At a Recent Music Concert, a Survey Was Conducted That$\text { SPEARMAN RANK CORRELATION COEFFICIENT }=0.8306$

The Answer of At a Recent Music Concert, a Survey Was Conducted That$\text { SPEARMAN RANK CORRELATION COEFFICIENT }=0.8306$

At a Recent Music Concert, a Survey Was Conducted That$\text { SPEARMAN RANK CORRELATION COEFFICIENT }=0.8306$

The Answer of At a Recent Music Concert, a Survey Was Conducted That$\text { SPEARMAN RANK CORRELATION COEFFICIENT }=0.8306$

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At a Recent Music Concert, a Survey Was Conducted That

question 164

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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 $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.$ = -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 $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.$ .
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.

Definitions:

ENS

The Enteric Nervous System (ENS) is a network of neurons lining the gastrointestinal tract, controlling digestion and gut function independently of the central nervous system.

Neuron Types

are various kinds of nerve cells classified based on their function, structure, neurotransmitter released, and direction of signal sent; including sensory, motor, and interneurons.

Neural Circuits

Complex networks of neurons that work together to carry out specific functions in the nervous system.