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: Understand the correlation coefficient

The correlation coefficient \(r = 0.8241\). A value of \(r\) close to \(1\) (in this case \(r = 0.8241\) which is relatively close to \(1\)) indicates a strong positive linear relationship.

Step2: Analyze the scatter - plot

Looking at the scatter - plot, the points generally follow a linear trend. Although there is some deviation, the overall pattern is linear.

Answer:

A linear model is appropriate for the data. The correlation coefficient \(r = 0.8241\) (a relatively strong positive correlation) and the scatter - plot shows a general linear trend.