Question 1

If two individuals have the same observed score on the dependent variable Y, their residual scores will be which one of the following?

Accepted Answer

A)  Always be equal. 
B)  Be equal only when they have the same score on X. 
C)  Be equal only when the slope equals zero. 
D)  Both b and c 
A)  Always be equal. 
B)  Be equal only when they have the same score on X. 
C)  Be equal only when the slope equals zero. 
D)  Both b and c D

Question 2

It is known that $\mu$X = 1.5, $\sigma$X2 = 25, $\mu$Y = 10, $\sigma$Y2 = 0. A simple linear regression model was estimated. Which of the following is the variance of the predicted values of Y?

Accepted Answer

A)  0 
B)  15 
C)  25 
D)  250 
E)  It depends on the correlation between X and Y. 
A)  0 
B)  15 
C)  25 
D)  250 
E)  It depends on the correlation between X and Y. A

Question 3

In the scenario as described in Question 3, Sarah now used the regression line she obtained to predict the weight of her three-year old niece, who is 34 inches tall. The predicted weight for her niece, however, turned out to be 0 lb. What is the problem with Sarah's prediction?

Accepted Answer

A)  Sarah must have incorrectly estimated the intercept of the regression line. 
B)  The regression line was correct, but a computational error was made in the prediction. 
C)  Sarah should have included the error term (ei) in the regression model when she made the prediction. 
D)  Sarah was extrapolating beyond the sample predictor data. 
E)  There is no problem with Sarah's prediction. This is how statistics work. 
A)  Sarah must have incorrectly estimated the intercept of the regression line. 
B)  The regression line was correct, but a computational error was made in the prediction. 
C)  Sarah should have included the error term (ei) in the regression model when she made the prediction. 
D)  Sarah was extrapolating beyond the sample predictor data. 
E)  There is no problem with Sarah's prediction. This is how statistics work. D

Question 4

Bob and Brian both used simple linear regression to predict the consumption of ice cream (ml/person) (Y) based on temperature (°F) (X). However, they used two different data sets to estimate the model: Bob's sample includes only children younger than 12 (rXY = 0.6), while Brian's sample includes only adult consumers (rXY = 0.4). Which of the following statements is always true?

Accepted Answer

A)  Bob and Brian will get different estimates of intercept. 
B)  Bob and Brian will get different estimates of slope. 
C)  Bob and Brian will get different prediction equations. 
D)  Bob and Brian will get different R2 for their models. 
A)  Bob and Brian will get different estimates of intercept. 
B)  Bob and Brian will get different estimates of slope. 
C)  Bob and Brian will get different prediction equations. 
D)  Bob and Brian will get different R2 for their models.

Question 5

In a simple linear regression, if SSres = 150 and SStotal = 200, what is the proportion of variation in Y that is predictable from X?

Accepted Answer

A)  25% 
B)  42.86% 
C)  56.25% 
D)  75% 
A)  25% 
B)  42.86% 
C)  56.25% 
D)  75%

Question 6

The prediction equation for predicting Y (the amount of ice cream in pints consumed per person) from X (temperature in Fahrenheit) is Y' = 0.003X + 0.2. What is the observed mean for Y if $\mu$X = 70 and $\sigma$X2 = 25?

Accepted Answer

Because prediction equation is

Question 7

If rXY = 1, which of the following statements is true?

Accepted Answer

A)  All points will fall on the regression line. 
B)  The regression line will have an intercept of 0. 
C)  The regression line will have a slope of 1. 
D)  The prediction of future observations will be 100% accurate. 
A)  All points will fall on the regression line. 
B)  The regression line will have an intercept of 0. 
C)  The regression line will have a slope of 1. 
D)  The prediction of future observations will be 100% accurate.

Question 8

You are given the following pairs of scores on X (Percentage of students whose families are below poverty line) and Y (Percentage of students at or above proficiency level) for nine schools.
a. Find the linear regression model for predicting Y from X.
 $\begin{array}{cc}
\hline X & Y \
\hline 92.3 & 18.9 \
0.9 & 87.3 \
25.1 & 48.0 \
67.1 & 45.4 \
24.7 & 80.2 \
90.7 & 13.7 \
44.0 & 26.9 \
65.5 & 58.6 \
40.6 & 46.3 \
\hline
\end{array}$ 
b. Use the prediction model obtained to predict the value of Y for a school that has 50% of students whose families are below the poverty line.

Accepted Answer

(a) Intercept a = 80.177, slope b = -.65

Question 9

In simple linear regression, if the slope is found to be -0.002,

Accepted Answer

A)  the value of Y is equal to -.002 when X is 0. 
B)  the value of Y is equal to -.002 when X is 1. 
C)  the value of Y will decrease by 0.002 units when X increases by 1 unit. 
D)  there is a negative, but very weak relationship between X and Y. 
A)  the value of Y is equal to -.002 when X is 0. 
B)  the value of Y is equal to -.002 when X is 1. 
C)  the value of Y will decrease by 0.002 units when X increases by 1 unit. 
D)  there is a negative, but very weak relationship between X and Y.

Question 10

Doug wanted to use simple linear regression to study the relation between the time to complete a marathon (in hours) (Y) and the fluid intake (in ml) during the race (X). Based on the same data set, he estimated two models.
Model 1: X1 = total amount of fluid intake; Y = .00028X1 + 3.97. R12 = .014.
Model 2: X2 = amount of fluid intake per hour; Y = -.0052X2 + 7.84. R22 = .65.
Suppose for both models, all assumptions for linear regression are satisfied. Compare the two models.

Accepted Answer

A)  Doug should use model 1, because the correlation between X1 and Y is stronger than that between X2 and Y (bYX1 > bYX2). 
B)  Doug should use model 2, because it gives more accurate prediction of Y (the finishing time) than model 1 (R12 22). 
C)  Doug should use model 1, because model 2 will give unreasonable (negative) predicted values of Y when X is large. 
D)  Both models are problematic, because the units of X are different from the unit of Y. 
A)  Doug should use model 1, because the correlation between X1 and Y is stronger than that between X2 and Y (bYX1 > bYX2). 
B)  Doug should use model 2, because it gives more accurate prediction of Y (the finishing time) than model 1 (R12 22). 
C)  Doug should use model 1, because model 2 will give unreasonable (negative) predicted values of Y when X is large. 
D)  Both models are problematic, because the units of X are different from the unit of Y.

Question 11

You are given the following pairs of scores on X (Pretest score) and Y (Posttest score).
a. Find the linear regression model for predicting Y from X.
 $\begin{array}{cc}
\hline X& Y \
\hline 65 & 74 \
82 & 87 \
70 & 82 \
46 & 53 \
55 & 69 \
75 & 81 \
\hline
\end{array}$ 
b. Use the prediction model obtained to predict the value of Y for a new person who scored 80 on the pretest.

Accepted Answer

(a) Intercept a = 15.919, slope b = .892

Question 12

The prediction equation for predicting Y (the amount of ice cream in pints consumed per person) from X (temperature in Fahrenheit) is Y' = 0.003X + 0.2. What is the observed mean for Y if $\mu$X = 70 and $\sigma$X2 = 25?

Accepted Answer

Because prediction equation is

Question 13

The assumptions of the simple linear regression model do not include:

Accepted Answer

A)  The errors are normally distributed. 
B)  The errors have constant variance across different values of X. 
C)  The errors are independent of each other. 
D)  The errors have mean of 0 and variance of 1. 
A)  The errors are normally distributed. 
B)  The errors have constant variance across different values of X. 
C)  The errors are independent of each other. 
D)  The errors have mean of 0 and variance of 1.

Question 14

It is known that rXY = 0.5, sX2 = 1, sY2 = 1. A simple linear regression model is estimated. The regression line will have a slope of which one of the following?

Accepted Answer

A)  0 
B)  0.5 
C)  0.5 or -0.5 
D)  1 or -1 
E)  It depends on the values of $\bar{X}$ and $\bar{Y}$ . 
A)  0 
B)  0.5 
C)  0.5 or -0.5 
D)  1 or -1 
E)  It depends on the values of $\bar{X}$ and $\bar{Y}$ .

Question 15

In the scenario described in Question 13, suppose Bob and Brian have both converted their data to z score scale and estimated regression models using the standardized scores. Which of the following statements is false?

Accepted Answer

A)  Bob and Brian will get different estimates of intercept. 
B)  Bob and Brian will get different estimates of slope. 
C)  Bob and Brian will get different prediction equations. 
D)  Bob and Brian will get different R2 for their model. 
A)  Bob and Brian will get different estimates of intercept. 
B)  Bob and Brian will get different estimates of slope. 
C)  Bob and Brian will get different prediction equations. 
D)  Bob and Brian will get different R2 for their model.

Question 16

You are given the following pairs of scores on X (Percentage of students whose families are below poverty line) and Y (Percentage of students at or above proficiency level) for nine schools.
a. Find the linear regression model for predicting Y from X.
 $\begin{array}{cc}
\hline X & Y \
\hline 92.3 & 18.9 \
0.9 & 87.3 \
25.1 & 48.0 \
67.1 & 45.4 \
24.7 & 80.2 \
90.7 & 13.7 \
44.0 & 26.9 \
65.5 & 58.6 \
40.6 & 46.3 \
\hline
\end{array}$ 
b. Use the prediction model obtained to predict the value of Y for a school that has 50% of students whose families are below the poverty line.

Accepted Answer

(a) Intercept a = 80.177, slope b = -.65

Question 17

In a study of the relation between hours watching TV per day (X) and scores on the final exam (Y), the equation of regression line is found to be Y' = -7X + 100. Suppose Jamie watches TV two hours per day, and he scored a 91 on the exam. What is the residual score for Jamie?

Accepted Answer

A)  -7 
B)  -5 
C)  0 
D)  5 
E)  100 
A)  -7 
B)  -5 
C)  0 
D)  5 
E)  100

Question 18

You are given the following pairs of scores on X (height in inches) and Y (weight in lbs).
Perform the following computations using $\alpha$ = .05.
 $\begin{array}{cc}
X & Y \
\hline 66 & 140 \
69 & 155 \
72 & 195 \
74 & 160 \
72 & 155 \
67 & 145 \
66 & 135 \
71 & 170 \
70 & 130 \
68 & 170 \
72 & 190 \
69 & 145 \
73 & 155 \
68 & 150 \
68 & 130 \
69 & 145 \
69 & 150 \
66 & 120 \
62 & 131 \
62 & 120 \
64 & 102 \
68 & 110 \
63 & 116 \
64 & 125 \
62 & 110 \
\hline
\end{array}$ 
a. The regression equation of Y predicted by X.
b. Test of the significance of X as a predictor.
c. Plot Y versus X.
d. Compute the residuals.
e. Plot residuals versus X.

Accepted Answer

(a) Intercept a = -199.139, slope b = 5.

Question 19

It is known that $\mu$X = 10, $\sigma$X2 = 16, $\mu$Y = 52, $\sigma$Y2 = 8, $\rho$XY = 0. A simple linear regression model is estimated. Which of the following statements is true?

Accepted Answer

A)  X and Y are completely unrelated. 
B)  The slope of the regression model will be zero. 
C)  The intercept of the regression model will be zero. 
D)  The prediction of Y based on the linear model will be very accurate. 
A)  X and Y are completely unrelated. 
B)  The slope of the regression model will be zero. 
C)  The intercept of the regression model will be zero. 
D)  The prediction of Y based on the linear model will be very accurate.

Question 20

In simple linear regression, the assumption of normality states that

Accepted Answer

A)  the observed scores on Y are normally distributed. 
B)  the conditional distributions of Y are normal in shape. 
C)  the observed scores on X are normally distributed. 
D)  the distributions of regression coefficients are normal in shape. 
E)  there are no outliers. 
A)  the observed scores on Y are normally distributed. 
B)  the conditional distributions of Y are normal in shape. 
C)  the observed scores on X are normally distributed. 
D)  the distributions of regression coefficients are normal in shape. 
E)  there are no outliers.

If two individuals have the same observed score on the dependent variable Y, their residual scores will be which one of the following?

It is known that $\mu$ _X = 1.5, $\sigma$ _X² = 25, $\mu$ _Y = 10, $\sigma$ _Y² = 0. A simple linear regression model was estimated. Which of the following is the variance of the predicted values of Y?

In the scenario as described in Question 3, Sarah now used the regression line she obtained to predict the weight of her three-year old niece, who is 34 inches tall. The predicted weight for her niece, however, turned out to be 0 lb. What is the problem with Sarah's prediction?

In a simple linear regression, if SS_res = 150 and SS_total = 200, what is the proportion of variation in Y that is predictable from X?

The prediction equation for predicting Y (the amount of ice cream in pints consumed per person) from X (temperature in Fahrenheit) is Y' = 0.003X + 0.2. What is the observed mean for Y if $\mu$ _X = 70 and $\sigma$ _X² = 25?

If r_XY = 1, which of the following statements is true?

In simple linear regression, if the slope is found to be -0.002,

You are given the following pairs of scores on X (Pretest score) and Y (Posttest score). a. Find the linear regression model for predicting Y from X. X Y 65 74 82 87 70 82 46 53 55 69 75 81 b. Use the prediction model obtained to predict the value of Y for a new person who scored 80 on the pretest.

The prediction equation for predicting Y (the amount of ice cream in pints consumed per person) from X (temperature in Fahrenheit) is Y' = 0.003X + 0.2. What is the observed mean for Y if $\mu$ _X = 70 and $\sigma$ _X² = 25?

The assumptions of the simple linear regression model do not include:

It is known that r_XY = 0.5, s_X² = 1, s_Y² = 1. A simple linear regression model is estimated. The regression line will have a slope of which one of the following?

In the scenario described in Question 13, suppose Bob and Brian have both converted their data to z score scale and estimated regression models using the standardized scores. Which of the following statements is false?

In a study of the relation between hours watching TV per day (X) and scores on the final exam (Y), the equation of regression line is found to be Y' = -7X + 100. Suppose Jamie watches TV two hours per day, and he scored a 91 on the exam. What is the residual score for Jamie?

It is known that $\mu$ _X = 10, $\sigma$ _X² = 16, $\mu$ _Y = 52, $\sigma$ _Y² = 8, $\rho$ _XY = 0. A simple linear regression model is estimated. Which of the following statements is true?

In simple linear regression, the assumption of normality states that

Introduction

Data Representation

Univariate Population Parameters and Sample Statistics

Normal Distribution and Standard Scores

Introduction to Probability and Sample Statistics

Inferences About a Single Mean

Inferences About the Difference Between Two Means

Inferences About Proportions

Inferences About Variances

Bivariate Measures of Association

One-Factor Anova: Fixed-Effects Model

Multiple Comparison Procedures

Factorial Anova: Fixed-Effects Model

One-Factor Fixed-Effects Ancova With Single Covariate

Random- and Mixed-Effects Analysis of Variance Models

Hierarchical and Randomized Block Analysis of Variance Models

Multiple Regression

Logistic Regression

Filters

Exam 17: Simple Linear Regression

If two individuals have the same observed score on the dependent variable Y, their residual scores will be which one of the following?

It is known that μ\muμ X = 1.5, σ\sigmaσ X2 = 25, μ\muμ Y = 10, σ\sigmaσ Y2 = 0. A simple linear regression model was estimated. Which of the following is the variance of the predicted values of Y?

In the scenario as described in Question 3, Sarah now used the regression line she obtained to predict the weight of her three-year old niece, who is 34 inches tall. The predicted weight for her niece, however, turned out to be 0 lb. What is the problem with Sarah's prediction?

In a simple linear regression, if SSres = 150 and SStotal = 200, what is the proportion of variation in Y that is predictable from X?

The prediction equation for predicting Y (the amount of ice cream in pints consumed per person) from X (temperature in Fahrenheit) is Y' = 0.003X + 0.2. What is the observed mean for Y if μ\muμ X = 70 and σ\sigmaσ X2 = 25?

If rXY = 1, which of the following statements is true?

In simple linear regression, if the slope is found to be -0.002,

You are given the following pairs of scores on X (Pretest score) and Y (Posttest score). a. Find the linear regression model for predicting Y from X. X Y 65 74 82 87 70 82 46 53 55 69 75 81 b. Use the prediction model obtained to predict the value of Y for a new person who scored 80 on the pretest.

The prediction equation for predicting Y (the amount of ice cream in pints consumed per person) from X (temperature in Fahrenheit) is Y' = 0.003X + 0.2. What is the observed mean for Y if μ\muμ X = 70 and σ\sigmaσ X2 = 25?

The assumptions of the simple linear regression model do not include:

It is known that rXY = 0.5, sX2 = 1, sY2 = 1. A simple linear regression model is estimated. The regression line will have a slope of which one of the following?

In the scenario described in Question 13, suppose Bob and Brian have both converted their data to z score scale and estimated regression models using the standardized scores. Which of the following statements is false?

In a study of the relation between hours watching TV per day (X) and scores on the final exam (Y), the equation of regression line is found to be Y' = -7X + 100. Suppose Jamie watches TV two hours per day, and he scored a 91 on the exam. What is the residual score for Jamie?

It is known that μ\muμ X = 10, σ\sigmaσ X2 = 16, μ\muμ Y = 52, σ\sigmaσ Y2 = 8, ρ\rhoρ XY = 0. A simple linear regression model is estimated. Which of the following statements is true?

In simple linear regression, the assumption of normality states that

Introduction

Data Representation

Univariate Population Parameters and Sample Statistics

Normal Distribution and Standard Scores

Introduction to Probability and Sample Statistics

Inferences About a Single Mean

Inferences About the Difference Between Two Means

Inferences About Proportions

Inferences About Variances

Bivariate Measures of Association

One-Factor Anova: Fixed-Effects Model

Multiple Comparison Procedures

Factorial Anova: Fixed-Effects Model

One-Factor Fixed-Effects Ancova With Single Covariate

Random- and Mixed-Effects Analysis of Variance Models

Hierarchical and Randomized Block Analysis of Variance Models

Multiple Regression

Logistic Regression

Filters

It is known that $\mu$ _X = 1.5, $\sigma$ _X² = 25, $\mu$ _Y = 10, $\sigma$ _Y² = 0. A simple linear regression model was estimated. Which of the following is the variance of the predicted values of Y?

In a simple linear regression, if SS_res = 150 and SS_total = 200, what is the proportion of variation in Y that is predictable from X?

The prediction equation for predicting Y (the amount of ice cream in pints consumed per person) from X (temperature in Fahrenheit) is Y' = 0.003X + 0.2. What is the observed mean for Y if $\mu$ _X = 70 and $\sigma$ _X² = 25?

If r_XY = 1, which of the following statements is true?

The prediction equation for predicting Y (the amount of ice cream in pints consumed per person) from X (temperature in Fahrenheit) is Y' = 0.003X + 0.2. What is the observed mean for Y if $\mu$ _X = 70 and $\sigma$ _X² = 25?

It is known that r_XY = 0.5, s_X² = 1, s_Y² = 1. A simple linear regression model is estimated. The regression line will have a slope of which one of the following?

It is known that $\mu$ _X = 10, $\sigma$ _X² = 16, $\mu$ _Y = 52, $\sigma$ _Y² = 8, $\rho$ _XY = 0. A simple linear regression model is estimated. Which of the following statements is true?