Question 1

In regression analysis, if the coefficient of determination is 1.0, then:

Accepted Answer

A)  the sum of squares for error must be 1.0. 
B)  the sum of squares for regression must be 1.0. 
C)  the sum of squares for error must be 0.0. 
D)  the sum of squares for regression must be 0.0. 
A)  the sum of squares for error must be 1.0. 
B)  the sum of squares for regression must be 1.0. 
C)  the sum of squares for error must be 0.0. 
D)  the sum of squares for regression must be 0.0.

Question 2

Given the data points (x,y) = (3,3), (4,4), (5,5), (6,6), (7,7), the least squares estimates of the y-intercept and slope are respectively:

Accepted Answer

A)  0 and 1. 
B)  -1 and 0. 
C)  5 and 5. 
D)  5 and 0. 
A)  0 and 1. 
B)  -1 and 0. 
C)  5 and 5. 
D)  5 and 0.

Question 3

Which of the following statements best describes why a linear regression is also called a least squares regression model?

Accepted Answer

A)  A linear regression is also called a least squares regression model because the regression line is calculated by minimizing the square of the difference between each actual x data value and the predicted x value. 
B)  A linear regression is also called a least squares regression model because the regression line is calculated by minimizing the sum of the difference between each actual y data value and the predicted y value. 
C)  A linear regression is also called a least squares regression model because the regression line is calculated by minimizing the square of each actual y data value and the predicted y value. 
D)  why a A linear regression is also called a least squares regression model because the regression line is calculated by minimizing the sum of the square of the differences between each actual y data value and the predicted y value. 
A)  A linear regression is also called a least squares regression model because the regression line is calculated by minimizing the square of the difference between each actual x data value and the predicted x value. 
B)  A linear regression is also called a least squares regression model because the regression line is calculated by minimizing the sum of the difference between each actual y data value and the predicted y value. 
C)  A linear regression is also called a least squares regression model because the regression line is calculated by minimizing the square of each actual y data value and the predicted y value. 
D)  why a A linear regression is also called a least squares regression model because the regression line is calculated by minimizing the sum of the square of the differences between each actual y data value and the predicted y value.

Question 4

Pop-up coffee vendors have been popular in the city of Adelaide in 2013. A vendor is interested in knowing how temperature (in degrees Celsius) impacts daily hot coffee sales revenue (in $00's).
A random sample of 6 days was taken, with the daily hot coffee sales revenue and the corresponding temperature of that day noted. $$\begin{array} { | c | c | } 
\hline \text { Coffee sales revenue } & \text { Temperature } \
\hline 6.50 & 25 \
\hline 10.00 & 17 \
\hline 5.50 & 30 \
\hline 4.50 & 35 \
\hline 3.50 & 40 \
\hline 28.00 & 9 \
\hline
\end{array}$$ a. Find the least squares regression line.
b. Interpret the slope.

Accepted Answer

@#IMG-DLM& a. Estimated daily hot coffee sales rev

Question 5

The Pearson coefficient of correlation r equals 1 when there is/are no:

Accepted Answer

A)  explained variation. 
B)  unexplained variation. 
C)  y-intercept in the model. 
D)  outliers. 
A)  explained variation. 
B)  unexplained variation. 
C)  y-intercept in the model. 
D)  outliers.

Question 6

Given the least squares regression line y-hat = 3.52 - 1.27x, and a coefficient of determination of 0.81, the coefficient of correlation is:

Accepted Answer

A)  -0.85. 
B)  0.85. 
C)  -0.90. 
D)  0.90. 
A)  -0.85. 
B)  0.85. 
C)  -0.90. 
D)  0.90.

Question 7

A financier whose specialty is investing in movie productions has observed that, in general, movies with 'big-name' stars seem to generate more revenue than those movies whose stars are less well known. To examine his belief, he records the gross revenue and the payment (in $ million) given to the two highest-paid performers in the movie for 10 recently released movies. $$\begin{array} { | c | c | c | } 
\hline \text { Movie } & \begin{array} { c } 
\text { Cost of two highest- } \
\text { paid performers } ( \$ \mathrm {~m} )
\end{array} & \begin{array} { c } 
\text { Gross revenue } \
( \$ \mathrm {~m} )
\end{array} \
\hline 1 & 5.3 & 48 \
\hline 2 & 7.2 & 65 \
\hline 3 & 1.3 & 18 \
\hline 4 & 1.8 & 20 \
\hline 5 & 3.5 & 31 \
\hline 6 & 2.6 & 26 \
\hline 7 & 8.0 & 73 \
\hline 8 & 2.4 & 23 \
\hline 9 & 4.5 & 39 \
\hline 10 & 6.7 & 58 \
\hline
\end{array}$$ Assume that the conditions for the tests conducted in the previous two questions are not met. Do the data allow us to infer at the 5% significance level that payment to the two highest-paid performers and gross revenue are linearly related?

Accepted Answer

H₀ : @#LAT-DLM& _s = 0. H₁ : @#LAT-DLM& _s @#LAT-DLM& 0. Rejection

Question 8

A financier whose specialty is investing in movie productions has observed that, in general, movies with 'big-name' stars seem to generate more revenue than those movies whose stars are less well known. To examine his belief, he records the gross revenue and the payment (in $ million) given to the two highest-paid performers in the movie for 10 recently released movies. $$\begin{array} { | c | c | c | } 
\hline \text { Movie } & \begin{array} { c } 
\text { Cost of two highest- } \
\text { paid performers } ( \$ \mathrm {~m} )
\end{array} & \begin{array} { c } 
\text { Gross revenue } \
( \$ \mathrm {~m} )
\end{array} \
\hline 1 & 5.3 & 48 \
\hline 2 & 7.2 & 65 \
\hline 3 & 1.3 & 18 \
\hline 4 & 1.8 & 20 \
\hline 5 & 3.5 & 31 \
\hline 6 & 2.6 & 26 \
\hline 7 & 8.0 & 73 \
\hline 8 & 2.4 & 23 \
\hline 9 & 4.5 & 39 \
\hline 10 & 6.7 & 58 \
\hline
\end{array}$$ a. Determine the least squares regression line.
b. Interpret the value of the slope of the regression line.
c. Determine the standard error of estimate, and describe what this statistic tells you about the regression line.

Accepted Answer

a. @#IMG-DLM& @#LAT-DLM& 4.225 + 8.285x
b. For eac

Question 9

Which of the following best describes the relationship of the least squares regression line: Estimated y = 2 - x?

Accepted Answer

A)  As x increases by 1 unit, y increases by 1 unit, estimated, on average. 
B)  As x increases by 1 unit y decreases by (2 -x) units, estimated, on average. 
C)  As x increases by 1 unit, y decreases by 1 unit, estimated, on average. 
D)  All of these choices are correct. 
A)  As x increases by 1 unit, y increases by 1 unit, estimated, on average. 
B)  As x increases by 1 unit y decreases by (2 -x) units, estimated, on average. 
C)  As x increases by 1 unit, y decreases by 1 unit, estimated, on average. 
D)  All of these choices are correct.

Question 10

If all the points in a scatter diagram lie on the least squares regression line, then the coefficient of correlation must be:

Accepted Answer

A)  1.0. 
B)  -1.0. 
C)  either 1.0 or -1.0. 
D)  0.0. 
A)  1.0. 
B)  -1.0. 
C)  either 1.0 or -1.0. 
D)  0.0.

Question 11

The standard error of estimate, $$S _  { \varepsilon }$$ , is given by:

Accepted Answer

A)  SSE/(n - 2). 
B)  $$\sqrt { S S E } / ( n - 2 )$$ . 
C)  $$\sqrt { S S E / ( n - 2 ) }$$ . 
D)  SSE/ $$\sqrt { n - 2 }$$ . 
A)  SSE/(n - 2). 
B)  $$\sqrt { S S E } / ( n - 2 )$$ . 
C)  $$\sqrt { S S E / ( n - 2 ) }$$ . 
D)  SSE/ $$\sqrt { n - 2 }$$ .

Question 12

A direct relationship between an independent variable x and a dependent variably y means that the variables x and y increase or decrease together.

Accepted Answer

A) True 
 B)False

Question 13

When the variance, $$\sigma _ { \varepsilon } ^ { 2 }$$ , of the error variable $$\varepsilon$$ is a constant no matter what the value of x is, this condition is called:

Accepted Answer

A)  homocausality. 
B)  heteroscedasticity. 
C)  homoscedasticity. 
D)  heterocausality. 
A)  homocausality. 
B)  heteroscedasticity. 
C)  homoscedasticity. 
D)  heterocausality.

Question 14

Which of the following statements is correct when all the actual values of y are on an upward sloping regression line?

Accepted Answer

A)  The coefficient of correlation is equal to one and the sign of the coefficient of correlation will be negative but the sign of the slope with be positive. 
B)  The coefficient of correlation and the slope must both be equal to 1. 
C)  The coefficient of correlation is equal to one and the sign of the coefficient of correlation and the sign of the slope will both be positive. 
D)  The coefficient of correlation and the slope must be equal to - 1. 
A)  The coefficient of correlation is equal to one and the sign of the coefficient of correlation will be negative but the sign of the slope with be positive. 
B)  The coefficient of correlation and the slope must both be equal to 1. 
C)  The coefficient of correlation is equal to one and the sign of the coefficient of correlation and the sign of the slope will both be positive. 
D)  The coefficient of correlation and the slope must be equal to - 1.

Question 15

In the first-order linear regression model, the population parameters of the y-intercept and the slope are:

Accepted Answer

A)  $$b _ { 0 }$$ and $$b _ { 1 }$$ . 
B)  $$b _ { 0 }$$ and $$\beta _ { 1 }$$ . 
C)  $$\beta _ { 0 }$$ and $$b _ { 1 }$$ . 
D)  $$\beta _ { 0 }$$ and $$\beta _ { 1 }$$ . 
A)  $$b _ { 0 }$$ and $$b _ { 1 }$$ . 
B)  $$b _ { 0 }$$ and $$\beta _ { 1 }$$ . 
C)  $$\beta _ { 0 }$$ and $$b _ { 1 }$$ . 
D)  $$\beta _ { 0 }$$ and $$\beta _ { 1 }$$ .

Question 16

The method of least squares requires that the sum of the squared deviations between actual y values in the scatter diagram and y values predicted by the regression line be minimised.

Accepted Answer

A) True 
 B)False

Question 17

The value of the sum of squares for regression, SSR, can never be larger than the value of sum of squares for error, SSE.

Accepted Answer

A) True 
 B)False

Question 18

A professor of economics wants to study the relationship between income y (in $1000s) and education x (in years). A random sample of eight individuals is taken and the results are shown below. $$\begin{array} { | l | c | c | c | c | c | c | c | c | } 
\hline \text { Education } & 16 & 11 & 15 & 8 & 12 & 10 & 13 & 14 \
\hline \text { Income } & 58 & 40 & 55 & 35 & 43 & 41 & 52 & 49 \
\hline
\end{array}$$ Conduct a test of the population slope to determine at the 5% significance level whether a linear relationship exists between years of education and income.

Accepted Answer

@#LAT-DLM& . @#LAT-DLM& .
Rejection region: | t |

Question 19

The editor of a major academic book publisher claims that a large part of the cost of books is the cost of paper. This implies that larger books will cost more money. As an experiment to analyse the claim, a university student visits the bookstore and records the number of pages and the selling price of 12 randomly selected books. These data are listed below. $$\begin{array} { | c | c | c | } 
\hline \text { Book } & \text { Number of pages } & \text { Selling price (\$) } \
\hline 1 & 844 & 55 \
\hline 2 & 727 & 50 \
\hline 3 & 360 & 35 \
\hline 4 & 915 & 60 \
\hline 5 & 295 & 30 \
\hline 6 & 706 & 50 \
\hline 7 & 410 & 40 \
\hline 8 & 905 & 53 \
\hline 9 & 1058 & 65 \
\hline 10 & 865 & 54 \
\hline 11 & 677 & 42 \
\hline 12 & 912 & 58 \
\hline
\end{array}$$ Draw a scatter diagram of the data and plot the least squares regression line on it.

Accepted Answer

The answer of The editor of a major academic book...

Question 20

A professor of economics wants to study the relationship between income y (in $1000s) and education x (in years). A random sample of eight individuals is taken and the results are shown below. $$\begin{array} { | l | c | c | c | c | c | c | c | c | } 
\hline \text { Education } & 16 & 11 & 15 & 8 & 12 & 10 & 13 & 14 \
\hline \text { Income } & 58 & 40 & 55 & 35 & 43 & 41 & 52 & 49 \
\hline
\end{array}$$ Predict with 95% confidence the average income of all individuals with 10 years of education.

Accepted Answer

39.715 ± 1

In regression analysis, if the coefficient of determination is 1.0, then:

Given the data points (x,y) = (3,3), (4,4), (5,5), (6,6), (7,7), the least squares estimates of the y-intercept and slope are respectively:

Which of the following statements best describes why a linear regression is also called a least squares regression model?

The Pearson coefficient of correlation r equals 1 when there is/are no:

Given the least squares regression line y-hat = 3.52 - 1.27x, and a coefficient of determination of 0.81, the coefficient of correlation is:

Which of the following best describes the relationship of the least squares regression line: Estimated y = 2 - x?

If all the points in a scatter diagram lie on the least squares regression line, then the coefficient of correlation must be:

The standard error of estimate, $S _ { \varepsilon }$ , is given by:

A direct relationship between an independent variable x and a dependent variably y means that the variables x and y increase or decrease together.

When the variance, $\sigma _ { \varepsilon } ^ { 2 }$ , of the error variable $\varepsilon$ is a constant no matter what the value of x is, this condition is called:

Which of the following statements is correct when all the actual values of y are on an upward sloping regression line?

In the first-order linear regression model, the population parameters of the y-intercept and the slope are:

The method of least squares requires that the sum of the squared deviations between actual y values in the scatter diagram and y values predicted by the regression line be minimised.

The value of the sum of squares for regression, SSR, can never be larger than the value of sum of squares for error, SSE.

What Is Statistics

Types of Data, Data Collection and Sampling

Graphical Descriptive Methods Nominal Data

Graphical Descriptive Techniques Numerical Data

Numerical Descriptive Measures

Probability

Random Variables and Discrete Probability Distributions

Continuous Probability Distributions

Statistical Inference: Introduction

Sampling Distributions

Estimation: Describing a Single Population

Estimation: Comparing Two Populations

Hypothesis Testing: Describing a Single Population

Hypothesis Testing: Comparing Two Populations

Inference About Population Variances

Analysis of Variance

Additional Tests for Nominal Data: Chi-Squared Tests

Multiple Regression

Model Building

Nonparametric Techniques

Statistical Inference: Conclusion

Time-Series Analysis and Forecasting

Index Numbers

Decision Analysis

Filters

Exam 18: Simple Linear Regression and Correlation

In regression analysis, if the coefficient of determination is 1.0, then:

Given the data points (x,y) = (3,3), (4,4), (5,5), (6,6), (7,7), the least squares estimates of the y-intercept and slope are respectively:

Which of the following statements best describes why a linear regression is also called a least squares regression model?

The Pearson coefficient of correlation r equals 1 when there is/are no:

Given the least squares regression line y-hat = 3.52 - 1.27x, and a coefficient of determination of 0.81, the coefficient of correlation is:

Which of the following best describes the relationship of the least squares regression line: Estimated y = 2 - x?

If all the points in a scatter diagram lie on the least squares regression line, then the coefficient of correlation must be:

The standard error of estimate, SεS _ { \varepsilon }Sε​ , is given by:

A direct relationship between an independent variable x and a dependent variably y means that the variables x and y increase or decrease together.

When the variance, σε2\sigma _ { \varepsilon } ^ { 2 }σε2​ , of the error variable ε\varepsilonε is a constant no matter what the value of x is, this condition is called:

Which of the following statements is correct when all the actual values of y are on an upward sloping regression line?

In the first-order linear regression model, the population parameters of the y-intercept and the slope are:

The method of least squares requires that the sum of the squared deviations between actual y values in the scatter diagram and y values predicted by the regression line be minimised.

The value of the sum of squares for regression, SSR, can never be larger than the value of sum of squares for error, SSE.

What Is Statistics

Types of Data, Data Collection and Sampling

Graphical Descriptive Methods Nominal Data

Graphical Descriptive Techniques Numerical Data

Numerical Descriptive Measures

Probability

Random Variables and Discrete Probability Distributions

Continuous Probability Distributions

Statistical Inference: Introduction

Sampling Distributions

Estimation: Describing a Single Population

Estimation: Comparing Two Populations

Hypothesis Testing: Describing a Single Population

Hypothesis Testing: Comparing Two Populations

Inference About Population Variances

Analysis of Variance

Additional Tests for Nominal Data: Chi-Squared Tests

Multiple Regression

Model Building

Nonparametric Techniques

Statistical Inference: Conclusion

Time-Series Analysis and Forecasting

Index Numbers

Decision Analysis

Filters

The standard error of estimate, $S _ { \varepsilon }$ , is given by:

When the variance, $\sigma _ { \varepsilon } ^ { 2 }$ , of the error variable $\varepsilon$ is a constant no matter what the value of x is, this condition is called: