Home > Statistics > Independent and Dependent Variables

If the coefficient of determination for a data set is 0.25 and the SSE for the data set is 12, what is the SST?

Answer 1

David Armstrong

#SST = 16#

#R^2 =1 - (SSE)/(SST) => SST = (SSE)/(1-R^2) = (12)/(1-0.25)=16#

By signing up, you agree to our Terms of Service and Privacy Policy

Answer 2

Emery Adams

To find the total sum of squares (SST), you can use the formula:

[ SST = SSR + SSE ]

Given that the coefficient of determination ( R^2 = 0.25 ) and the sum of squared errors (SSE) is 12, we know that:

[ R^2 = \frac{SSR}{SST} ]

We're given ( SSE = 12 ). We can find SSR using the formula ( SSR = SST - SSE ).

Substituting the given values:

[ 0.25 = \frac{SSR}{SST} ] [ SST = SSR + SSE ] [ 12 = SSR + 12 ]

Now, solve for SSR:

[ SSR = SST - SSE ] [ SSR = SST - 12 ]

Now, use the equation ( R^2 = \frac{SSR}{SST} ) to find ( SST ):

[ 0.25 = \frac{SST - 12}{SST} ]

Multiply both sides by SST:

[ 0.25SST = SST - 12 ]

Subtract ( 0.25SST ) from both sides:

[ 0.75SST = 12 ]

Now, solve for SST:

[ SST = \frac{12}{0.75} = 16 ]

Therefore, the total sum of squares (SST) is 16.

By signing up, you agree to our Terms of Service and Privacy Policy

Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.