Question 1

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. $$\begin{array} { | c | c | c | } 
\hline \text { Day } & \text { Precipitation } & \text { Number of accidents } \
\hline 1 & 0.05 & 5 \
\hline 2 & 0.12 & 6 \
\hline 3 & 0.05 & 2 \
\hline 4 & 0.08 & 4 \
\hline 5 & 0.10 & 8 \
\hline 6 & 0.35 & 14 \
\hline 7 & 0.15 & 7 \
\hline 8 & 0.30 & 13 \
\hline 9 & 0.10 & 7 \
\hline 10 & 0.20 & 10 \
\hline
\end{array}$$ Predict with 95% confidence the number of accidents that occur when there is 0.40 inches of rain.

Accepted Answer

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

Question 2

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. $\begin{array}{|c|c|}
\hline \text { Oil degrees API } & \text { Frice per barrel (in } \$ \text { ) } \
\hline 27.0 & 12.02 \
\hline 28.5 & 12.04 \
\hline 30.8 & 12.32 \
\hline 31.3 & 12.27 \
\hline 31.9 & 12.49 \
\hline 34.5 & 12.70 \
\hline 34.0 & 12.80 \
\hline 34.7 & 13.00 \
\hline 37.0 & 13.00 \
\hline 41.0 & 13.17 \
\hline 41.0 & 13.19 \
\hline 38.8 & 13.22 \
\hline 39.3 & 13.27 \
\hline
\end{array}$ 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 $$\begin{array} { | l | r | r | r | r | } 
\hline \text { Fredictor } & \text { Coef } & \text { StDev } & \mathrm { T } & \mathrm { P } \
\hline \text { Constant } & 9.4349 & 0.2867 & 32.91 & 0.000 \
\hline \text { Degrees } & 0.095235 & 0.008220 & 11.59 & 0.000 \
\hline
\end{array}$$ 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.

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Question 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. $$\begin{array} { | l | c | c | c | c | c | c | c | c | c | c | } 
\hline \text { Age } & 62 & 57 & 40 & 49 & 67 & 54 & 43 & 65 & 54 & 41 \
\hline \text { Number of concerts } & 6 & 5 & 4 & 3 & 5 & 5 & 2 & 6 & 3 & 1 \
\hline
\end{array}$$ $$\begin{array} { | l | c | c | c | c | c | c | c | c | c | c | } 
\hline \text { Age } & 44 & 48 & 55 & 60 & 59 & 63 & 69 & 40 & 38 & 52 \
\hline \text { Number of Concerts } & 3 & 2 & 4 & 5 & 4 & 5 & 4 & 2 & 1 & 3 \
\hline
\end{array}$$ $\begin{array}{ll}
\text { SUMMARY OUTPUT }&\text { DESCRIPTIVE STATISTICS }\
\begin{array}{lc}
\hline {\text { Reqression Statiatics }} \
\hline \text { Multiple R } & 0.80203 \
\text { R Square } & 0.64326 \
\text { Adjusted R Square } & 0.62344 \
\text { Standard Error } & 0.93965 \
\text { Observations } & 20 \
\hline
\end{array}&\begin{array}{lclc}
\hline {\text { Age }} &&{\text { Concerts }} \
\hline \text { Mean } & 53 & \text { Mean } & 3.65 \
\text { Standard Error } & 2.1849 & \text { Standard Error } & 0.3424 \
\text { Standard Deviation } & 9.7711 & \text { Standard Deviation } & 1.5313 \
\text { Sample Variance } & 95.4737 & \text { Sample Variance } & 2.3447 \
\text { Count } & 20 & \text { Count } & 20\\hline
\end{array}\
\end{array}$
$\text { SPEARMAN RANK CORRELATION COEFFICIENT }=0.8306$

$\begin{array}{lccccc} \text { ANOVA }\
\hline& \text { df } & \text { SS } & \text { MS } & F & \text { Significance F } \
\hline \text { Regression } & 1 & 28.65711 & 28.65711 & 32.45653 & 2.1082 \mathrm{E}-05 \
\text { Residual } & 18 & 15.89289 & 0.88294 & & \
\text { Total } & 19 & 44.55 & & &\\hline
\end{array}$

$\begin{array}{lcccccc}
\hline & \text { Coefficients } & \text {Standard Error } & \text { t Stat } & \text { P-value } & \text { Lower } 95 \% & \text { Upper 95\% } \
\hline \text { Intercept } & -3.01152 & 1.18802 & -2.53491 & 0.02074 & -5.50746 & -0.5156 \
\text { Age } & 0.12569 & 0.02206 & 5.69706 & 0.00002 & 0.07934 & 0.1720
\end{array}$ a. Draw a scatter diagram of the data to determine whether a linear model appears to be appropriate to describe the relationship between the age and number of concerts attended by the respondents.
b. Determine the least squares regression line.
c. Plot the least squares regression line.
d. Interpret the value of the slope of the regression line.

Accepted Answer

The answer of At a recent music concert, a survey...

Question 4

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.

Accepted Answer

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

Question 5

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. $$\begin{array} { | l | c | c | c | c | c | c | c | c | c | c | } 
\hline \text { Age } & 62 & 57 & 40 & 49 & 67 & 54 & 43 & 65 & 54 & 41 \
\hline \text { Number of concerts } & 6 & 5 & 4 & 3 & 5 & 5 & 2 & 6 & 3 & 1 \
\hline
\end{array}$$ $$\begin{array} { | l | c | c | c | c | c | c | c | c | c | c | } 
\hline \text { Age } & 44 & 48 & 55 & 60 & 59 & 63 & 69 & 40 & 38 & 52 \
\hline \text { Number of Concerts } & 3 & 2 & 4 & 5 & 4 & 5 & 4 & 2 & 1 & 3 \
\hline
\end{array}$$ $\begin{array}{ll}
\text { SUMMARY OUTPUT }&\text { DESCRIPTIVE STATISTICS }\
\begin{array}{lc}
\hline {\text { Reqression Statiatics }} \
\hline \text { Multiple R } & 0.80203 \
\text { R Square } & 0.64326 \
\text { Adjusted R Square } & 0.62344 \
\text { Standard Error } & 0.93965 \
\text { Observations } & 20 \
\hline
\end{array}&\begin{array}{lclc}
\hline {\text { Age }} &&{\text { Concerts }} \
\hline \text { Mean } & 53 & \text { Mean } & 3.65 \
\text { Standard Error } & 2.1849 & \text { Standard Error } & 0.3424 \
\text { Standard Deviation } & 9.7711 & \text { Standard Deviation } & 1.5313 \
\text { Sample Variance } & 95.4737 & \text { Sample Variance } & 2.3447 \
\text { Count } & 20 & \text { Count } & 20\\hline
\end{array}\
\end{array}$
$\text { SPEARMAN RANK CORRELATION COEFFICIENT }=0.8306$

$\begin{array}{lccccc} \text { ANOVA }\
\hline& \text { df } & \text { SS } & \text { MS } & F & \text { Significance F } \
\hline \text { Regression } & 1 & 28.65711 & 28.65711 & 32.45653 & 2.1082 \mathrm{E}-05 \
\text { Residual } & 18 & 15.89289 & 0.88294 & & \
\text { Total } & 19 & 44.55 & & &\\hline
\end{array}$

$\begin{array}{lcccccc}
\hline & \text { Coefficients } & \text {Standard Error } & \text { t Stat } & \text { P-value } & \text { Lower } 95 \% & \text { Upper 95\% } \
\hline \text { Intercept } & -3.01152 & 1.18802 & -2.53491 & 0.02074 & -5.50746 & -0.5156 \
\text { Age } & 0.12569 & 0.02206 & 5.69706 & 0.00002 & 0.07934 & 0.1720
\end{array}$ 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.

Accepted Answer

The answer of At a recent music concert, a survey...

Question 6

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. $$\begin{array} { | l | c | c | c | c | c | c | c | c | c | c | } 
\hline \text { Age } & 62 & 57 & 40 & 49 & 67 & 54 & 43 & 65 & 54 & 41 \
\hline \text { Number of concerts } & 6 & 5 & 4 & 3 & 5 & 5 & 2 & 6 & 3 & 1 \
\hline
\end{array}$$ $$\begin{array} { | l | c | c | c | c | c | c | c | c | c | c | } 
\hline \text { Age } & 44 & 48 & 55 & 60 & 59 & 63 & 69 & 40 & 38 & 52 \
\hline \text { Number of Concerts } & 3 & 2 & 4 & 5 & 4 & 5 & 4 & 2 & 1 & 3 \
\hline
\end{array}$$ $\begin{array}{ll}
\text { SUMMARY OUTPUT }&\text { DESCRIPTIVE STATISTICS }\
\begin{array}{lc}
\hline {\text { Reqression Statiatics }} \
\hline \text { Multiple R } & 0.80203 \
\text { R Square } & 0.64326 \
\text { Adjusted R Square } & 0.62344 \
\text { Standard Error } & 0.93965 \
\text { Observations } & 20 \
\hline
\end{array}&\begin{array}{lclc}
\hline {\text { Age }} &&{\text { Concerts }} \
\hline \text { Mean } & 53 & \text { Mean } & 3.65 \
\text { Standard Error } & 2.1849 & \text { Standard Error } & 0.3424 \
\text { Standard Deviation } & 9.7711 & \text { Standard Deviation } & 1.5313 \
\text { Sample Variance } & 95.4737 & \text { Sample Variance } & 2.3447 \
\text { Count } & 20 & \text { Count } & 20\\hline
\end{array}\
\end{array}$
$\text { SPEARMAN RANK CORRELATION COEFFICIENT }=0.8306$

$\begin{array}{lccccc} \text { ANOVA }\
\hline& \text { df } & \text { SS } & \text { MS } & F & \text { Significance F } \
\hline \text { Regression } & 1 & 28.65711 & 28.65711 & 32.45653 & 2.1082 \mathrm{E}-05 \
\text { Residual } & 18 & 15.89289 & 0.88294 & & \
\text { Total } & 19 & 44.55 & & &\\hline
\end{array}$

$\begin{array}{lcccccc}
\hline & \text { Coefficients } & \text {Standard Error } & \text { t Stat } & \text { P-value } & \text { Lower } 95 \% & \text { Upper 95\% } \
\hline \text { Intercept } & -3.01152 & 1.18802 & -2.53491 & 0.02074 & -5.50746 & -0.5156 \
\text { Age } & 0.12569 & 0.02206 & 5.69706 & 0.00002 & 0.07934 & 0.1720
\end{array}$ a. Determine the standard error of estimate and describe what this statistic tells you about the model's fit.
b. Interpret the coefficient of correlation.
c. Interpret the coefficient of determination, and discuss what its value tells you about the two variables.

Accepted Answer

The answer of At a recent music concert, a survey...

Question 7

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. $$\begin{array} { | l | c | c | c | c | c | c | c | c | c | c | } 
\hline \text { Age } & 62 & 57 & 40 & 49 & 67 & 54 & 43 & 65 & 54 & 41 \
\hline \text { Number of concerts } & 6 & 5 & 4 & 3 & 5 & 5 & 2 & 6 & 3 & 1 \
\hline
\end{array}$$ $$\begin{array} { | l | c | c | c | c | c | c | c | c | c | c | } 
\hline \text { Age } & 44 & 48 & 55 & 60 & 59 & 63 & 69 & 40 & 38 & 52 \
\hline \text { Number of Concerts } & 3 & 2 & 4 & 5 & 4 & 5 & 4 & 2 & 1 & 3 \
\hline
\end{array}$$ $\begin{array}{ll}
\text { SUMMARY OUTPUT }&\text { DESCRIPTIVE STATISTICS }\
\begin{array}{lc}
\hline {\text { Reqression Statiatics }} \
\hline \text { Multiple R } & 0.80203 \
\text { R Square } & 0.64326 \
\text { Adjusted R Square } & 0.62344 \
\text { Standard Error } & 0.93965 \
\text { Observations } & 20 \
\hline
\end{array}&\begin{array}{lclc}
\hline {\text { Age }} &&{\text { Concerts }} \
\hline \text { Mean } & 53 & \text { Mean } & 3.65 \
\text { Standard Error } & 2.1849 & \text { Standard Error } & 0.3424 \
\text { Standard Deviation } & 9.7711 & \text { Standard Deviation } & 1.5313 \
\text { Sample Variance } & 95.4737 & \text { Sample Variance } & 2.3447 \
\text { Count } & 20 & \text { Count } & 20\\hline
\end{array}\
\end{array}$
$\text { SPEARMAN RANK CORRELATION COEFFICIENT }=0.8306$

$\begin{array}{lccccc} \text { ANOVA }\
\hline& \text { df } & \text { SS } & \text { MS } & F & \text { Significance F } \
\hline \text { Regression } & 1 & 28.65711 & 28.65711 & 32.45653 & 2.1082 \mathrm{E}-05 \
\text { Residual } & 18 & 15.89289 & 0.88294 & & \
\text { Total } & 19 & 44.55 & & &\\hline
\end{array}$

$\begin{array}{lcccccc}
\hline & \text { Coefficients } & \text {Standard Error } & \text { t Stat } & \text { P-value } & \text { Lower } 95 \% & \text { Upper 95\% } \
\hline \text { Intercept } & -3.01152 & 1.18802 & -2.53491 & 0.02074 & -5.50746 & -0.5156 \
\text { Age } & 0.12569 & 0.02206 & 5.69706 & 0.00002 & 0.07934 & 0.1720
\end{array}$ a. Calculate the Pearson correlation coefficient. What sign does it have? Why?
b. Conduct a test of the population coefficient of correlation to determine at the 5% significance level whether a linear relationship exists between age and number of concerts attended.

Accepted Answer

The answer of At a recent music concert, a survey...

Question 8

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. $$\begin{array} { | c | c | c | } 
\hline \text { Day } & \text { Precipitation } & \text { Number of accidents } \
\hline 1 & 0.05 & 5 \
\hline 2 & 0.12 & 6 \
\hline 3 & 0.05 & 2 \
\hline 4 & 0.08 & 4 \
\hline 5 & 0.10 & 8 \
\hline 6 & 0.35 & 14 \
\hline 7 & 0.15 & 7 \
\hline 8 & 0.30 & 13 \
\hline 9 & 0.10 & 7 \
\hline 10 & 0.20 & 10 \
\hline
\end{array}$$ Estimate with 95% confidence the mean daily number of accidents when the daily precipitation is 0.25 inches.

Accepted Answer

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

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 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. $$\begin{array} { | c | c | c | } 
\hline \text { Day } & \text { Precipitation } & \text { Number of accidents } \
\hline 1 & 0.05 & 5 \
\hline 2 & 0.12 & 6 \
\hline 3 & 0.05 & 2 \
\hline 4 & 0.08 & 4 \
\hline 5 & 0.10 & 8 \
\hline 6 & 0.35 & 14 \
\hline 7 & 0.15 & 7 \
\hline 8 & 0.30 & 13 \
\hline 9 & 0.10 & 7 \
\hline 10 & 0.20 & 10 \
\hline
\end{array}$$ Find the least squares regression line.

Accepted Answer

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

Question 11

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. $$\begin{array} { | c | c | c | } 
\hline \text { Day } & \text { Precipitation } & \text { Number of accidents } \
\hline 1 & 0.05 & 5 \
\hline 2 & 0.12 & 6 \
\hline 3 & 0.05 & 2 \
\hline 4 & 0.08 & 4 \
\hline 5 & 0.10 & 8 \
\hline 6 & 0.35 & 14 \
\hline 7 & 0.15 & 7 \
\hline 8 & 0.30 & 13 \
\hline 9 & 0.10 & 7 \
\hline 10 & 0.20 & 10 \
\hline
\end{array}$$ Calculate the standard error of estimate, and describe what this statistic tells you about the regression line.

Accepted Answer

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

Question 12

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. $$\begin{array} { | c | c | c | } 
\hline \text { Day } & \text { Precipitation } & \text { Number of accidents } \
\hline 1 & 0.05 & 5 \
\hline 2 & 0.12 & 6 \
\hline 3 & 0.05 & 2 \
\hline 4 & 0.08 & 4 \
\hline 5 & 0.10 & 8 \
\hline 6 & 0.35 & 14 \
\hline 7 & 0.15 & 7 \
\hline 8 & 0.30 & 13 \
\hline 9 & 0.10 & 7 \
\hline 10 & 0.20 & 10 \
\hline
\end{array}$$ Calculate the Spearman rank correlation coefficient, and test to determine at the 5% significance level whether we can infer that a linear relationship exists between the number of accidents and the amount of precipitation.

Accepted Answer

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

Question 13

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. $$\begin{array} { | l | c | c | c | c | c | c | c | c | c | c | } 
\hline \text { Age } & 62 & 57 & 40 & 49 & 67 & 54 & 43 & 65 & 54 & 41 \
\hline \text { Number of concerts } & 6 & 5 & 4 & 3 & 5 & 5 & 2 & 6 & 3 & 1 \
\hline
\end{array}$$ $$\begin{array} { | l | c | c | c | c | c | c | c | c | c | c | } 
\hline \text { Age } & 44 & 48 & 55 & 60 & 59 & 63 & 69 & 40 & 38 & 52 \
\hline \text { Number of Concerts } & 3 & 2 & 4 & 5 & 4 & 5 & 4 & 2 & 1 & 3 \
\hline
\end{array}$$ $\begin{array}{ll}
\text { SUMMARY OUTPUT }&\text { DESCRIPTIVE STATISTICS }\
\begin{array}{lc}
\hline {\text { Reqression Statiatics }} \
\hline \text { Multiple R } & 0.80203 \
\text { R Square } & 0.64326 \
\text { Adjusted R Square } & 0.62344 \
\text { Standard Error } & 0.93965 \
\text { Observations } & 20 \
\hline
\end{array}&\begin{array}{lclc}
\hline {\text { Age }} &&{\text { Concerts }} \
\hline \text { Mean } & 53 & \text { Mean } & 3.65 \
\text { Standard Error } & 2.1849 & \text { Standard Error } & 0.3424 \
\text { Standard Deviation } & 9.7711 & \text { Standard Deviation } & 1.5313 \
\text { Sample Variance } & 95.4737 & \text { Sample Variance } & 2.3447 \
\text { Count } & 20 & \text { Count } & 20\\hline
\end{array}\
\end{array}$
$\text { SPEARMAN RANK CORRELATION COEFFICIENT }=0.8306$

$\begin{array}{lccccc} \text { ANOVA }\
\hline& \text { df } & \text { SS } & \text { MS } & F & \text { Significance F } \
\hline \text { Regression } & 1 & 28.65711 & 28.65711 & 32.45653 & 2.1082 \mathrm{E}-05 \
\text { Residual } & 18 & 15.89289 & 0.88294 & & \
\text { Total } & 19 & 44.55 & & &\\hline
\end{array}$

$\begin{array}{lcccccc}
\hline & \text { Coefficients } & \text {Standard Error } & \text { t Stat } & \text { P-value } & \text { Lower } 95 \% & \text { Upper 95\% } \
\hline \text { Intercept } & -3.01152 & 1.18802 & -2.53491 & 0.02074 & -5.50746 & -0.5156 \
\text { Age } & 0.12569 & 0.02206 & 5.69706 & 0.00002 & 0.07934 & 0.1720
\end{array}$ a. Use the regression equation = -3.0115 + 0.1257x to determine the predicted values of y.
b. Use the predicted values and the actual values of y to calculate the residuals.
c. Plot the residuals against the predicted values  .
d. Does it appear that heteroscedasticity is a problem? Explain.
e. Draw a histogram of the residuals.
f. Does it appear that the errors are normally distributed? Explain.
g. Use the residuals to compute the standardised residuals.
h. Identify possible outliers.

Accepted Answer

The answer of At a recent music concert, a survey...

Question 14

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 $$\begin{array} { | l | r | r | r | r | } 
\hline \text { Fredictor } & \text { Coef } & \text { StDev } & \mathrm { T } & \mathrm { P } \
\hline \text { Constant } & 9.4349 & 0.2867 & 32.91 & 0.000 \
\hline \text { Degrees } & 0.095235 & 0.008220 & 11.59 & 0.000 \
\hline
\end{array}$$ S = 0.1314 R-Sq = 92.46% R-Sq(adj) = 91.7%
Analysis of Variance $$\begin{array} { | l | r | r | r | r | r | } 
\hline \text { Source } & \text { DF } & \text { SS } & \text { MS } & \text { F } & \text { P } \
\hline \text { Regression } & 1 & 2.3162 & 2.3162 & 134.24 & 0.000 \
\hline \text { Residual Error } & 11 & 0.1898 & 0.0173 & & \
\hline \text { Total } & 12 & 2.5060 & & & \
\hline
\end{array}$$ a. Draw a scatter diagram of the data to determine whether a linear model appears to be appropriate to describe the relationship between the quality of oil and price per barrel.
b. Determine the least squares regression line.
c. Redraw the scatter diagram and plot the least squares regression line on it.
d. Interpret the value of the slope of the regression line.

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Question 15

The editor of a major academic book publisher claims that a large part of the cost of books is the cost of paper. This implies that larger books will cost more money. As an experiment to analyse the claim, a university student visits the bookstore and records the number of pages and the selling price of 12 randomly selected books. These data are listed below. $$\begin{array} { | c | c | c | } 
\hline \text { Book } & \text { Number of pages } & \text { Selling price } ( \$ ) \
\hline 1 & 844 & 55 \
\hline 2 & 727 & 50 \
\hline 3 & 360 & 35 \
\hline 4 & 915 & 60 \
\hline 5 & 295 & 30 \
\hline 6 & 706 & 50 \
\hline 7 & 410 & 40 \
\hline 8 & 905 & 53 \
\hline 9 & 1058 & 65 \
\hline 10 & 865 & 54 \
\hline 11 & 677 & 42 \
\hline 12 & 912 & 58 \
\hline
\end{array}$$ Estimate with 90% confidence the selling price of a book with 900 pages.

Accepted Answer

The answer of The editor of a major academic book...

Question 16

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 $$\begin{array} { | l | r | r | r | r | } 
\hline \text { Fredictor } & \text { Coef } & \text { StDev } & \mathrm { T } & \mathrm { P } \
\hline \text { Constant } & 9.4349 & 0.2867 & 32.91 & 0.000 \
\hline \text { Degrees } & 0.095235 & 0.008220 & 11.59 & 0.000 \
\hline
\end{array}$$ 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 coefficient of correlation to determine at the 5% significance level whether a linear relationship exists between the quality of oil and price per barrel.

Accepted Answer

The answer of The quality of oil is measured in...

Question 17

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. $$\begin{array} { | l | c | c | c | c | c | c | c | c | c | c | } 
\hline \text { Age } & 62 & 57 & 40 & 49 & 67 & 54 & 43 & 65 & 54 & 41 \
\hline \text { Number of concerts } & 6 & 5 & 4 & 3 & 5 & 5 & 2 & 6 & 3 & 1 \
\hline
\end{array}$$ $$\begin{array} { | l | c | c | c | c | c | c | c | c | c | c | } 
\hline \text { Age } & 44 & 48 & 55 & 60 & 59 & 63 & 69 & 40 & 38 & 52 \
\hline \text { Number of Concerts } & 3 & 2 & 4 & 5 & 4 & 5 & 4 & 2 & 1 & 3 \
\hline
\end{array}$$ $\begin{array}{ll}
\text { SUMMARY OUTPUT }&\text { DESCRIPTIVE STATISTICS }\
\begin{array}{lc}
\hline {\text { Reqression Statiatics }} \
\hline \text { Multiple R } & 0.80203 \
\text { R Square } & 0.64326 \
\text { Adjusted R Square } & 0.62344 \
\text { Standard Error } & 0.93965 \
\text { Observations } & 20 \
\hline
\end{array}&\begin{array}{lclc}
\hline {\text { Age }} &&{\text { Concerts }} \
\hline \text { Mean } & 53 & \text { Mean } & 3.65 \
\text { Standard Error } & 2.1849 & \text { Standard Error } & 0.3424 \
\text { Standard Deviation } & 9.7711 & \text { Standard Deviation } & 1.5313 \
\text { Sample Variance } & 95.4737 & \text { Sample Variance } & 2.3447 \
\text { Count } & 20 & \text { Count } & 20\\hline
\end{array}\
\end{array}$
$\text { SPEARMAN RANK CORRELATION COEFFICIENT }=0.8306$

$\begin{array}{lccccc} \text { ANOVA }\
\hline& \text { df } & \text { SS } & \text { MS } & F & \text { Significance F } \
\hline \text { Regression } & 1 & 28.65711 & 28.65711 & 32.45653 & 2.1082 \mathrm{E}-05 \
\text { Residual } & 18 & 15.89289 & 0.88294 & & \
\text { Total } & 19 & 44.55 & & &\\hline
\end{array}$

$\begin{array}{lcccccc}
\hline & \text { Coefficients } & \text {Standard Error } & \text { t Stat } & \text { P-value } & \text { Lower } 95 \% & \text { Upper 95\% } \
\hline \text { Intercept } & -3.01152 & 1.18802 & -2.53491 & 0.02074 & -5.50746 & -0.5156 \
\text { Age } & 0.12569 & 0.02206 & 5.69706 & 0.00002 & 0.07934 & 0.1720
\end{array}$ Conduct a test of the population slope to determine at the 5% significance level whether a linear relationship exists between age and number of concerts attended.

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Question 18

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 $$\begin{array} { | l | r | r | r | r | } 
\hline \text { Fredictor } & \text { Coef } & \text { StDev } & \mathrm { T } & \mathrm { P } \
\hline \text { Constant } & 9.4349 & 0.2867 & 32.91 & 0.000 \
\hline \text { Degrees } & 0.095235 & 0.008220 & 11.59 & 0.000 \
\hline
\end{array}$$ S = 0.1314 R-Sq = 92.46% R-Sq(adj) = 91.7%
Analysis of Variance $$\begin{array} { | l | r | r | r | r | r | } 
\hline \text { Source } & \text { DF } & \text { SS } & \text { MS } & \text { F } & \text { P } \
\hline \text { Regression } & 1 & 2.3162 & 2.3162 & 134.24 & 0.000 \
\hline \text { Residual Error } & 11 & 0.1898 & 0.0173 & & \
\hline \text { Total } & 12 & 2.5060 & & & \
\hline
\end{array}$$ a. Determine the standard error of estimate and describe what this statistic tells you.
b. Determine the coefficient of determination and discuss what its value tells you about the two variables.
c. Calculate the Pearson correlation coefficient. What sign does it have? Why?

Accepted Answer

The answer of The quality of oil is measured in...

Question 19

The editor of a major academic book publisher claims that a large part of the cost of books is the cost of paper. This implies that larger books will cost more money. As an experiment to analyse the claim, a university student visits the bookstore and records the number of pages and the selling price of 12 randomly selected books. These data are listed below. $$\begin{array} { | c | c | c | } 
\hline \text { Book } & \text { Number of pages } & \text { Selling price } ( \$ ) \
\hline 1 & 844 & 55 \
\hline 2 & 727 & 50 \
\hline 3 & 360 & 35 \
\hline 4 & 915 & 60 \
\hline 5 & 295 & 30 \
\hline 6 & 706 & 50 \
\hline 7 & 410 & 40 \
\hline 8 & 905 & 53 \
\hline 9 & 1058 & 65 \
\hline 10 & 865 & 54 \
\hline 11 & 677 & 42 \
\hline 12 & 912 & 58 \
\hline
\end{array}$$ Estimate with 90% confidence the mean selling price of all books with 900 pages.

Accepted Answer

The answer of The editor of a major academic book...

Quiz 18: Simple Linear Regression and Correlation