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.

Excel Output:

Regression Statistics
Multiple R	0.8165
R Square	0.6666
Adjusted R Square	0.6564
Standard Error	3.9002
Observations	35

	Coefficients	Standard Error	t-Stat	P-value
(Intercept)	31.5385	5.0273	6.2735	4.32 E -7
wrist	5.7874	0.7126	8.122	2.25 E -9

Round answers to 4 decimal places.

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

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 (6.9,80.6). Calculate the residual for this point, hint: y−ˆyy-y^ .

_____ inches

f) The mean wrist circumference for this data is 6.994 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

Answer 1

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.

Excel Output:

Regression Statistics
Multiple R	0.8165
R Square	0.6666
Adjusted R Square	0.6564
Standard Error	3.9002
Observations	35

	Coefficients	Standard Error	t-Stat	P-value
(Intercept)	31.5385	5.0273	6.2735	4.32 E -7
wrist	5.7874	0.7126	8.122	2.25 E -9

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

y^= 31.5385 +5.7874 *x

b) the correlation coefficient is 0.8165

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

Coefficient of determination:66.66

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

y^= 31.5385 +5.7874 *6 = 66.2629 inches

e) One of the points on the scatterplot is (6.9,80.6). Calculate the residual for this point, hint: y-y^ .

y^= 31.5385 +5.7874 *6.9=71.47

y-y^ = 80.6-71.47 = 9.12844

f) The mean wrist circumference for this data is 6.994 inches. Predict the mean height for this data.

y^= 31.5385 +5.7874 *6.994 = 72.016

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

Standard error of estimate: 3.9002