At a Recent Music Concert, a Survey Was Conducted That

question 38

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. $$\begin{array} { | l | c | c | c | c | c | c | c | c | c | c | } \hline \text { Age } & 62 & 57 & 40 & 49 & 67 & 54 & 43 & 65 & 54 & 41 \\\hline \text { Number of concerts } & 6 & 5 & 4 & 3 & 5 & 5 & 2 & 6 & 3 & 1 \\\hline\end{array}$$ $$\begin{array} { | l | c | c | c | c | c | c | c | c | c | c | } \hline \text { Age } & 44 & 48 & 55 & 60 & 59 & 63 & 69 & 40 & 38 & 52 \\\hline \text { Number of Concerts } & 3 & 2 & 4 & 5 & 4 & 5 & 4 & 2 & 1 & 3 \\\hline\end{array}$$ a. Use the regression equation $\hat { y }$ = -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 $\hat { y }$ .
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.

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Definitions:

Founding Father

A member of the group of leaders who established the foundation of a nation, state, or political platform, often referred to in the context of the United States.

Collective Violence

Acts of violence committed by groups of individuals, ranging from spontaneous acts of public violence to organized acts by larger groups against others.

Frontier Regions

Areas located at the edge of a nation's settled regions, often characterized by their sparse population, rugged geography, and intercultural contact or conflict.

Wobblies

Nickname for members of the Industrial Workers of the World (IWW), a labor union founded in 1905 in the United States, known for its radical approach to workers' rights.