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:

	Estimate	Std Err	t-value	p-value
(Intercept)	29.7403	5.1272	5.8004	1.74 E -6
wrist	6.0758	0.7135	8.5154	7.70 E -10

     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 (R²)= 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.