Question 1

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? $$\begin{array} { | c | c | c | } 
\hline \begin{array} { c } 
\text { Beer } \
\text { drinker }
\end{array} & \begin{array} { c } 
\text { Typical weekly } \
\text { consumption }
\end{array} & \text { Rating } \
\hline 1 & 4 & 6 \
\hline 2 & 3 & 6 \
\hline 3 & 12 & 9 \
\hline 4 & 15 & 8 \
\hline 5 & 7 & 8 \
\hline 6 & 9 & 6 \
\hline 7 & 1 & 5 \
\hline 8 & 10 & 8 \
\hline
\end{array}$$

Accepted Answer

The answer of A consultant for a beer company wanted...

Question 2

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

Accepted Answer

A) True 
 B)False

Question 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. $$\begin{array} { | c | c | c | } 
\hline \text { Contestant } & \begin{array} { c } 
\text { Years of } \
\text { education }
\end{array} & \text { Winnings } \
\hline 1 & 11 & 750 \
\hline 2 & 15 & 400 \
\hline 3 & 12 & 600 \
\hline 4 & 16 & 350 \
\hline 5 & 11 & 800 \
\hline 6 & 16 & 300 \
\hline 7 & 13 & 650 \
\hline 8 & 14 & 400 \
\hline
\end{array}$$ Calculate the Pearson correlation coefficient. What sign does it have? Why?

Accepted Answer

The answer of An ardent fan of television game shows...

Question 4

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. $$\begin{array} { | c | c | c | } 
\hline \text { Movie } & \begin{array} { c } 
\text { Cost of two highest- } \
\text { paid performers } ( \$ \mathrm {~m} )
\end{array} & \begin{array} { c } 
\text { Gross revenue } \
( \$ \mathrm {~m} )
\end{array} \
\hline 1 & 5.3 & 48 \
\hline 2 & 7.2 & 65 \
\hline 3 & 1.3 & 18 \
\hline 4 & 1.8 & 20 \
\hline 5 & 3.5 & 31 \
\hline 6 & 2.6 & 26 \
\hline 7 & 8.0 & 73 \
\hline 8 & 2.4 & 23 \
\hline 9 & 4.5 & 39 \
\hline 10 & 6.7 & 58 \
\hline
\end{array}$$ Use the regression equation to determine the predicted values of y.

Accepted Answer

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Question 5

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? $\begin{array}{|l|l|}
\hline A&\text { -0.81}\
\hline B&\text {0.90 }\
\hline C&\text { 0.81}\
\hline D&\text { -0.90}\
\hline 
\end{array}$

Accepted Answer

The answer of If the coefficient of determination is 81%,...

Question 6

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%.

Accepted Answer

A) True 
 B)False

Question 7

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} $. }\
\hline 
\end{array}$

Accepted Answer

The answer of A regression analysis between height y (in...

Question 8

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

Accepted Answer

A) True 
 B)False

Question 9

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?

Accepted Answer

The answer of A statistician investigating the relationship between the...

Question 10

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. $$\begin{array} { | c | c | c | } 
\hline \text { Movie } & \begin{array} { c } 
\text { Cost of two highest- } \
\text { paid performers } ( \$ \mathrm {~m} )
\end{array} & \begin{array} { c } 
\text { Gross revenue } \
( \$ \mathrm {~m} )
\end{array} \
\hline 1 & 5.3 & 48 \
\hline 2 & 7.2 & 65 \
\hline 3 & 1.3 & 18 \
\hline 4 & 1.8 & 20 \
\hline 5 & 3.5 & 31 \
\hline 6 & 2.6 & 26 \
\hline 7 & 8.0 & 73 \
\hline 8 & 2.4 & 23 \
\hline 9 & 4.5 & 39 \
\hline 10 & 6.7 & 58 \
\hline
\end{array}$$ Calculate the Pearson correlation coefficient. What sign does it have? Why?

Accepted Answer

The answer of A financier whose specialty is investing in...

Question 11

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. $$\begin{array} { | l | c | c | c | c | c | c | c | c | } 
\hline \text { Education } & 16 & 11 & 15 & 8 & 12 & 10 & 13 & 14 \
\hline \text { Income } & 58 & 40 & 55 & 35 & 43 & 41 & 52 & 49 \
\hline
\end{array}$$ Draw a scatter diagram of the data to determine whether a linear model appears to be appropriate.

Accepted Answer

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Question 12

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

Accepted Answer

A) True 
 B)False

Question 13

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

Accepted Answer

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

Question 14

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: $\begin{array}{|l|l|}
\hline\text { A. } & \text {correlation coefficient is 0 . }\
\hline \text { B. } & \text {correlation coefficient is 1 . } \
\hline \text { C. } &\text {correlation coefficient is -1 . }\
\hline \text { D. } &\text {coefficient of determination is between 0 and 1 . }\
\hline
\end{array}$

Accepted Answer

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

Question 15

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.

Accepted Answer

The answer of A professor of economics wants to study...

Question 16

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 $ \$ 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}$

Accepted Answer

The answer of A regression analysis between sales (in $1000)...

Question 17

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

Accepted Answer

A) True 
 B)False

Question 18

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. $$\begin{array} { | l | c | c | c | c | c | c | c | c | } 
\hline \text { Education } & 16 & 11 & 15 & 8 & 12 & 10 & 13 & 14 \
\hline \text { Income } & 58 & 40 & 55 & 35 & 43 & 41 & 52 & 49 \
\hline
\end{array}$$ Calculate the Pearson correlation coefficient. What sign does it have? Why?

Accepted Answer

The answer of A professor of economics wants to study...

Question 19

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

Accepted Answer

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

Question 20

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

Accepted Answer

A) True 
 B)False

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? $\begin{array}{|l|l|}\hline A&\text { -0.81}\\\hline B&\text {0.90 }\\\hline C&\text { 0.81}\\\hline D&\text { -0.90}\\\hline \end{array}$

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.

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

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

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 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.

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.

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

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