Question 16

Another name for an explanatory variable is the dependent variable.

Question 17

Simple linear regression includes more than one explanatory variable.

Question 18

The simple linear regression model can be written in the form

Question 19

The correlation coefficient can only range between 0 and 1.

Question 20

Covariance can be used to determine if the linear relationship between two variables is positive or negative.

Question 21

Which of the following statements is least accurate concerning correlation analysis?

A)Correlation does not imply causation.
B)The correlation coefficient captures only a linear relationship.
C)The correlation coefficient may not be a reliable measure when outliers are present in one or the both of the variables.
D)The correlation coefficient describes both the direction and strength of the relationship between two variables only if the two variables have the same units of measurement.

Question 22

Consider the following data: ,and .What is the sample regression equation?

A)
B)
C)
D)

Question 23

Given the augmented Phillips model: ,where y = actual rate of inflation (%),x₁ = unemployment rate (%),and x₂ = anticipated inflation rate (%).The response variable(s)in this model is(are)the:

A)Unemployment rate
B)Actual inflation rate
C)Anticipated inflation rate
D)Unemployment rate and anticipated inflation rate

Question 24

When testing whether the correlation coefficient differs from zero,the value of the test statistic is with a corresponding p-value of 0.0061.At the 5% significance level,can you conclude that the correlation coefficient differs from zero?

A)Yes,since the p-value is less than 0.05.
B)Yes,since the absolute value of the test statistic exceeds 0.05.
C)No,since the p-value is less than 0.05.
D)No,since the absolute value of the test statistic exceeds 0.05.

Question 25

Simple linear regression analysis differs from multiple regression analysis in that:

A)Simple linear regression uses only one explanatory variable.
B)The coefficient of correlation is meaningless in simple linear regression.
C)Goodness-of-fit measures cannot be calculated with simple linear regression.
D)The coefficient of determination is always higher in simple linear regression.

Question 26

The following scatterplot implies that the relationship between the two variables x and y is:

A)Weak and positive.
B)Strong and positive.
C)Strong and negative.
D)No relationship.

Question 27

A regression equation was estimated as .If and ,the predicted value of y would be:

A)29.
B)77.
C)233.
D)281.

Question 28

In the sample regression equation ,what is ?

A)The y-intercept
B)The slope of the equation
C)The value of y when x = 0
D)The predicted value of y,given a specific x value

Question 29

Consider the following simple linear regression model: .The explanatory variable is:

A)y
B)x
C)ε
D)β₀

Question 30

The variance of the rates of return is 0.25 for stock X and 0.01 for stock Y.The covariance between the returns of X and Y is -0.01.The correlation of the rates of return between X and Y is:

A)-0.25
B)-0.20
C)0.20
D)0.25

Question 31

When testing whether the correlation coefficient differs from zero,the value of the test statistic is with a corresponding p-value of 0.0653.At the 5% significance level,can you conclude that the correlation coefficient differs from zero?

A)Yes,since the p-value exceeds 0.05.
B)Yes,since the test statistic value of 1.95 exceeds 0.05.
C)No,since the p-value exceeds 0.05.
D)No,since the test statistic value of 1.95 exceeds 0.05.

Question 32

Consider the following simple linear regression model: .The random error term is:

A)y
B)x
C)ε
D)β₀

Question 33

A regression equation was estimated as .If ,the predicted value of y is:

A)-80
B)-90
C)110
D)120

Question 34

The sample standard deviations for x and y are 10 and 15,respectively.The covariance between x and y is -300.The correlation coefficient between x and y is:

A)-2
B)-0.5
C)0.5
D)2

Question 35

Consider the following data: ,and .Calculate the sample correlation coefficient, .

A)-0.40
B)-0.20
C)0.20
D)0.40

Question 36

Consider the following data: ,and .Calculate the sample correlation coefficient, .

A)-0.40
B)-0.20
C)0.20
D)0.40

Question 37

Consider the following data: ,and .What is the sample regression equation?

A)
B)
C)
D)

Question 38

What is the name of the variable that's used to predict another variable?

A)Response
B)Explanatory
C)Coefficient of determination
D)Standard error of the estimate

Question 39

Consider the following simple linear regression model: ;β₀ and β₁ are:

A)the response variables.
B)the random error terms.
C)the unknown parameters.
D)the explanatory variables.

Question 40

Consider the following simple linear regression model: .The response variable is:

A)y
B)x
C)ε
D)β₀

Question 41

Calculate the value of given the ANOVA portion of the following regression output:

A)0.151
B)0.515
C)0.849
D)1.000

Question 42

Using the same data set,four models are estimated using the same response variable,however,the number of explanatory variables differs.Which model provides the best fit?

A)Model 1
B)Model 2
C)Model 3
D)Model 4

Question 43

In a simple linear regression model,if the plots on a scatter diagram lie on a straight line,what is the coefficient of determination?

A)-1
B)0
C)+1
D)Infinity

Question 44

Consider the sample regression equation: ,with an R² value of 0.81.What is the value of the correlation coefficient between x and y?

A)-0.90
B)-0.81
C)0.81
D)0.90

Question 45

In the estimation of a multiple regression model with two explanatory variables and 20 observations, and .What is the value of R²?

A)0.10
B)0.45
C)0.55
D)0.90

Question 46

In a simple linear regression model,if the plots on a scatter diagram lie on a straight line,what is the standard error of the estimate?

A)-1
B)0
C)+1
D)Infinity

Question 47

The standard error of the estimate measures

A)the variability of the explanatory variables.
B)the variability of the values of the sample regression coefficients.
C)the variability of the observed y-values around the predicted y-values.
D)the variability of the predicted y-values around the mean of the observed y-values.

Question 48

The coefficient of determination R² is ________.

A)sometimes negative.
B)always lower than adjusted R²
C)usually higher than adjusted R²
D)always equal to adjusted R²

Question 49

Consider the sample regression equation: ,with an R² value of 0.65.What is the value of the correlation coefficient between x and y?

A)-0.81
B)-0.65
C)0.81
D)0.65

Question 50

Which of the following is not true of the standard error of the estimate?

A)It can take on negative values.
B)Theoretically,its value has no predefined upper limit.
C)It is a measure of the accuracy of the regression model.
D)It is based on the squared deviations between the actual and predicted values of the response variable.

Question 51

The capital asset pricing model is given by: ,where = expected return on the market, = risk-free market return,and = expected return on a stock or portfolio of interest.The explanatory variable in this model is:

A) .
B) .
C) .
D)

Question 52

Consider the sample regression equation: .When x₁ increases 1 unit and x₂ increases 2 units,while x₃ and x₄ remain unchanged,what change would you expect in the predicted y?

A)Decrease by 2
B)Decrease by 4
C)Decrease by 7
D)No change in predicted y

Question 53

Consider the sample regression equation: .When x₁ increases 1 unit and x₂ increases 2 units,while x₃ and x₄ remain unchanged,what change would you expect in the predicted y?

A)Decrease by 2
B)Decrease by 10
C)Increase by 2
D)No change in the predicted y

Question 54

The R² of a multiple regression of y on x₁ and x₂ measures the

A)Percent variability of y that is explained by the variability of x₁.
B)Percent variability of y that is explained by the variability of x₂
C)Statistical significance of the coefficients in the regression equation.
D)Percent variability of y that is explained by the variability of x₁ and x₂.

Question 55

Given the augmented Phillips model: ,where y = actual rate of inflation (%),x₁ = unemployment rate (%),and x₂ = anticipated inflation rate (%).The explanatory variable(s)in this model is(are)the:

A)Unemployment rate
B)Actual inflation rate
C)Anticipated inflation rate
D)Unemployment rate and anticipated inflation rate

Question 56

The standard error of the estimate measures

A)the standard deviation of the residuals.
B)the standard deviation of the response variable.
C)the standard deviation of the explanatory variable.
D)the standard deviation of the correlation coefficient.

Question 57

The capital asset pricing model is given by: ,where = expected return on the market, = risk-free market return,and = expected return on a stock or portfolio of interest.The response variable in this model is:

A) .
B) .
C) .
D)

Question 58

A simple linear regression of the return of firm A ( )on the return of firm B ( ),based on 18 observations,is = 2.2 + 0.4 .If the coefficient of determination from this regression is 0.09 calculate the correlation between and .

A)0.03
B)0.04
C)0.09
D)0.30

Question 59

When two regression models applied on the same data set have the same response variable but a different number of explanatory variables,the model that would evidently provide the better fit is the one with a

A)Lower standard error of the estimate and a higher coefficient of determination.
B)Higher standard error of the estimate and a higher coefficient of determination.
C)Higher coefficient of determination and a lower adjusted coefficient of determination.
D)Lower standard error of the estimate and a higher adjusted coefficient of determination.

Question 60

Unlike the coefficient of determination,the coefficient of correlation in a simple linear regression

A)Can never have an absolute value greater than 1.
B)Measures the percentage of variation explained by the regression line.
C)Indicates whether the slope of the regression line is positive or negative.
D)Measures the strength of association between the two variables more exactly.

Question 61

Exhibit 14-5.An marketing analyst wants to examine the relationship between sales (in $1,000s)and advertising (in $100s)for firms in the food and beverage industry and collects monthly data for 25 firms.He estimates the model .The following table below shows a portion of the regression results. Refer to Exhibit 14-5.Calculate the coefficient of determination.

A)0.1348
B)0.1558
C)0.8442
D)0.8652

Question 62

Exhibit 14-5.An marketing analyst wants to examine the relationship between sales (in $1,000s)and advertising (in $100s)for firms in the food and beverage industry and collects monthly data for 25 firms.He estimates the model .The following table below shows a portion of the regression results. Refer to Exhibit 14-5.Interpret the slope coefficient.

A)If Advertising goes up by $100,then on average,Sales go up by $2,880.
B)If Sales go up by $100,then on average,Advertising goes up by $2,880.
C)If Advertising goes up by $100,then on average,Sales go up by $4,298.
D)If Sales go up by $100,then on average,Advertising goes up by $4,298.

Question 63

Exhibit 14-2.A statistics student is asked to estimate .She calculates the following values. Refer to Exhibit 14-2.What is the sample regression equation?

A)
B)
C)
D)

Question 64

In the estimation of a multiple regression model with two explanatory variables and 20 observations, and .The value of adjusted R² is closest to:

A)0.39
B)0.45
C)0.55
D)0.61

Question 65

Exhibit 14-3.Consider the following sample regression equation ,where y is the demand for Product A (in 1000s)and x is the price of the product (in $). Refer to Exhibit 14-3.If the price of Product A is $5,then we expect demand to be

A)50
B)500
C)5,000
D)50,000.

Question 66

Exhibit 14-2.A statistics student is asked to estimate .She calculates the following values. Refer to Exhibit 14-2.Calculate b₁.

A)-1.29
B)-0.51
C)0.51
D)1.29

Question 67

In the estimation of a multiple regression model with four explanatory variables and 25 observations, and .What is the value of R²?

A)0.16
B)0.34
C)0.66
D)0.84

Question 68

Exhibit 14-6.A manager at a local bank analyzed the relationship between monthly salary (y,in $)and length of service (x,measured in months)for 30 employees.She estimates .The following table summarizes a portion of the regression results: Refer to Exhibit 14-6.The monthly salary of an employee that has worked for 48 months at the bank is closest to:

A)$441.
B)$785.
C)$1050.
D)$1226.

Question 69

In the estimation of a multiple regression model with four explanatory variables and 25 observations, and .The value of adjusted R² is closest to:

A)0.21
B)0.34
C)0.66
D)0.79

Question 70

Exhibit 14-1.Over the past 30 years,the sample standard deviations of the rates of return for stock X and Stock Y were 0.20 and 0.12,respectively.The sample covariance between the returns of X and Y is 0.0096. Refer to Exhibit 14-1.The correlation of the rates of return between X and Y is closest to:

A)0.20
B)0.24
C)0.36
D)0.40

Question 71

Exhibit 14-1.Over the past 30 years,the sample standard deviations of the rates of return for stock X and Stock Y were 0.20 and 0.12,respectively.The sample covariance between the returns of X and Y is 0.0096. Refer to Exhibit 14-1.When testing whether the correlation coefficient differs from zero,the value of the test statistic is .At the 5% significance level,the critical value is .The conclusion to the hypothesis test is to:

A)Reject H₀;we can conclude that the correlation coefficient differs from zero.
B)Reject H₀;we cannot conclude that the correlation coefficient differs from zero.
C)Do not reject H₀;we can conclude that the correlation coefficient differs from zero.
D)Do not reject H₀;we cannot conclude that the correlation coefficient differs from zero.

Question 72

Exhibit 14-4.Consider the following sample regression equation ,where y is the supply for Product A (in 1000s)and x is the price of Product A (in $). Refer to Exhibit 14-4.If the price of Product A increases by $3,then we expect the supply for Product A to

A)increase by 30.
B)decrease by 30.
C)increase by 30,000.
D)decrease by 30,000.

Question 73

Exhibit 14-4.Consider the following sample regression equation ,where y is the supply for Product A (in 1000s)and x is the price of Product A (in $). Refer to Exhibit 14-4.If the price of Product A is $5,then we expect supply to be

A)250
B)2,500
C)25,000
D)250,000.

Question 74

Exhibit 14-3.Consider the following sample regression equation ,where y is the demand for Product A (in 1000s)and x is the price of the product (in $). Refer to Exhibit 14-3.If the price of the good increases by $3,then we expect demand for Product A to

A)increase by 60.
B)decrease by 60.
C)decrease by 60000.
D)increase by 60000.

Question 75

Exhibit 14-2.A statistics student is asked to estimate .She calculates the following values. Refer to Exhibit 14-2.What is y if x equals 2?

A)6.62
B)11.78
C)58.22
D)63.38

Question 76

Exhibit 14-1.Over the past 30 years,the sample standard deviations of the rates of return for stock X and Stock Y were 0.20 and 0.12,respectively.The sample covariance between the returns of X and Y is 0.0096. Refer to Exhibit 14-1.In order to determine whether the correlation coefficient is significantly different from zero,the appropriate hypotheses are:

A)
B)
C)
D)

Question 77

Exhibit 14-5.An marketing analyst wants to examine the relationship between sales (in $1,000s)and advertising (in $100s)for firms in the food and beverage industry and collects monthly data for 25 firms.He estimates the model .The following table below shows a portion of the regression results. Refer to Exhibit 14-5.Predict Sales for a firm with Advertising of $500.

A)$1,480
B)$40,100
C)$54,500
D)$148,000

Question 78

Exhibit 14-4.Consider the following sample regression equation ,where y is the supply for Product A (in 1000s)and x is the price of Product A (in $). Refer to Exhibit 14-4.The slope coefficient indicates that if

A)the price of Product A increases by $1,then on average,supply decreases by 10.
B)the price of Product A increases by $1,then on average,supply increases by 10.
C)the price of Product A increases by $1,then on average,supply decreases by 10,000.
D)the price of Product A increases by $1,then on average,supply increases by 10,000.

Question 79

Exhibit 14-5.An marketing analyst wants to examine the relationship between sales (in $1,000s)and advertising (in $100s)for firms in the food and beverage industry and collects monthly data for 25 firms.He estimates the model .The following table below shows a portion of the regression results. Refer to Exhibit 14-5.Calculate the standard error of the estimate.

A)4.68
B)8.86
C)21.91
D)78.53

Question 80

Exhibit 14-3.Consider the following sample regression equation ,where y is the demand for Product A (in 1000s)and x is the price of the product (in $). Refer to Exhibit 14-3.The slope coefficient indicates that if

A)the price of Product A increases by $1,then on average,demand decreases by 20.
B)the price of Product A increases by $1,then on average,demand increases by 20.
C)the price of Product A increases by $1,then on average,demand decreases by 20000.
D)the price of Product A increases by $1,then on average,demand increases by 20000.