Question

A least-squares simple linear regression model was fit predicting duration (in minutes) of a dive from depth of the dive (in meters) from a sample of 43 penguins' diving depths and times.
Calculate the R-squared value for the regression by filling in the ANOVA table.

	SS	df	MS	F-statistic
Regression
Residual			1182.955
Total	537814.901

		0.91
		0.0902
		0.0022
		4.92461123041641e-23

Answer 1

DF:

Since linear regression with one predictor is used, DF(Regression)=1

DF(Total)=43-1=42 as 43 observations are there

DF(Residual)=42-1=41

SS:

Given that MS(Residual)=SS(residual)/41=1182.955 so that SS(Residual)=41*1182.955=48501.15

SS(Regression)=SS(Total)-SS(Residual)=537814.901-48501.15=489313.8

MS:

MS(Regression)=SS(regression)/1=489313.8

F statistic=MS(Regression)/MS(Residual)=489313.8/48501.15= 10.08871

R Square=SS(Regression)/SS(Total)=489313.8/537814.901=0.9098182=.91 (approx to two decimal)

Thus first option is the correct