Body frame size is determined by a person's wrist circumference in relation to height. A researcher

measures the wrist circumference and height of a random sample of individuals. The data is displayed

below.

Wrist Circumference $($in$)$

Coefficients:

Residual standard error: $3\mathrm{.}8836$ on $28$ degrees of freedom

R$-$squared: $0\mathrm{.}6205,$ Adjusted R$-$squared: $0\mathrm{.}6069$

F$-$statistic: $45\mathrm{.}7761$ on $1$ and $28$ DF$,$ p$-$value: $2\mathrm{.}39E-7$

a$)$ Write the equation of the best$-$fit line. Use $x$ and $y$ for your variables.

b$)$ Calculate the correlation coefficient.

c$)$ Identify the coefficient of determination.

d$)$ Use the equation of the best$-$fit line to predict the height of a person with a wrist circumference of $6$

inches. inches

e$)$ One of the points on the scatterplot is $(8,83\mathrm{.}2).$ Calculate the residual for this point. inches

f$)$ The mean wrist circumference for this data is $6\mathrm{.}97$ inches. Calculate the mean height for this data.

inches

g$)$ When predicting heights, what is a "typical" error using this linear model? $,$ inches

h$)$ What fraction of variability in heights can be explained using the linear model of height vs wrist

circumference? Enter your response as a decimal.

i$)$ Calculate the correlation coefficient if the heights are measured in feet. $($All heights divided by $12.)$