Deck 14: Regression Analysis

Question 1

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.

Answer 1

False

Question 2

Simple linear regression includes more than one explanatory variable.

Answer 2

False

Question 3

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

Answer 3

True

Question 4

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

Question 5

In the simple linear regression model,β₀ is the y-intercept of the line y =β₀ + β₁x+ ε.

Question 6

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

Question 7

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

Question 8

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

Question 9

_______ correlation can make two variables appear closely related when no casual relation exists.

Question 10

In testing the population correlation coefficient,the alternative hypothesis is H_A: ρ_xy ≠ 1.

Question 11

Another name for an explanatory variable is the dependent variable.

Question 12

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

Question 13

The correlation coefficient captures only a ______ relationship.

Question 14

The actual value y may differ from the expected value E(y).Therefore,we add a ______ ____ term ε to develop a simple linear regression model.

Question 15

The correlation coefficient can only range between 0 and 1.

Question 16

The simple linear regression model can be written in the form y = β₀ + β₁x₁ + β₂x₂ + ε.

Question 17

The sample correlation coefficient cannot equal zero.

Question 18

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

Question 19

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

Question 20

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

Question 21

A regression equation was estimated as = 155 - 34x₁ - 12x_2.If x₁ = 3 and x₂ = 2,the predicted value of y would be _____.

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

Question 22

Which of the following statements is the leastaccurate 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 23

The relationship between the response variable and the explanatory variables is _________ if the value of the response variable is uniquely determined by the explanatory variables.

Question 24

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 25

With regression analysis,we explicitly assume that one variable,called the _______ variable,is influenced by other variable,called the explanatory variable.

Question 26

Consider the following simple linear regression model: y = β₀ + β₁x +ε.The response variable is ____.

A) y
B) x
C) ε
D) β₀

Question 27

The _______ regression model allows us to study how the response variable is influenced by two or more explanatory variables.

Question 28

If _____ is substantially greater than zero and the number of explanatory variables is large compared with sample size,then the adjusted R² will differ substantially from R².

Question 29

We use ______ to derive the coefficient of determination.

Question 30

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 these choices is correct.

Question 31

When testing whether the correlation coefficient differs from zero,the value of the test statistic is t₂₀ = -2.95 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 32

The following scatterplot indicates 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 33

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 34

When testing whether the correlation coefficient differs from zero,the value of the test statistic is t₂₀ = 1.95 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 35

The numerical measure that gauges dispersion from the sample regression equation is the sample _______ of the residual.

Question 36

A regression equation was estimated as = -100 + 0.5x.If x = 20,the predicted value of y is _____.

A) −80
B) −90
C) 110
D) 120

Question 37

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

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

Question 38

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 39

The following scatterplot indicates 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 40

The sample standard deviations for x and y are 10 and 15,respectively.The covariance between x and y is −120.The correlation coefficient between x and y is _____.

A) −0.8
B) −0.5
C) 0.5
D) 0.8

Question 41

Consider the sample regression equation 100 + 10x,with an R² value of 0.81.Which of the following is the value of the sample correlation between y and ?

A) −0.90
B) −0.81
C) 0.81
D) 0.90

Question 42

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

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

Question 43

Given the augmented Phillips model: y = β₀ + β₁x₁+β₂x₂ +ε,where y = actual rate of inflation (%),x₁ = unemployment rate (%),and x₂ = anticipated inflation rate (%).The response variable or variables(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 44

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 45

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 46

The capital asset pricing model is given by R - R_F = α + β(R_M - R_f)+ ε,where R_M = expected return on the market,R_f = risk-free market return,and R = expected return on a stock or portfolio of interest.The response variable in this model is ________.

A) R
B) R - R_f
C) R_M
D) R_M - R_f

Question 47

In the sample regression equation = b₀ + b₁x,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 48

Consider the following data: = 20,s_x = 2, = -5,s_y = 4,and b₁ = -0.8.Which of the following is the sample regression equation?

A)
B)
C)
D)

Question 49

Consider the following simple linear regression model: y = β₀ + β₁x +ε.β₀ and β₁ are __________________.

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

Question 50

Given the augmented Phillips model: Given the augmented Phillips model: y = β₀ + β₁x₁+β₂x₂ +ε,where y = actual rate of inflation (%),x₁ = unemployment rate (%),and x₂ = anticipated inflation rate (%).The response variable or variables(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 51

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

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

Question 52

Calculate the value of R² given the ANOVA portion of the following regression output:

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

Question 53

Consider the following simple linear regression model: y = β₀ + β₁x +ε.The explanatory variable is ____.

A) y
B) x
C) ε
D) β₀

Question 54

Consider the following data: = 20,s_x = 2, = -5,s_y = 4,and b₁ = 0.40.Which of the following is the sample regression equation?

A)
B)
C)
D)

Question 55

Consider the following data: = 20,s_x =2, = -5,s_y =4,and b₁ = -0.8.The sample correlation coefficient,r_xy is equal to ____.

A) −0.40
B) −0.20
C) 0.20
D) 0.40

Question 56

Consider the sample regression equation = 10 - 5x,with an R² value of 0.65.Which of the following is the value of the sample correlation between y and ?

A) −0.81
B) −0.65
C) 0.81
D) 0.65

Question 57

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 58

The capital asset pricing model is given by R - R_F = α + β(R_M - R_f)+ ε,where R_M = expected return on the market,R_f = risk-free market return,and R = expected return on a stock or portfolio of interest.The explanatory variable in this model is _________.

A) R
B) R - R_f
C) R_M
D) R_M - R_f

Question 59

Consider the following data: = 20,s_x = 2, = -5,s_y = 4,and b₁ = 0.40.The sample correlation coefficient,r_xy is equal to ____.

A) −0.40
B) −0.20
C) 0.20
D) 0.40

Question 60

Consider the following simple linear regression model: y = β₀ + β₁x +ε.The random error term is ____.

A) y
B) x
C) ε
D) β₀

Question 61

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

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

Question 62

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

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

Question 63

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.To determine whether the correlation coefficient is significantly different from zero,the appropriate hypotheses are: ____________.

A)
B)
C)
D)

Question 64

Consider the sample regression equation = 12 + 3x₁ - 5x₂ + 7x₃ - 2x₄.When x₁ increases by 1 unit and x₂ increases by 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 65

In the estimation of a multiple regression model with four explanatory variables and 25 observations,SSE = 660 and SST = 1,000.The value of adjusted R² is the closest to ____.

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

Question 66

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.When testing whether the correlation coefficient differs from zero,the value of the test statistic is t₂₈ = 2.31.At the 5% significance level,the critical value is t_0.025,28 = 2.048.The conclusion to the hypothesis test is to ___________.

A) to reject H₀;we can conclude that the correlation coefficient differs from zero.
B) to 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 67

Over the past 30 years,the sample standard deviations of the rates of return for stock X and sStock Y were 0.20 and 0.12,respectively.The sample covariance between the returns of X and Y is 0.0096.The correlation of the rates of return between X and Y is the closest to ____.

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

Question 68

A statistics student is asked to estimate y = β₀ + β₁x + ε.She calculates the following values: = 440, , = 1,120,n = 11.The value of the slope b₁ is ____.

A) −1.29
B) −0.51
C) 0.51
D) 1.29

Question 69

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 70

Consider the following sample regression equation = 150 - 20x,where y is the demand for Product A (in 1,000s)and x is the price of the product (in $).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 71

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 72

A statistics student is asked to estimate y = β₀ + β₁x + ε.She calculates the following values: = 440, , = 1,120,n = 11.Which of the following is the value of y if x equals 2?

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

Question 73

A statistics student is asked to estimate y = β₀ + β₁x + ε.She calculates the following values: = 440, , = 1,120,n = 11.Which of the following is the sample regression equation?

A)
B)
C)
D)

Question 74

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 75

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 76

Consider the following sample regression equation = 150 - 20x,where y is the demand for Product A (in 1,000s)and x is the price of the product (in $).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 20,000
D) the price of Product A increases by $1,then on average,demand increases by 20,000

Question 77

Consider the sample regression equation: = 12 + 2x₁ - 6x₂ + 6x₃ + 2x₄.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 78

In the estimation of a multiple regression model with four explanatory variables and 25 observations,SSE = 660 and SST = 1,000.Which of the following is the correct value of R²?

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

Question 79

In the estimation of a multiple regression model with two explanatory variables and 20 observations,SSE = 550 and SST = 1,000.The value of adjusted R² is the closest to ____.

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

Question 80

In the estimation of a multiple regression model with two explanatory variables and 20 observations,SSE = 550 and SST = 1000.Which of the following is the correct value of R²?

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