Question

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.

55.566.577.588.595560657075808590Wrist Circumference (in)Height
(in)

Coefficients:
Residual standard error: 4.101 on 33 degrees of freedom R-squared: 0.6872, Adjusted R-squared: 0.6778 F-statistic: 72.512 on 1 and 33 DF, p-value: 7.70 E -10 |

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 (8.5,90). Calculate the
residual for this point. inches

f) The mean wrist circumference for this data is 7.12 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.)

Answer #1

From the given regression output:

a) The equation of best fit line is

** Y = 29.7403 + 6.0758 X**

b) Correlation coefficient is the square root of r square = ?0.6872

**Correlation coefficient r = 0.8289**

c)
The coefficient of determination is R square
(R^{2})**= 0.6872**

d) The height of person with wrist circumference of 6 inches is 29.7403 + 6.0758 (6) = 66.1951

** The predicted
height when wrist circumference of 6 inches is 66.1951
inches.**

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