At a Recent Music Concert, a Survey Was Conducted That

question 1

Essay

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.