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.

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

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: $\begin{array}{|l|l|} \hline\text { A. } & \text {homocausality. }\\ \hline \text { B. } & \text {heteroscedasticity. } \\ \hline \text { C. } &\text {homoscedasticity. }\\ \hline \text { D. } &\text {heterocausality. }\\ \hline \end{array}$

The answer of When the variance, \(\sigma _ { \varepsilon...

Which of the following statements is correct when all the actual values of y are on an upward sloping regression line? $\begin{array}{|l|l|} \hline A&\text {The coefficient of correlation is equal to one and the sign of the coefficient of correlation }\\ &\text { will be negative but the sign of the slope with be positive.}\\ \hline B&\text {The coefficient of correlation and the slope must both be equal to 1 . }\\ \hline C&\text {The coefficient of correlation is equal to one and the sign of the coefficient of correlation }\\ &\text { and the sign of the slope will both be positive.}\\ \hline D&\text {The coefficient of correlation and the slope must be equal to -1 . }\\ \hline \end{array}$

The answer of Which of the following statements is correct...

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. \[\begin{array} { | c | c | c | } \hline \text { Book } & \text { Number of pages } & \text { Selling price } ( \$ ) \\ \hline 1 & 844 & 55 \\ \hline 2 & 727 & 50 \\ \hline 3 & 360 & 35 \\ \hline 4 & 915 & 60 \\ \hline 5 & 295 & 30 \\ \hline 6 & 706 & 50 \\ \hline 7 & 410 & 40 \\ \hline 8 & 905 & 53 \\ \hline 9 & 1058 & 65 \\ \hline 10 & 865 & 54 \\ \hline 11 & 677 & 42 \\ \hline 12 & 912 & 58 \\ \hline \end{array}\] Determine the coefficient of determination, and discuss what its value tells you.

@#IMG-DLM& 0.9378, which means that 93.7

In a regression problem, if all the values of the independent variable are equal, then the coefficient of determination must be: \[\begin{array} { | l | l | } \hline \text { A. } & 1.0 . \\ \hline \text { B. } & 0.5 . \\ \hline \text { C. } & 0.0 . \\ \hline \text { D. } & - 1.0 . \\ \hline \end{array}\]

The answer of In a regression problem, if all the...

If the standard error of estimate $S _ { \varepsilon }$ = 15 and n = 12, then the sum of squares for error, SSE, is: \[\begin{array} { | l | l | } \hline \text { A. } & 150 . \\ \hline \text { B. } & 180 . \\ \hline \text { C. } & 225 . \\ \hline \text { D. } & 2250 . \\ \hline \end{array}\]

The answer of If the standard error of estimate \(S...

If all the points in a scatter diagram lie on the least squares regression line, then the coefficient of correlation must be: $\begin{array}{|l|l|} \hline A&\text {1.0 }\\ \hline B&\text { -1.0}\\ \hline C&\text { either } 1.0 \text { or }-1.0\\ \hline D&\text { 0.0 }\\ \hline \end{array}$

The answer of If all the points in a scatter...

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.

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

The manager of a fast food restaurant wants to determine how sales in a given week are related to the number of discount vouchers (#) printed in the local newspaper during the week. The number of vouchers and sales ($000s) from 10 randomly selected weeks is given below with the predicted sales. Calculate the residuals. \[\begin{array} { | c | c | c | } \hline \text { Observation } & \text { Sales } & \text { Predicted Sales } \\ \hline 1 & 12.8 & 13.4147 \\ \hline 2 & 15.4 & 14.8000 \\ \hline 3 & 13.9 & 13.8765 \\ \hline 4 & 11.2 & 12.9529 \\ \hline 5 & 18.7 & 20.3412 \\ \hline 6 & 17.9 & 16.1853 \\ \hline 7 & 16.8 & 15.2618 \\ \hline 8 & 15.9 & 14.3382 \\ \hline 9 & 11.5 & 12.9529 \\ \hline 10 & 13.9 & 13.8765 \\ \hline \end{array}\]

The answer of The manager of a fast food restaurant...

The standardised residual is defined as: $\begin{array}{|l|l|} \hline A&\text {residual divided by the standard error of estimate. }\\ \hline B&\text {residual multiplied by the square root of the standard error of estimate. }\\ \hline C&\text { residual divided by the square of the standard error of estimate.}\\ \hline D&\text { residual multiplied by the standard error of estimate.}\\ \hline \end{array}$

The answer of The standardised residual is defined as: \(\begin{array}{|l|l|} \hline...

Consider the following data values of variables x and y. \[\begin{array} { | c | c | c | c | c | c | c | } \hline x & 3 & 5 & 7 & 9 & 11 & 14 \\ \hline y & 7 & 10 & 17 & 20 & 27 & 35 \\ \hline \end{array}\] Calculate the coefficient of determination, and describe what this statistic tells you about the relationship between the two variables.

@#IMG-DLM& 0.990. This means that 99% of

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. Excel output given below. \[\begin{array} { | c | c | } \hline \text { Coffee sales revenue } & \text { Temperature } \\ \hline 6.50 & 25 \\ \hline 10.00 & 17 \\ \hline 5.50 & 30 \\ \hline 4.50 & 35 \\ \hline 3.50 & 40 \\ \hline 28.00 & 9 \\ \hline \end{array}\] \(\begin{array}{|l|r|r|r|r|r|c|}\hline \begin{array}{l} \text { SUMMARY } \\ \text { OUTPUT } \end{array} \\ \hline \begin{array}{c} \text { Regression } \\ \text { Stotistics } \end{array} \\ \hline \text { Multiple R } & 0.8644 \\ \hline \text { RSquare } & 0.7472 \\ \hline \text { Adjusted R Square } & 0.6840 \\ \hline \text { Stan dard Error } & 5.2027 \\ \hline \text { Observations } & 6 \\ \hline\\ \hline \text { ANOVA }\\ \hline & & & & & \text { Significance } \\ & \text { df } & S & M S & F &{F} \\ \hline \text { Regression } & 1 & 320.0617 & 320.0617 & 11.8244 & 0.0263 \\ \hline \text { Residual } & 4 & 108.2716 & 27.0679 & & \\ \hline \text { Total } & 5 & 428.3333 & & & \\ \hline\\ \hline & \text { Coefficients } & \begin{array}{c} \text { Standord } \\ \text { Error } \end{array} & \text { t Stat } & \text { p-value } & \text { Lower 95\% } & \begin{array}{c} \text { Upper } \\ 95 \% \end{array} \\ \hline \text { Intercept } & 27.7179 & 5.6629 & 4.8946 & 0.0081 & 11.9952 & 43.4406 \\ \hline \text { Temperature } & -0.6943 & 0.2019 & -3.4387 & 0.0263 & -1.2549 & -0.1337 \\ \hline \end{array}\) Test the hypothesis that the population intercept is positive, at the 5% level of significance.

Ho: β 0 = 0 H A : β 0 > 0 p-value = (

Exam 18: Simple Linear Regression and Correlation

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. Movie Cost of two highest- paid performers (\ ) Gross revenue (\ ) 1 5.3 48 2 7.2 65 3 1.3 18 4 1.8 20 5 3.5 31 6 2.6 26 7 8.0 73 8 2.4 23 9 4.5 39 10 6.7 58 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.

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Question 21

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

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Question 22

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

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Question 23

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. Book Number of pages Selling price (\ ) 1 844 55 2 727 50 3 360 35 4 915 60 5 295 30 6 706 50 7 410 40 8 905 53 9 1058 65 10 865 54 11 677 42 12 912 58 Determine the coefficient of determination, and discuss what its value tells you.

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Question 24

In a regression problem, if all the values of the independent variable are equal, then the coefficient of determination must be: A. 1.0. B. 0.5. C. 0.0. D. -1.0.

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Question 25

If the standard error of estimate $S _ { \varepsilon }$ = 15 and n = 12, then the sum of squares for error, SSE, is: A. 150. B. 180. C. 225. D. 2250.

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Question 26

Do the tests provide the same results? Explain.

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Question 27

If all the points in a scatter diagram lie on the least squares regression line, then the coefficient of correlation must be: A 1.0 B -1.0 C either 1.0 or -1.0 D 0.0

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Question 28

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. Book Number of pages Selling price (\ ) 1 844 55 2 727 50 3 360 35 4 915 60 5 295 30 6 706 50 7 410 40 8 905 53 9 1058 65 10 865 54 11 677 42 12 912 58 Draw a scatter diagram of the data and plot the least squares regression line on it.

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Question 29

The value of the sum of squares for regression, SSR, can never be equal to the value of total sum of squares, SST.

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Question 30

The manager of a fast food restaurant wants to determine how sales in a given week are related to the number of discount vouchers (#) printed in the local newspaper during the week. The number of vouchers and sales ($000s) from 10 randomly selected weeks is given below with the predicted sales. Calculate the residuals. Observation Sales Predicted Sales 1 12.8 13.4147 2 15.4 14.8000 3 13.9 13.8765 4 11.2 12.9529 5 18.7 20.3412 6 17.9 16.1853 7 16.8 15.2618 8 15.9 14.3382 9 11.5 12.9529 10 13.9 13.8765

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Question 31

The standardised residual is defined as: A residual divided by the standard error of estimate. B residual multiplied by the square root of the standard error of estimate. C residual divided by the square of the standard error of estimate. D residual multiplied by the standard error of estimate.

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Question 32

Plot the residuals against the predicted values of y. Does the variance appear to be constant?

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Question 33

Consider the following data values of variables x and y. x 3 5 7 9 11 14 y 7 10 17 20 27 35 Calculate the coefficient of determination, and describe what this statistic tells you about the relationship between the two variables.

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Question 34

One method of diagnosing autocorrelation is to plot the residuals against the time periods to see whether some pattern emerges.

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Question 35

The dean of a faculty of business in Victoria believes that students who do well in 'soft' courses like organisational behaviour do poorly in 'hard' courses like business statistics. In order to test his belief, he takes a random sample of 10 students and records their test grades in organisational behaviour and statistics. The results are shown below. Do these data provide sufficient evidence at the 5% significance level to support the dean's claim? Student Organisational B ehaviour Grade Business Statistics Grade 1 C A 2 D A 3 A C 4 B C 5 A D 6 C B 7 B C 8 A C 9 C A 10 B C

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Question 36

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. Excel output given below. Coffee sales revenue Temperature 6.50 25 10.00 17 5.50 30 4.50 35 3.50 40 28.00 9 SUMMARY OUTPUT Regression Stotistics Multiple R 0.8644 RSquare 0.7472 Adjusted R Square 0.6840 Stan dard Error 5.2027 Observations 6 ANOVA Significance df S MS F F Regression 1 320.0617 320.0617 11.8244 0.0263 Residual 4 108.2716 27.0679 Total 5 428.3333 Coefficients Standord Error t Stat p-value Lower 95\% Upper 95\% Intercept 27.7179 5.6629 4.8946 0.0081 11.9952 43.4406 Temperature -0.6943 0.2019 -3.4387 0.0263 -1.2549 -0.1337 Test the hypothesis that the population intercept is positive, at the 5% level of significance.

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Question 37

The manager of a fast food restaurant wants to determine how sales in a given week are related to the number of discount vouchers (#) printed in the local newspaper during the week. The number of vouchers and sales ($000s) from 10 randomly selected weeks is given below with the predicted sales. Compute the standardised residuals.

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Question 38

An ardent fan of television game shows has observed that, in general, the more educated the contestant, the less money he or she wins. To test her belief, she gathers data about the last eight winners of her favourite game show. She records their winnings in dollars and their years of education and performs a simple linear regression, with the Excel output provided . Contestant Years of education Winnings 1 11 750 2 15 400 3 12 600 4 16 350 5 11 800 6 16 300 7 13 650 8 14 400 $An ardent fan of television game shows has observed that, in general, the more educated the contestant, the less money he or she wins. To test her belief, she gathers data about the last eight winners of her favourite game show. She records their winnings in dollars and their years of education and performs a simple linear regression, with the Excel output provided . \begin{array} { | c | c | c | } \hline \text { Contestant } & \begin{array} { c } \text { Years of } \\ \text { education } \end{array} & \text { Winnings } \\ \hline 1 & 11 & 750 \\ \hline 2 & 15 & 400 \\ \hline 3 & 12 & 600 \\ \hline 4 & 16 & 350 \\ \hline 5 & 11 & 800 \\ \hline 6 & 16 & 300 \\ \hline 7 & 13 & 650 \\ \hline 8 & 14 & 400 \\ \hline \end{array} a. Determine the least squares regression line. b. Interpret the value of the slope of the regression line. c. Determine the standard error of estimate, and describe what this statistic tells you about the regression line. d. Interpret the coefficient of correlation$ 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. d. Interpret the coefficient of correlation

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Question 39

A simple linear regression equation is given by $= 5.25 + 3.8 x$ . The point estimate of $y$ when $x$ = 4 is 20.45.

(True/False)

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Question 40

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

In a regression problem, if all the values of the independent variable are equal, then the coefficient of determination must be: A. 1.0. B. 0.5. C. 0.0. D. -1.0.

If the standard error of estimate $S _ { \varepsilon }$ = 15 and n = 12, then the sum of squares for error, SSE, is: A. 150. B. 180. C. 225. D. 2250.

Do the tests provide the same results? Explain.

If all the points in a scatter diagram lie on the least squares regression line, then the coefficient of correlation must be: A 1.0 B -1.0 C either 1.0 or -1.0 D 0.0

The value of the sum of squares for regression, SSR, can never be equal to the value of total sum of squares, SST.

The standardised residual is defined as: A residual divided by the standard error of estimate. B residual multiplied by the square root of the standard error of estimate. C residual divided by the square of the standard error of estimate. D residual multiplied by the standard error of estimate.

Plot the residuals against the predicted values of y. Does the variance appear to be constant?

Consider the following data values of variables x and y. x 3 5 7 9 11 14 y 7 10 17 20 27 35 Calculate the coefficient of determination, and describe what this statistic tells you about the relationship between the two variables.

One method of diagnosing autocorrelation is to plot the residuals against the time periods to see whether some pattern emerges.

A simple linear regression equation is given by $= 5.25 + 3.8 x$ . The point estimate of $y$ when $x$ = 4 is 20.45.

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

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

In a regression problem, if all the values of the independent variable are equal, then the coefficient of determination must be: A. 1.0. B. 0.5. C. 0.0. D. -1.0.

If the standard error of estimate SεS _ { \varepsilon }Sε​ = 15 and n = 12, then the sum of squares for error, SSE, is: A. 150. B. 180. C. 225. D. 2250.

Do the tests provide the same results? Explain.

If all the points in a scatter diagram lie on the least squares regression line, then the coefficient of correlation must be: A 1.0 B -1.0 C either 1.0 or -1.0 D 0.0

The value of the sum of squares for regression, SSR, can never be equal to the value of total sum of squares, SST.

The standardised residual is defined as: A residual divided by the standard error of estimate. B residual multiplied by the square root of the standard error of estimate. C residual divided by the square of the standard error of estimate. D residual multiplied by the standard error of estimate.

Plot the residuals against the predicted values of y. Does the variance appear to be constant?

Consider the following data values of variables x and y. x 3 5 7 9 11 14 y 7 10 17 20 27 35 Calculate the coefficient of determination, and describe what this statistic tells you about the relationship between the two variables.

One method of diagnosing autocorrelation is to plot the residuals against the time periods to see whether some pattern emerges.

A simple linear regression equation is given by =5.25+3.8x = 5.25 + 3.8 x=5.25+3.8x . The point estimate of yyy when xxx = 4 is 20.45.

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

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

If the standard error of estimate $S _ { \varepsilon }$ = 15 and n = 12, then the sum of squares for error, SSE, is: A. 150. B. 180. C. 225. D. 2250.

A simple linear regression equation is given by $= 5.25 + 3.8 x$ . The point estimate of $y$ when $x$ = 4 is 20.45.