ANOVA determining percentage of variation

Question

The Financial Review wished to estimate the amount of annual government spending using tax revenue and level of nationwide debt. Data from 1958-2008 (inclusive) was used. All variables were measured in billions of dollars. It was found that the mean square error for the regression was 15 and the total sum of squares was 12200. Hence, what percentage of the variation in annual government spending is explained by the regression equation? Give your answer correct to two decimal places.

My Perspective:

Mean square of error (MSE) = 15
Total sum of squares (SST) = 12200

The question is asking for R squared, so

$R^2 = SSR / SST$, but so far we only have $SST$. How do we derive $SSR$ from the $MSE$ in this case?

anova correlation self study variance

My Perspective:

Mean square of error (MSE) = 15
Total sum of squares (SST) = 12200

The question is asking for R squared, so

$R^2 = SSR / SST$, but so far we only have $SST$. How do we derive $SSR$ from the $MSE$ in this case?

user292123 · Answer

The question wants to find out R-sq
Rsq = Variance of Variables in the model/Total variance
Variance = MSE/df; hence df is required.
let n be number of years of observation =51.
Let k be number of variables (treatments) in the model = 2 (tax revenue, natl debt)
Hence; SSTr = MSTr/treatment df = (12200-15)/(51-2)
And
Rsq = {(12200-15)/(51-2)}/(12200/51-1)

gung - Reinstate Monica · Answer

Think about how many degrees of freedom there must be (total, residual & regression).  Then you can work backwards from the $MSE$ to get the missing $SS$s.

ANOVA determining percentage of variation

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