Question

1. the linear regression function for the given data is ( y = 3.93x - 11.33 ), ( r = 0.8241 ). consider the scatterplot and the correlation coefficient. state whether a linear model is appropriate for the data.

Explanation:

Step1: Analyze the correlation coefficient

The correlation coefficient \(r = 0.8241\). Since \(|r|\) (where \(|r|=\vert0.8241\vert = 0.8241\)) is relatively close to \(1\) (a common rule - of - thumb is that if \(|r|\gt0.7\), there is a strong linear relationship).

Step2: Consider the scatter - plot (implied by the data)

Although we don't have the visual scatter - plot, the formula of the linear regression \(y = 3.93x-11.33\) and the relatively high value of \(r\) suggest a linear trend. The data points (even with some variability) follow a general linear pattern.

Answer:

A linear model is appropriate for the data.