In simple linear regression, which of the following statements indicates no linear relationship between the variables x and y? $\begin{array}{|l|l|} \hline\text { A. } & \text { The coefficient of determination is 1.0 .}\\ \hline \text { B. } & \text { The coefficient of correlation is 0.0 .} \\ \hline \text { C. } &\text { The sum of squares for error is 0.0 .}\\ \hline \text { D. } &\text {The sum of squares for regression is relatively large. }\\ \hline \end{array}$

The answer of In simple linear regression, which of the...

On the least squares regression line Estimated y= 2 - 3x, the predicted value of y equals: $\begin{array}{|l|l|} \hline A.& -1.0~ when~ x=-1.0.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\\ \hline B.& 1.0~ when~ x=1.0.\\ \hline C.& 5.0~ when~ x=-1.0.\\ \hline D.& 5.0~ when~ x=1.0.\\\hline \end{array}$

The answer of On the least squares regression line Estimated...

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. \[\begin{array} { | l | c | c | c | c | c | c | c | c | } \hline \text { Education } & 16 & 11 & 15 & 8 & 12 & 10 & 13 & 14 \\ \hline \text { Income } & 58 & 40 & 55 & 35 & 43 & 41 & 52 & 49 \\ \hline \end{array}\] Determine the coefficient of determination, and discuss what its value tells you about the two variables.

@#IMG-DLM& 0.9223, which means that 92.0

The Spearman rank correlation coefficient must be used to determine whether a relationship exists between two variables when: $\begin{array}{|l|l|} \hline\text { A. } & \text { one of the variables may be ordinal.}\\ \hline \text { B. } & \text { both of the variables may be ordinal.} \\ \hline \text { C. } &\text { both variables are interval and the normality requirement may not be satisfied.}\\ \hline \text { D. } &\text { All of these choices are correct.}\\ \hline \end{array}$

The answer of The Spearman rank correlation coefficient must be...

Which value of the coefficient of correlation r indicates a stronger correlation than − 0.85? \[\begin{array} { | c | c | } \hline \text { A. } & - 0.50 \\ \hline \text { B. } & 0.75 \\ \hline \text { C. } & - 0.90 \\ \hline \text { D. } & 0.85 \\ \hline \end{array}\]

The answer of Which value of the coefficient of correlation...

Exam 18: Simple Linear Regression and Correlation

Given the following linear regression model of Weekly sales ($000's) in a fast food restaurant against number of vouchers printed in the local newspaper, interpret the intercept. Does this make sense? Estimated Sales = 11.5676 + 0.4618.Vouchers

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Question 101

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

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Question 102

In simple linear regression, which of the following statements indicates no linear relationship between the variables x and y? A. The coefficient of determination is 1.0 . B. The coefficient of correlation is 0.0 . C. The sum of squares for error is 0.0 . D. The sum of squares for regression is relatively large.

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Question 103

On the least squares regression line Estimated y= 2 - 3x, the predicted value of y equals: A. -1.0\nobreakspacewhen\nobreakspacex=-1.0.\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace B. 1.0\nobreakspacewhen\nobreakspacex=1.0. C. 5.0\nobreakspacewhen\nobreakspacex=-1.0. D. 5.0\nobreakspacewhen\nobreakspacex=1.0.

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Question 104

Correlation analysis is used to determine the strength of a non-linear relationship between an independent variable x and a dependent variable y.

(True/False)

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Question 105

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 Determine the coefficient of determination, and discuss what its value tells you about the two variables.

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Question 106

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 107

In order to estimate with 95% confidence a particular value of $y$ for a given value of $x$ in a simple linear regression problem, a random sample of 20 observations is taken. The appropriate table value that would be used is 2.101.

(True/False)

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Question 108

Given that SSE = 84 and SSR = 358.12, the coefficient of correlation (also called the Pearson coefficient of correlation) must be 0.90.

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Question 109

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 Calculate the standard error of estimate, and describe what this statistic tells you about the regression line.

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Question 110

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 vouchers 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 SUMMARY OUTPUT Regression Statistics Multiple R 0.8524 R Square 0.7267 Adjuted R Square 0.6925 Standard Error 1.4301 Observations 10.0000 ANOVA Sgnificance df SS MS F F Regression 1.0000 43.4982 43.4982 21.2682 0.0017 Residual 8.0000 16.3618 2.0452 Total 9.0000 59.8600 Coefficients Standard Error t Stat P-value Lower 95\% Upper 95\% Interoept 11.5676 0.8341 13.8679 0.0000 9.6441 13.4912 Number of voudhers 0.4618 0.1001 4.6117 0.0017 0.2309 0.6927 Interpret the coefficient of determination.

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Question 111

The vertical spread of the data points about the regression line is measured by the y-intercept.

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Question 112

The Spearman rank correlation coefficient must be used to determine whether a relationship exists between two variables when: A. one of the variables may be ordinal. B. both of the variables may be ordinal. C. both variables are interval and the normality requirement may not be satisfied. D. All of these choices are correct.

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Question 113

If the coefficient of correlation is −0.50, the percentage of the variation in the dependent variable y that is explained by the variation in the independent variable x is: A. -50\% B. 25\%. C. 50\% D. -25\%.

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Question 114

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 standard error of estimate, and describe what this statistic tells you about the regression line.

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Question 115

When the actual values y of a dependent variable and the corresponding predicted values are the same, the standard error of the estimate will be 1.0.

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Question 116

Which value of the coefficient of correlation r indicates a stronger correlation than − 0.85? A. -0.50 B. 0.75 C. -0.90 D. 0.85

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Question 117

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 Use the predicted and actual values of y to calculate the residuals.

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Question 118

The confidence interval estimate of the expected value of y will be narrower than the prediction interval for the same given value of x and confidence level. This is because there is less error in estimating a mean value than in predicting an individual value.

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Question 119

In order to estimate with 95% confidence the expected value of y in a simple linear regression problem, a random sample of 10 observations is taken. Which of the following t-table values listed below would be used? A. 2.228. B. 2.306. C. 1.860. D. 1.812.

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Question 120

Given the following linear regression model of Weekly sales ($000's) in a fast food restaurant against number of vouchers printed in the local newspaper, interpret the intercept. Does this make sense? Estimated Sales = 11.5676 + 0.4618.Vouchers

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

Correlation analysis is used to determine the strength of a non-linear relationship between an independent variable x and a dependent variable y.

In order to estimate with 95% confidence a particular value of $y$ for a given value of $x$ in a simple linear regression problem, a random sample of 20 observations is taken. The appropriate table value that would be used is 2.101.

Given that SSE = 84 and SSR = 358.12, the coefficient of correlation (also called the Pearson coefficient of correlation) must be 0.90.

The vertical spread of the data points about the regression line is measured by the y-intercept.

If the coefficient of correlation is −0.50, the percentage of the variation in the dependent variable y that is explained by the variation in the independent variable x is: A. -50\% B. 25\%. C. 50\% D. -25\%.

When the actual values y of a dependent variable and the corresponding predicted values are the same, the standard error of the estimate will be 1.0.

Which value of the coefficient of correlation r indicates a stronger correlation than − 0.85? A. -0.50 B. 0.75 C. -0.90 D. 0.85

The confidence interval estimate of the expected value of y will be narrower than the prediction interval for the same given value of x and confidence level. This is because there is less error in estimating a mean value than in predicting an individual value.

In order to estimate with 95% confidence the expected value of y in a simple linear regression problem, a random sample of 10 observations is taken. Which of the following t-table values listed below would be used? A. 2.228. B. 2.306. C. 1.860. D. 1.812.

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

Given the following linear regression model of Weekly sales ($000's) in a fast food restaurant against number of vouchers printed in the local newspaper, interpret the intercept. Does this make sense? Estimated Sales = 11.5676 + 0.4618.Vouchers

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

Correlation analysis is used to determine the strength of a non-linear relationship between an independent variable x and a dependent variable y.

In order to estimate with 95% confidence a particular value of yyy for a given value of xxx in a simple linear regression problem, a random sample of 20 observations is taken. The appropriate table value that would be used is 2.101.

Given that SSE = 84 and SSR = 358.12, the coefficient of correlation (also called the Pearson coefficient of correlation) must be 0.90.

The vertical spread of the data points about the regression line is measured by the y-intercept.

If the coefficient of correlation is −0.50, the percentage of the variation in the dependent variable y that is explained by the variation in the independent variable x is: A. -50\% B. 25\%. C. 50\% D. -25\%.

When the actual values y of a dependent variable and the corresponding predicted values are the same, the standard error of the estimate will be 1.0.

Which value of the coefficient of correlation r indicates a stronger correlation than − 0.85? A. -0.50 B. 0.75 C. -0.90 D. 0.85

The confidence interval estimate of the expected value of y will be narrower than the prediction interval for the same given value of x and confidence level. This is because there is less error in estimating a mean value than in predicting an individual value.

In order to estimate with 95% confidence the expected value of y in a simple linear regression problem, a random sample of 10 observations is taken. Which of the following t-table values listed below would be used? A. 2.228. B. 2.306. C. 1.860. D. 1.812.

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

In order to estimate with 95% confidence a particular value of $y$ for a given value of $x$ in a simple linear regression problem, a random sample of 20 observations is taken. The appropriate table value that would be used is 2.101.