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.

5
5.5
6
6.5
7
7.5
8
8.5
9
55
60
65
70
75
80
Wrist Circumference (in)
Height (in)

Excel Output:

Regression Statistics
Multiple R 0.8145
R Square 0.6634
Adjusted R Square 0.651
Standard Error 3.677
Observations 29
Coefficients Standard Error t-Stat P-value
(Intercept) 30.5556 5.4714 5.5846 6.36 E -6
wrist 5.6492 0.7744 7.2952 7.58 E -8
Round answers to 4 decimal places.

a) Write the equation of the best-fit line.

ˆ
y
=

b) Identify the correlation coefficient.

c) What fraction of variability in heights can be explained using the linear model of height vs wrist circumference?

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 (6.9,76.7). Calculate the residual for this point, hint:
y
−
ˆ
y
.

inches

f) The mean wrist circumference for this data is 7.01 inches. Predict the mean height for this data.

inches

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

Standard error of estimate:
inches