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. \[\begin{array} { | c | c | c | } \hline \text { Movie } & \begin{array} { c } \text { Cost of two highest- } \\ \text { paid performers } ( \$ \mathrm {~m} ) \end{array} & \begin{array} { c } \text { Gross revenue } \\ ( \$ \mathrm {~m} ) \end{array} \\ \hline 1 & 5.3 & 48 \\ \hline 2 & 7.2 & 65 \\ \hline 3 & 1.3 & 18 \\ \hline 4 & 1.8 & 20 \\ \hline 5 & 3.5 & 31 \\ \hline 6 & 2.6 & 26 \\ \hline 7 & 8.0 & 73 \\ \hline 8 & 2.4 & 23 \\ \hline 9 & 4.5 & 39 \\ \hline 10 & 6.7 & 58 \\ \hline \end{array}\] Conduct a test of the population slope to determine at the 5% significance level whether a linear relationship exists between payment to the two highest-paid performers and gross revenue.

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

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. \[\begin{array} { | l | c | c | c | c | c | c | c | c | } \hline \text { Education } & 16 & 11 & 15 & 8 & 12 & 10 & 13 & 14 \\ \hline \text { Income } & 58 & 40 & 55 & 35 & 43 & 41 & 52 & 49 \\ \hline \end{array}\] 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 years of education and income are linearly related?

H 0 : @#LAT-DLM& s = 0. H 1 : @#LAT-DLM& s @#LAT-DLM& 0. Rejection

Exam 18: Simple Linear Regression and Correlation

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 Excel regression output. Number of vo uchers Sales 4 12.8 7 15.4 5 13.9 3 11.2 19 18.7 10 17.9 8 16.8 6 15.9 3 11.5 5 13.9 $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 ($000s) from 10 randomly selected weeks is given below with Excel regression output. \begin{array} { | c | c | } \hline \text { Number of vo uchers } & \text { Sales } \\ \hline 4 & 12.8 \\ \hline 7 & 15.4 \\ \hline 5 & 13.9 \\ \hline 3 & 11.2 \\ \hline 19 & 18.7 \\ \hline 10 & 17.9 \\ \hline 8 & 16.8 \\ \hline 6 & 15.9 \\ \hline 3 & 11.5 \\ \hline 5 & 13.9 \\ \hline \end{array} a. Write down the regression equation b. Interpret the slope.$ a. Write down the regression equation b. Interpret the slope.

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Question 181

The value of the sum of squares for regression, SSR, can never be smaller than 0.0.

(True/False)

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Question 182

At a recent music concert, a survey was conducted that asked a random sample of 20 people their age and how many concerts they have attended since the beginning of the year. The following data were collected. Age 62 57 40 49 67 54 43 65 54 41 Number of concerts 6 5 4 3 5 5 2 6 3 1 Age 44 48 55 60 59 63 69 40 38 52 Number of Concerts 3 2 4 5 4 5 4 2 1 3 $At a recent music concert, a survey was conducted that asked a random sample of 20 people their age and how many concerts they have attended since the beginning of the year. The following data were collected. \begin{array}{l} \begin{array} { | l | c | c | c | c | c | c | c | c | c | c | } \hline \text { Age } & 62 & 57 & 40 & 49 & 67 & 54 & 43 & 65 & 54 & 41 \\ \hline \text { Number of concerts } & 6 & 5 & 4 & 3 & 5 & 5 & 2 & 6 & 3 & 1 \\ \hline \end{array}\\\\ \begin{array} { | l | c | c | c | c | c | c | c | c | c | c | } \hline \text { Age } & 44 & 48 & 55 & 60 & 59 & 63 & 69 & 40 & 38 & 52 \\ \hline \text { Number of Concerts } & 3 & 2 & 4 & 5 & 4 & 5 & 4 & 2 & 1 & 3 \\ \hline \end{array} \end{array} a. Determine the standard error of estimate and describe what this statistic tells you about the model's fit. b. Interpret the coefficient of correlation. c. Interpret the coefficient of determination, and discuss what its value tells you about the two variables.$ a. Determine the standard error of estimate and describe what this statistic tells you about the model's fit. b. Interpret the coefficient of correlation. c. Interpret the coefficient of determination, and discuss what its value tells you about the two variables.

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Question 183

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 Calculate the Pearson correlation coefficient. What sign does it have? Why?

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Question 184

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. The results are as follows. 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 Predict with 95% confidence the winnings of a contestant who has 10 years of education.

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Question 185

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 regression output given below. (a) Estimate daily hot coffee sales revenue on a day of 38 degrees Celsius. (b) Is your prediction in part (a) reasonable?

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Question 186

If the value of the sum of squares for error, SSE, equals zero, then the coefficient of determination must equal zero.

(True/False)

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Question 187

Given that cov(x,y) = 8, $S _ { y } ^ { 2 }$ = 14, $S _ { x } ^ { 2 }$ = 10 and n = 6, the value of the sum of squares for error, SSE, is 38.

(True/False)

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Question 188

A regression analysis between weight $y$ (in kilograms) and height $x$ (in centimetres) yielded the least squares line = 135 + 6 $x$ . We estimate that for each 1 cm in height, that weight will cedrease by 6 kilograms, on average.

(True/False)

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Question 189

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 Conduct a test of the population slope to determine at the 5% significance level whether a linear relationship exists between payment to the two highest-paid performers and gross revenue.

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Question 190

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. Education 16 11 15 8 12 10 13 14 Income 58 40 55 35 43 41 52 49 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 years of education and income are linearly related?

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Question 191

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 regression 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 $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 $00's). A random sample of 6 days was taken, with the daily hot coffee sales revenue and the corresponding temperature of that day noted. Excel regression output given below. \begin{array} { | c | c | } \hline \text { Coffee sales revenue } & \text { Temperature } \\ \hline 6.50 & 25 \\ \hline 10.00 & 17 \\ \hline 5.50 & 30 \\ \hline 4.50 & 35 \\ \hline 3.50 & 40 \\ \hline 28.00 & 9 \\ \hline \end{array} Test the significance of the slope, against a two-tailed alternative, at the 5% level of significance.$ Test the significance of the slope, against a two-tailed alternative, at the 5% level of significance.

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Question 192

Given that ss_x = 2500, ss_y = 3750, ss_xy = 500 and n = 6, the standard error of estimate is:

(Multiple Choice)

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Question 193

If the error variable $\varepsilon$ is normally distributed, the test statistic for testing $H _ { 0 } : \beta _ { 1 } = 0$ in a simple linear regression follows the Student t-distribution with n - 1 degrees of freedom.

(True/False)

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Question 194

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. Education 16 11 15 8 12 10 13 14 Income 58 40 55 35 43 41 52 49 Calculate the Pearson correlation coefficient. What sign does it have? Why?

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Question 195

A direct relationship between an independent variable x and a dependent variably y means that x and y move in the same directions.

(True/False)

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Question 196

In simple linear regression, which of the following statements indicates no linear relationship between the variables x and y?

(Multiple Choice)

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Question 197

In a simple linear regression model, testing whether the slope, $\beta _ { 1 }$ , of the population regression line is zero is the same as testing whether the population coefficient of correlation, $P$ , equals zero.

(True/False)

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Question 198

In a simple linear regression, which of the following is equivalent to testing the significance of the population slope?

(Multiple Choice)

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Question 199

Which of the following best describes the value of the slope, if the coefficient of determination is 0.95?

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Question 200

Showing 181 - 200 of 213

The value of the sum of squares for regression, SSR, can never be smaller than 0.0.

If the value of the sum of squares for error, SSE, equals zero, then the coefficient of determination must equal zero.

Given that cov(x,y) = 8, $S _ { y } ^ { 2 }$ = 14, $S _ { x } ^ { 2 }$ = 10 and n = 6, the value of the sum of squares for error, SSE, is 38.

A regression analysis between weight $y$ (in kilograms) and height $x$ (in centimetres) yielded the least squares line = 135 + 6 $x$ . We estimate that for each 1 cm in height, that weight will cedrease by 6 kilograms, on average.

Given that ss_x = 2500, ss_y = 3750, ss_xy = 500 and n = 6, the standard error of estimate is:

If the error variable $\varepsilon$ is normally distributed, the test statistic for testing $H _ { 0 } : \beta _ { 1 } = 0$ in a simple linear regression follows the Student t-distribution with n - 1 degrees of freedom.

A direct relationship between an independent variable x and a dependent variably y means that x and y move in the same directions.

In simple linear regression, which of the following statements indicates no linear relationship between the variables x and y?

In a simple linear regression model, testing whether the slope, $\beta _ { 1 }$ , of the population regression line is zero is the same as testing whether the population coefficient of correlation, $P$ , equals zero.

In a simple linear regression, which of the following is equivalent to testing the significance of the population slope?

Which of the following best describes the value of the slope, if the coefficient of determination is 0.95?

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

The value of the sum of squares for regression, SSR, can never be smaller than 0.0.

If the value of the sum of squares for error, SSE, equals zero, then the coefficient of determination must equal zero.

Given that cov(x,y) = 8, Sy2S _ { y } ^ { 2 }Sy2​ = 14, Sx2S _ { x } ^ { 2 }Sx2​ = 10 and n = 6, the value of the sum of squares for error, SSE, is 38.

A regression analysis between weight yyy (in kilograms) and height xxx (in centimetres) yielded the least squares line = 135 + 6 xxx . We estimate that for each 1 cm in height, that weight will cedrease by 6 kilograms, on average.

Given that ssx = 2500, ssy = 3750, ssxy = 500 and n = 6, the standard error of estimate is:

If the error variable ε\varepsilonε is normally distributed, the test statistic for testing H0:β1=0H _ { 0 } : \beta _ { 1 } = 0H0​:β1​=0 in a simple linear regression follows the Student t-distribution with n - 1 degrees of freedom.

A direct relationship between an independent variable x and a dependent variably y means that x and y move in the same directions.

In simple linear regression, which of the following statements indicates no linear relationship between the variables x and y?

In a simple linear regression model, testing whether the slope, β1\beta _ { 1 }β1​ , of the population regression line is zero is the same as testing whether the population coefficient of correlation, PPP , equals zero.

In a simple linear regression, which of the following is equivalent to testing the significance of the population slope?

Which of the following best describes the value of the slope, if the coefficient of determination is 0.95?

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

Given that cov(x,y) = 8, $S _ { y } ^ { 2 }$ = 14, $S _ { x } ^ { 2 }$ = 10 and n = 6, the value of the sum of squares for error, SSE, is 38.

A regression analysis between weight $y$ (in kilograms) and height $x$ (in centimetres) yielded the least squares line = 135 + 6 $x$ . We estimate that for each 1 cm in height, that weight will cedrease by 6 kilograms, on average.

Given that ss_x = 2500, ss_y = 3750, ss_xy = 500 and n = 6, the standard error of estimate is:

If the error variable $\varepsilon$ is normally distributed, the test statistic for testing $H _ { 0 } : \beta _ { 1 } = 0$ in a simple linear regression follows the Student t-distribution with n - 1 degrees of freedom.

In a simple linear regression model, testing whether the slope, $\beta _ { 1 }$ , of the population regression line is zero is the same as testing whether the population coefficient of correlation, $P$ , equals zero.