A college professor recorded several variables about his students including thei

Question

A college professor recorded several variables about his students including their height and their current college GPA. The resulting data was used to create the following regression ANOVA table.

How many students were included in this study?

Consider the ANOVA table in the previous problem. What is the Coefficient of Determination (R-squared) for the relationship between GPA and height?

Source DF Sum of squares Mean Square F-value Pr>F Model 1 2.07 2.07 BBB 0.0201 Error 337 AAA 0.379 Corrected Total 338 129.73

Explanation / Answer

Ans:

Total df=N-1=338

So,total number of students,N=338+1=339

R-squared = 1 - SS(Error)/SS(Total)

SS(error)=SS(total)-SS(model)=129.73-2.07=127.66

So,

R-squared=1-(127.66/129.73)=1-0.984=0.016

Source DF Sum of squares Mean Square F-value Pr>F Model 1 2.07 2.07 5.462 0.0201 Error 337 127.66 0.379 Corrected Total 338 129.73

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