26. Sisters and brothers (3.1, 3.2) How strongly do physical characteristics of sisters and brothers correlate? Here are data on the heights (in inches)
of 11 adult pairs:

Brother	71	68	66	67	70	71	70	73	72	65	66
Sister	69	64	65	63	65	62	65	64	66	59	62

(a) Construct a scatterplot using brother’s height as the explanatory variable. Describe what you see.
(b) Use your calculator to compute the least-squares regression line for predicting sister’s height from brother’s height. Interpret the slope in context.
(c) Damien is $70$ inches tall. Predict the height of his sister Tonya.
(d) Do you expect your prediction in (c) to be very accurate? Give appropriate evidence to support your answer.

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.