91Ó°ÊÓ

To construct a scatter plot using brother’s height as the explanatory variable with the given data.

The horizontal axis represents the brother, while the vertical axis represents the sister. The scatter plot can be made as follows:

Because the scatterplot slopes upwards, the association is positive. Because the points appear to be far apart, the association is weak. So, there is a weak positive correlation between to variables.

To use the calculator to compute the least-squares regression line for predicting sister’s height from brother’s height. And interpret the slope in context.

The following is the output from a Ti-83 calculator:

As a result, the equation of the regression line is $\hat{y}=27.635+0.527x$.

To predict the height of his sister Tonya. Since, Damien is $70$ inches tall.

Tonya's height can be estimated as follows:
$\hat{y}=27.635+0.527x$
$=27.635+0.527\left(70\right)$
$=64.525$
Asa a result, the height of Tonya's is about $64.525$inches.

To determine the prediction in part (c) to be very accurate or not.

Using a $Ti-83$ calculator, the coefficient of determination can be calculated as follows:

Because the coefficient of determination is low.
As a result, the model isn't very accurate.