A television rating wants to determine whether married couples tend to agree about the quality of the television shows they watch. Ten couples are asked to rate a particular comedy series on a 7-point scale where 1 = terrible and 7 = excellent. The results are shown below. \[\begin{array} { | l | l | l | l | l | l | l | l | l | l | l | } \hline \text { Husband's rating } & 3 & 6 & 6 & 5 & 4 & 5 & 7 & 4 & 5 & 5 \\ \hline \text { Wife's rating } & 5 & 5 & 4 & 5 & 4 & 4 & 6 & 3 & 4 & 5 \\ \hline \end{array}\] Do these data provide sufficient evidence at the 5% significance level to conclude that the husband's and the wife's ratings are positively related?

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

The following sums of squares are produced: (yi-(y-bar))2 = 250, (yi-(yi-hat))2 = 100, ((yi-hat)-(y-bar))2 = 150 The percentage of the variation in y that is explained by the variation in x is:

A) 60% . B) 75% . C) 40% . D) 50% . A) 60% . B) 75% . C) 40% . D) 50% .

Exam 18: Simple Linear Regression and Correlation

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 Use the regression equation to determine the predicted values of y.

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Question 81

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 Predict with 95% confidence the number of accidents that occur when there is 0.40 inches of rain.

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Question 82

When the actual values y of a dependent variable and the corresponding predicted values $When the actual values y of a dependent variable and the corresponding predicted values are the same, the standard error of estimate, S _ { \varepsilon } , will be 0.0.$ are the same, the standard error of estimate, $S _ { \varepsilon }$ , will be 0.0.

(True/False)

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Question 83

A television rating wants to determine whether married couples tend to agree about the quality of the television shows they watch. Ten couples are asked to rate a particular comedy series on a 7-point scale where 1 = terrible and 7 = excellent. The results are shown below. Husband's rating 3 6 6 5 4 5 7 4 5 5 Wife's rating 5 5 4 5 4 4 6 3 4 5 Do these data provide sufficient evidence at the 5% significance level to conclude that the husband's and the wife's ratings are positively related?

(Essay)

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Question 84

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

(Multiple Choice)

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Question 85

The standard error of estimate, $S _ { \varepsilon }$ , is a measure of:

(Multiple Choice)

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Question 86

The least squares method requires that the variance $\sigma _ { \varepsilon } ^ { 2 }$ of the error variable ${ \varepsilon }$ is a constant no matter what the value of x is. When this requirement is violated, the condition is called:

(Multiple Choice)

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Question 87

The following sums of squares are produced: (y_i-(y-bar))² = 250, 11ef1ab2_4bf1_c05d_a741_c73dacf30ae9_TB5762_11(y_i-(y_i-hat))² = 100, 11ef1ab2_4bf1_c05d_a741_c73dacf30ae9_TB5762_11((y_i-hat)-(y-bar))² = 150 The percentage of the variation in y that is explained by the variation in x is:

(Multiple Choice)

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Question 88

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 89

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 Draw a scatter diagram of the data and plot the least squares regression line on it.

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Question 90

A regression line using 25 observations produced SSR = 118.68 and SSE = 56.32. The standard error of estimate was:

(Multiple Choice)

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Question 91

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 92

We standardise residuals in the same way that we standardise all variables, by subtracting the mean and dividing by the variance.

(True/False)

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Question 93

In developing a 95% confidence interval for the expected value of y from a simple linear regression problem involving a sample of size 10, the appropriate table value would be 2.306.

(True/False)

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Question 94

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 Find the least squares regression line.

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Question 95

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 Estimate with 95% confidence the mean daily number of accidents when the daily precipitation is 0.25 inches.

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Question 96

The symbol for the population coefficient of correlation is:

(Multiple Choice)

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Question 97

In a regression problem, if all the values of the independent variable are equal, then the coefficient of determination must be:

(Multiple Choice)

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Question 98

A regression analysis between y, sales (in $1000) and x, advertising (in $) yielded the least squares line = 60 + 5x. We can interpret the slope by saying that we estimate for each extra $1 spent on advertising that sales will increase by $5 000, on average.

(True/False)

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Question 99

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

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Question 100

Showing 81 - 100 of 213

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

The standard error of estimate, $S _ { \varepsilon }$ , is a measure of:

The least squares method requires that the variance $\sigma _ { \varepsilon } ^ { 2 }$ of the error variable ${ \varepsilon }$ is a constant no matter what the value of x is. When this requirement is violated, the condition is called:

The following sums of squares are produced: (y_i-(y-bar))² = 250, 11ef1ab2_4bf1_c05d_a741_c73dacf30ae9_TB5762_11(y_i-(y_i-hat))² = 100, 11ef1ab2_4bf1_c05d_a741_c73dacf30ae9_TB5762_11((y_i-hat)-(y-bar))² = 150 The percentage of the variation in y that is explained by the variation in x is:

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

A regression line using 25 observations produced SSR = 118.68 and SSE = 56.32. The standard error of estimate was:

We standardise residuals in the same way that we standardise all variables, by subtracting the mean and dividing by the variance.

In developing a 95% confidence interval for the expected value of y from a simple linear regression problem involving a sample of size 10, the appropriate table value would be 2.306.

The symbol for the population coefficient of correlation is:

In a regression problem, if all the values of the independent variable are equal, then the coefficient of determination must be:

A regression analysis between y, sales (in $1000) and x, advertising (in $) yielded the least squares line = 60 + 5x. We can interpret the slope by saying that we estimate for each extra $1 spent on advertising that sales will increase by $5 000, on average.

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 actual values y of a dependent variable and the corresponding predicted values are the same, the standard error of estimate, SεS _ { \varepsilon }Sε​ , will be 0.0.

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

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

The least squares method requires that the variance σε2\sigma _ { \varepsilon } ^ { 2 }σε2​ of the error variable ε { \varepsilon }ε is a constant no matter what the value of x is. When this requirement is violated, the condition is called:

The following sums of squares are produced: (yi-(y-bar))2 = 250, 11ef1ab2_4bf1_c05d_a741_c73dacf30ae9_TB5762_11(yi-(yi-hat))2 = 100, 11ef1ab2_4bf1_c05d_a741_c73dacf30ae9_TB5762_11((yi-hat)-(y-bar))2 = 150 The percentage of the variation in y that is explained by the variation in x is:

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

A regression line using 25 observations produced SSR = 118.68 and SSE = 56.32. The standard error of estimate was:

We standardise residuals in the same way that we standardise all variables, by subtracting the mean and dividing by the variance.

In developing a 95% confidence interval for the expected value of y from a simple linear regression problem involving a sample of size 10, the appropriate table value would be 2.306.

The symbol for the population coefficient of correlation is:

In a regression problem, if all the values of the independent variable are equal, then the coefficient of determination must be:

A regression analysis between y, sales (in $1000) and x, advertising (in $) yielded the least squares line = 60 + 5x. We can interpret the slope by saying that we estimate for each extra $1 spent on advertising that sales will increase by $5 000, on average.

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 a measure of:

The least squares method requires that the variance $\sigma _ { \varepsilon } ^ { 2 }$ of the error variable ${ \varepsilon }$ is a constant no matter what the value of x is. When this requirement is violated, the condition is called:

The following sums of squares are produced: (y_i-(y-bar))² = 250, 11ef1ab2_4bf1_c05d_a741_c73dacf30ae9_TB5762_11(y_i-(y_i-hat))² = 100, 11ef1ab2_4bf1_c05d_a741_c73dacf30ae9_TB5762_11((y_i-hat)-(y-bar))² = 150 The percentage of the variation in y that is explained by the variation in x is: