The quality of oil is measured in API gravity degrees - the higher the degrees API, the higher the quality. The table shown below is produced by an expert in the field, who believes that there is a relationship between quality and price per barrel. \[\begin{array} { | c | c | } \hline \text { Oil degrees API } & \text { Price per barrel (in } \$ \text { ) } \\ \hline 27.0 & 12.02 \\ \hline 28.5 & 12.04 \\ \hline 30.8 & 12.32 \\ \hline 31.3 & 12.27 \\ \hline 31.9 & 12.49 \\ \hline 34.5 & 12.70 \\ \hline 34.0 & 12.80 \\ \hline 34.7 & 13.00 \\ \hline 37.0 & 13.00 \\ \hline 41.0 & 13.17 \\ \hline 41.0 & 13.19 \\ \hline 38.8 & 13.22 \\ \hline 39.3 & 13.27 \\ \hline \end{array}\] A partial Minitab output follows. Descriptive Statistics \[\begin{array} { | l | r | r | r | r | } \hline \text { Variable } & \mathrm { N } & \text { Mean } & \text { StDev } & \text { SE Mean } \\ \hline \text { Degrees } & 13 & 34.60 & 4.613 & 1.280 \\ \hline \text { Frice } & 13 & 12.730 & 0.457 & 0.127 \\ \hline \end{array}\] Covariances \[\begin{array} { | l | r | r | } \hline & \text { Degrees } & \text { Price } \\ \hline \text { Degrees } & 21.281667 & \\ \hline \text { Price } & 2.026750 & 0.208833 \\ \hline \end{array}\] Regression Analysis \[\begin{array} { | l | r | r | r | r | } \hline \text { Predictor } & \text { Coef } & \text { StDev } & \mathrm { T } & \mathrm { P } \\ \hline \text { Constant } & 9.4349 & 0.2867 & 32.91 & 0.000 \\ \hline \text { Degrees } & 0.095235 & 0.008220 & 11.59 & 0.000 \\ \hline \end{array}\] S = 0.1314 R-Sq = 92.46% R-Sq(adj) = 91.7% Analysis of Variance \[\begin{array} { | l | r | r | r | r | r | } \hline \text { Source } & \text { DF } & \text { SS } & \text { MS } & \text { F } & \text { P } \\ \hline \text { Regression } & 1 & 2.3162 & 2.3162 & 134.24 & 0.000 \\ \hline \text { Residual Error } & 11 & 0.1898 & 0.0173 & & \\ \hline \text { Total } & 12 & 2.5060 & & & \\ \hline \end{array}\] Conduct a test of the population slope to determine at the 5% significance level whether a linear relationship exists between the quality of oil and price per barrel.

@#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. \[\begin{array} { | l | c | c | c | c | c | c | c | c | } \hline \text { Education } & 16 & 11 & 15 & 8 & 12 & 10 & 13 & 14 \\ \hline \text { Income } & 58 & 40 & 55 & 35 & 43 & 41 & 52 & 49 \\ \hline \end{array}\] Conduct a test of the population coefficient of correlation to determine at the 5% significance level whether a linear relationship exists between years of education and income.

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

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? \[\begin{array} { | c | c | c | } \hline \text { Student } & \begin{array} { c } \text { Organisational } \\ \text { Behaviour Grade } \end{array} & \begin{array} { c } \text { Business Statistics } \\ \text { Grade } \end{array} \\ \hline 1 & \mathrm { C } & \mathrm { A } \\ \hline 2 & \mathrm { D } & \mathrm { A } \\ \hline 3 & \mathrm {~A} & \mathrm { C } \\ \hline 4 & \mathrm {~B} & \mathrm { C } \\ \hline 5 & \mathrm {~A} & \mathrm { D } \\ \hline 6 & \mathrm { C } & \mathrm { B } \\ \hline 7 & \mathrm {~B} & \mathrm { C } \\ \hline 8 & \mathrm {~A} & \mathrm { C } \\ \hline 9 & \mathrm { C } & \mathrm { A } \\ \hline 10 & \mathrm {~B} & \mathrm { C } \\ \hline \end{array}\]

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

A statistician investigating the relationship between the amount of precipitation (in inches) and the number of car accidents gathered data for 10 randomly selected days. The results are presented below. \[\begin{array} { | c | c | c | } \hline \text { Day } & \text { Precipitation } & \text { Number of accidents } \\ \hline 1 & 0.05 & 5 \\ \hline 2 & 0.12 & 6 \\ \hline 3 & 0.05 & 2 \\ \hline 4 & 0.08 & 4 \\ \hline 5 & 0.10 & 8 \\ \hline 6 & 0.35 & 14 \\ \hline 7 & 0.15 & 7 \\ \hline 8 & 0.30 & 13 \\ \hline 9 & 0.10 & 7 \\ \hline 10 & 0.20 & 10 \\ \hline \end{array}\] Determine the coefficient of determination and discuss what its value tells you about the two variables.

@#LAT-DLM& 0.893, which means that 89.3%

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. \[\begin{array} { | c | c | c | } \hline \text { Contestant } & \begin{array} { c } \text { Years of } \\ \text { education } \end{array} & \text { Winnings } \\ \hline 1 & 11 & 750 \\ \hline 2 & 15 & 400 \\ \hline 3 & 12 & 600 \\ \hline 4 & 16 & 350 \\ \hline 5 & 11 & 800 \\ \hline 6 & 16 & 300 \\ \hline 7 & 13 & 650 \\ \hline 8 & 14 & 400 \\ \hline \end{array}\] Conduct a test of the population coefficient of correlation to determine at the 5% significance level whether a linear relationship exists between TV game show contestants' years of education and their winnings.

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

Exam 18: Simple Linear Regression and Correlation

A medical statistician wanted to examine the relationship between the amount of sunshine (x) and incidence of skin cancer (y). As an experiment he found the number of skin cancers detected per 100 000 of population and the average daily sunshine in eight country towns around NSW. These data are shown below. Average daily sunshine (hours) 5 7 6 7 8 6 4 3 Skin cancer per 100000 7 11 9 12 15 10 7 5 Calculate the coefficient of determination and interpret it.

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Question 141

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 $At a recent music concert, a survey was conducted that asked a random sample of 20 people their age and how many concerts they have attended since the beginning of the year. The following data were collected. \begin{array}{l} \begin{array} { | l | c | c | c | c | c | c | c | c | c | c | } \hline \text { Age } & 62 & 57 & 40 & 49 & 67 & 54 & 43 & 65 & 54 & 41 \\ \hline \text { Number of concerts } & 6 & 5 & 4 & 3 & 5 & 5 & 2 & 6 & 3 & 1 \\ \hline \end{array}\\\\ \begin{array} { | l | c | c | c | c | c | c | c | c | c | c | } \hline \text { Age } & 44 & 48 & 55 & 60 & 59 & 63 & 69 & 40 & 38 & 52 \\ \hline \text { Number of Concerts } & 3 & 2 & 4 & 5 & 4 & 5 & 4 & 2 & 1 & 3 \\ \hline \end{array} \end{array} a. Predict with 95% confidence the number of concerts attended by a 45-year-old individual. b. Predict with 95% confidence the average number of concerts attended by all 45-year-old individuals.$ a. Predict with 95% confidence the number of concerts attended by a 45-year-old individual. b. Predict with 95% confidence the average number of concerts attended by all 45-year-old individuals.

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Question 142

The quality of oil is measured in API gravity degrees - the higher the degrees API, the higher the quality. The table shown below is produced by an expert in the field, who believes that there is a relationship between quality and price per barrel. Oil degrees API Price per barrel (in \ ) 27.0 12.02 28.5 12.04 30.8 12.32 31.3 12.27 31.9 12.49 34.5 12.70 34.0 12.80 34.7 13.00 37.0 13.00 41.0 13.17 41.0 13.19 38.8 13.22 39.3 13.27 A partial Minitab output follows. Descriptive Statistics Variable Mean StDev SE Mean Degrees 13 34.60 4.613 1.280 Frice 13 12.730 0.457 0.127 Covariances Degrees Price Degrees 21.281667 Price 2.026750 0.208833 Regression Analysis Predictor Coef StDev Constant 9.4349 0.2867 32.91 0.000 Degrees 0.095235 0.008220 11.59 0.000 S = 0.1314 R-Sq = 92.46% R-Sq(adj) = 91.7% Analysis of Variance Source DF SS MS F P Regression 1 2.3162 2.3162 134.24 0.000 Residual Error 11 0.1898 0.0173 Total 12 2.5060 Conduct a test of the population slope to determine at the 5% significance level whether a linear relationship exists between the quality of oil and price per barrel.

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Question 143

If the coefficient of correlation between x and y is close to −1.0, which of the following statements is correct?

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Question 144

The residual $r _ { i }$ is defined as the difference between the actual value $y _ { i }$ and the estimated value $The residual r _ { i } is defined as the difference between the actual value y _ { i } and the estimated value .$ .

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Question 145

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 Conduct a test of the population coefficient of correlation to determine at the 5% significance level whether a linear relationship exists between years of education and income.

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Question 146

If the coefficient of correlation is 0.80, the percentage of the variation in y that is explained by the variation in x is:

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Question 147

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 ($000s) from 10 randomly selected weeks is given below with Excel regression output. \begin{array} { | c | c | } \hline \text { Number of vo uchers } & \text { Sales } \\ \hline 4 & 12.8 \\ \hline 7 & 15.4 \\ \hline 5 & 13.9 \\ \hline 3 & 11.2 \\ \hline 19 & 18.7 \\ \hline 10 & 17.9 \\ \hline 8 & 16.8 \\ \hline 6 & 15.9 \\ \hline 3 & 11.5 \\ \hline 5 & 13.9 \\ \hline \end{array} Test the significance of the slope against a suitable alternative, at the 5% level of significance. Justify your choice of the direction in your alternative hypothesis.$ Test the significance of the slope against a suitable alternative, at the 5% level of significance. Justify your choice of the direction in your alternative hypothesis.

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Question 148

Which of the following statements best describes the slope in the simple linear regression model?

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Question 149

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 Behaviour Grade Business Statistics Grade 1 2 3 4 5 6 7 8 9 10

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Question 150

If all the points in a scatter diagram lie on the least squares regression line, then the coefficient of correlation must be +1.0.

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Question 151

A statistician investigating the relationship between the amount of precipitation (in inches) and the number of car accidents gathered data for 10 randomly selected days. The results are presented below. Day Precipitation Number of accidents 1 0.05 5 2 0.12 6 3 0.05 2 4 0.08 4 5 0.10 8 6 0.35 14 7 0.15 7 8 0.30 13 9 0.10 7 10 0.20 10 Determine the coefficient of determination and discuss what its value tells you about the two variables.

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Question 152

In a regression problem, if the coefficient of determination is 0.95, this means that:

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Question 153

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 154

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. Coffee sales revenue Temperature 6.50 25 10.00 17 5.50 30 4.50 35 3.50 40 28.00 9 Calculate and interpret a 95% confidence interval for the population slope.

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Question 155

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 Conduct a test of the population coefficient of correlation to determine at the 5% significance level whether a linear relationship exists between TV game show contestants' years of education and their winnings.

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Question 156

If the sum of squared residuals is zero, then the:

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Question 157

Except for the values r = -1, 0 and 1, we cannot be specific in our interpretation of the coefficient of correlation r. However, when we square it, we produce a more meaningful statistic.

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Question 158

In regression analysis, the coefficient of determination, $R ^ { 2 }$ , measures the amount of variation in y that is:

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Question 159

A regression analysis between sales (in $1000) and advertising (in $) yielded the least squares line = 80 000 + 5x. This implies that an:

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Question 160

Showing 141 - 160 of 213

If the coefficient of correlation between x and y is close to −1.0, which of the following statements is correct?

The residual $r _ { i }$ is defined as the difference between the actual value $y _ { i }$ and the estimated value $The residual r _ { i } is defined as the difference between the actual value y _ { i } and the estimated value .$ .

If the coefficient of correlation is 0.80, the percentage of the variation in y that is explained by the variation in x is:

Which of the following statements best describes the slope in the simple linear regression model?

If all the points in a scatter diagram lie on the least squares regression line, then the coefficient of correlation must be +1.0.

In a regression problem, if the coefficient of determination is 0.95, this means that:

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

If the sum of squared residuals is zero, then the:

Except for the values r = -1, 0 and 1, we cannot be specific in our interpretation of the coefficient of correlation r. However, when we square it, we produce a more meaningful statistic.

In regression analysis, the coefficient of determination, $R ^ { 2 }$ , measures the amount of variation in y that is:

A regression analysis between sales (in $1000) and advertising (in $) yielded the least squares line = 80 000 + 5x. This implies that an:

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

If the coefficient of correlation between x and y is close to −1.0, which of the following statements is correct?

The residual rir _ { i }ri​ is defined as the difference between the actual value yiy _ { i }yi​ and the estimated value .

If the coefficient of correlation is 0.80, the percentage of the variation in y that is explained by the variation in x is:

Which of the following statements best describes the slope in the simple linear regression model?

If all the points in a scatter diagram lie on the least squares regression line, then the coefficient of correlation must be +1.0.

In a regression problem, if the coefficient of determination is 0.95, this means that:

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

If the sum of squared residuals is zero, then the:

Except for the values r = -1, 0 and 1, we cannot be specific in our interpretation of the coefficient of correlation r. However, when we square it, we produce a more meaningful statistic.

In regression analysis, the coefficient of determination, R2R ^ { 2 }R2 , measures the amount of variation in y that is:

A regression analysis between sales (in $1000) and advertising (in $) yielded the least squares line = 80 000 + 5x. This implies that an:

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 residual $r _ { i }$ is defined as the difference between the actual value $y _ { i }$ and the estimated value $The residual r _ { i } is defined as the difference between the actual value y _ { i } and the estimated value .$ .

In regression analysis, the coefficient of determination, $R ^ { 2 }$ , measures the amount of variation in y that is: