Question

Use the following convention table for R-square.

From 0.0 to 0.2	Poor
From 0.2 to 0.4	Decent
From 0.4 to 0.6	Good
From 0.6 to 0.85	Very Good
From 0.85 to 1.0	Excellent

Upload the ManBody data. Create a scattered plot chart with X representing the Knee size and Y representing the Ankle size (both in centimeters); plot the line and compute the R-square. Answer the questions:

I) If a person has knee size equal to 40 cm, according to the chart and the analysis, what is his predicted ankle size? (Round to two decimal places) (11.11 points)

• a. About 0.42 centimeters
• b. About 6.51 centimeters
• c. About 0.37 centimeters
• d. About 23.70 centimeters
• e. None of the above

II) If a person A has knee size equal to 30 cm and a person B has knee size equal to 32 cm, according to the chart and the analysis, which of the following can be concluded? (Round to two decimal place) (11.11 points)

• a. Person B will have on average 0.42 centimeters larger Ankle
• b. Person A will have on average 0.42 centimeters larger Ankle
• c. Person B will have on average 4.21 centimeters larger Ankle
• d. Person B will have on average 6.5 centimeters larger Ankle
• e. None of these

III) How strong is the relationship between the Knee size and Ankle size? (11.11 points)

• a. Poor
• b. Decent
• c. Good
• d. Very Good
• e. Excellent

link to data set: https://www.limes.one/Content/DataFiles/Man_body.txt

Answer 1

With X representing the Knee size and Y representing the Ankle size (both in centimeters) we obtain the following scatter plot and regression summary.

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.6116
R Square	0.3741
Adjusted R Square	0.3716
Standard Error	1.3436
Observations	252

	Coefficients	Standard Error	t Stat	P-value
Intercept	6.515920818	1.35962243	4.792448753	0.000002828618108
KNEE	0.4298070864	0.03516373729	12.22302063	0

So we obtain the regression equation as;

Y =  6.5159 + 0.4298 (KNEE)

I) Substituting the knee values in regression equation, we get.  d. About 23.70 centimeters

II) Substituting the knee values in regression equation, A and B will have the respective values as;

19.41013341	A
20.26974758	B
0.8596141728	Difference

Hence, e. None of these

III) b. Decent