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. \[\begin{array} { | c | c | c | } \hline \text { Day } & \text { Precipitation } & \text { Number of accidents } \\ \hline 1 & 0.05 & 5 \\ \hline 2 & 0.12 & 6 \\ \hline 3 & 0.05 & 2 \\ \hline 4 & 0.08 & 4 \\ \hline 5 & 0.10 & 8 \\ \hline 6 & 0.35 & 14 \\ \hline 7 & 0.15 & 7 \\ \hline 8 & 0.30 & 13 \\ \hline 9 & 0.10 & 7 \\ \hline 10 & 0.20 & 10 \\ \hline \end{array}\] Do these data allow us to conclude at the 10% significance level that the amount of precipitation and the number of accidents are linearly related?

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

If the sum of squared residuals is zero, then the: $\begin{array}{|l|l|} \hline\text { A. } & \text {coefficient of determination must be 1.0 . }\\ \hline \text { B. } & \text {coefficient of correlation must be 1.0 . } \\ \hline \text { C. } &\text {coefficient of determination must be 0.0 . }\\ \hline \text { D. } &\text {coefficient of correlation must be 0.0 . }\\ \hline \end{array}$

The answer of If the sum of squared residuals is...

In a regression problem the following pairs (x,y) are given: (1,2), (2.5,2), (3,2), (5,2) and (5.3,2). This indicates that the: $\begin{array}{|l|l|} \hline\text { A. } & \text {correlation coefficient is 0 . }\\ \hline \text { B. } & \text {correlation coefficient is 1 . } \\ \hline \text { C. } &\text {correlation coefficient is -1 . }\\ \hline \text { D. } &\text {coefficient of determination is between 0 and 1 . }\\ \hline \end{array}$

The answer of In a regression problem the following pairs...

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.

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

In regression analysis, if the coefficient of determination is 1.0, then: $\begin{array}{|l|l|} \hline\text { A. } & \text { the sum of squares for error must be 1.0 .}\\ \hline \text { B. } & \text { the sum of squares for regression must be 1.0. } \\ \hline \text { C. } &\text { the sum of squares for error must be 0.0 .}\\ \hline \text { D. } &\text {the sum of squares for regression must be 0.0 . }\\ \hline \end{array}$

The answer of In regression analysis, if the coefficient of...

Exam 18: Simple Linear Regression and Correlation

A consultant for a beer company wanted to determine whether those who drink a lot of beer actually enjoy the taste more than those who drink moderately or rarely. She took a random sample of eight men and asked each how many beers they typically drink per week. She also asked them to rate their favourite brand of beer on a 10-point scale (1 = bad, 10 = excellent). The results are shown below. Can we infer at the 5% significance level that frequent beer drinkers rate their favourite beer more highly than less frequent drinkers? Beer drinker Typical weekly consumption Rating 1 4 6 2 3 6 3 12 9 4 15 8 5 7 8 6 9 6 7 1 5 8 10 8

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Question 41

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

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Question 42

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

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Question 43

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

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Question 44

If the coefficient of determination is 81%, and the linear regression model has a negative slope, what is the value of the coefficient of correlation? A -0.81 B 0.90 C 0.81 D -0.90

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Question 45

If all the values of an independent variable x are equal, then regressing a dependent variable y on x will result in a coefficient of determination of 100%.

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Question 46

A regression analysis between height y (in cm) and age x (in years) of 2 to 10 years old boys yielded the least squares line y-hat = 87 + 6.5x. This implies that by each additional year height is expected to: $\begin{array}{|l|l|}\hline A&\text {increase by 93.5 \mathrm{~cm} . }\\\hline B&\text {increase by $ 6.5 \mathrm{~cm} $. }\\\hline C&\text {increase by $ 87 \mathrm{~cm} $. }\\\hline D&\text {decrease by $ 6.5 \mathrm{~cm} $. }\\\hline \end{array}$

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Question 47

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

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Question 48

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 Do these data allow us to conclude at the 10% significance level that the amount of precipitation and the number of accidents are linearly related?

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Question 49

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 50

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 Draw a scatter diagram of the data to determine whether a linear model appears to be appropriate.

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Question 51

Another name for the residual term in a regression equation is random error.

(True/False)

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Question 52

If the sum of squared residuals is zero, then the: A. coefficient of determination must be 1.0 . B. coefficient of correlation must be 1.0 . C. coefficient of determination must be 0.0 . D. coefficient of correlation must be 0.0 .

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Question 53

In a regression problem the following pairs (x,y) are given: (1,2), (2.5,2), (3,2), (5,2) and (5.3,2). This indicates that the: A. correlation coefficient is 0 . B. correlation coefficient is 1 . C. correlation coefficient is -1 . D. coefficient of determination is between 0 and 1 .

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Question 54

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 55

A regression analysis between sales (in $1000) and advertising (in $) yielded the least squares line $A regression analysis between sales (in $1000) and advertising (in $) yielded the least squares line = 80 000 + 5x. This implies that an: \begin{array}{|l|l|} \hline A&\text {increase of \$ 1 in advertising is expected to result in an increase of <span class=$ $\$ 5$ in sales. }\\ \hline B&\text { increase $\$ 5$ in advertising is expected to result in an increase of $\$ 5000$ in sales.}\\ \hline C&\text { increase of $\$ 1$ in advertising is expected to result in an increase of $\$ 80005$ in sales. }\\ \hline D&\text {increase of $\$ 1$ in advertising is expected to result in an increase of $\$ 5000$ in sales. }\\ \hline \end{array} " class="answers-bank-image d-inline" loading="lazy" > = 80 000 + 5x. This implies that an: A increase of \ 1 in advertising is expected to result in an increase of \ 5 in sales. B increase \ 5 in advertising is expected to result in an increase of \ 5000 in sales. C increase of \ 1 in advertising is expected to result in an increase of \ 80005 in sales. D increase of \ 1 in advertising is expected to result in an increase of \ 5000 in sales.

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Question 56

The variance of the error variable, $\sigma _ { \varepsilon } ^ { 2 }$ , is required to be constant. When this requirement is satisfied, the condition is called homoscedasticity.

(True/False)

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Question 57

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 58

In regression analysis, if the coefficient of determination is 1.0, then: A. the sum of squares for error must be 1.0 . B. the sum of squares for regression must be 1.0. C. the sum of squares for error must be 0.0 . D. the sum of squares for regression must be 0.0 .

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Question 59

An outlier is an observation that is unusually small or unusually large.

(True/False)

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Question 60

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

If the coefficient of determination is 81%, and the linear regression model has a negative slope, what is the value of the coefficient of correlation? A -0.81 B 0.90 C 0.81 D -0.90

If all the values of an independent variable x are equal, then regressing a dependent variable y on x will result in a coefficient of determination of 100%.

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

Another name for the residual term in a regression equation is random error.

If the sum of squared residuals is zero, then the: A. coefficient of determination must be 1.0 . B. coefficient of correlation must be 1.0 . C. coefficient of determination must be 0.0 . D. coefficient of correlation must be 0.0 .

In a regression problem the following pairs (x,y) are given: (1,2), (2.5,2), (3,2), (5,2) and (5.3,2). This indicates that the: A. correlation coefficient is 0 . B. correlation coefficient is 1 . C. correlation coefficient is -1 . D. coefficient of determination is between 0 and 1 .

The variance of the error variable, $\sigma _ { \varepsilon } ^ { 2 }$ , is required to be constant. When this requirement is satisfied, the condition is called homoscedasticity.

In regression analysis, if the coefficient of determination is 1.0, then: A. the sum of squares for error must be 1.0 . B. the sum of squares for regression must be 1.0. C. the sum of squares for error must be 0.0 . D. the sum of squares for regression must be 0.0 .

An outlier is an observation that is unusually small or unusually large.

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

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

If the coefficient of determination is 81%, and the linear regression model has a negative slope, what is the value of the coefficient of correlation? A -0.81 B 0.90 C 0.81 D -0.90

If all the values of an independent variable x are equal, then regressing a dependent variable y on x will result in a coefficient of determination of 100%.

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

Another name for the residual term in a regression equation is random error.

If the sum of squared residuals is zero, then the: A. coefficient of determination must be 1.0 . B. coefficient of correlation must be 1.0 . C. coefficient of determination must be 0.0 . D. coefficient of correlation must be 0.0 .

In a regression problem the following pairs (x,y) are given: (1,2), (2.5,2), (3,2), (5,2) and (5.3,2). This indicates that the: A. correlation coefficient is 0 . B. correlation coefficient is 1 . C. correlation coefficient is -1 . D. coefficient of determination is between 0 and 1 .

The variance of the error variable, σε2\sigma _ { \varepsilon } ^ { 2 }σε2​ , is required to be constant. When this requirement is satisfied, the condition is called homoscedasticity.

In regression analysis, if the coefficient of determination is 1.0, then: A. the sum of squares for error must be 1.0 . B. the sum of squares for regression must be 1.0. C. the sum of squares for error must be 0.0 . D. the sum of squares for regression must be 0.0 .

An outlier is an observation that is unusually small or unusually large.

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 variance of the error variable, $\sigma _ { \varepsilon } ^ { 2 }$ , is required to be constant. When this requirement is satisfied, the condition is called homoscedasticity.