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If SSR=30 and SSE=20​, determine​ SST, then compute the coefficient of​ determination, r2​, and interpret its meaning. SST=nothing r2=nothing ​(Type an integer or a decimal. Do not​ round.) Interpret the meaning of r2. Choose the correct answer below. A. It means that 1−r2 of the variation in the dependent variable cannot be explained by the variation in the independent variable. B. It means that r2•​100% of the variation in the dependent variable can be explained by the variation in the independent variable. C. It means that 1−r2•100% of the variation in the independent variable cannot be explained by the variation in the dependent variable. D. It means that r2 of the variation in the independent variable can be explained by the variation in the dependent variable.

Respuesta :

Answer:

R² value implies that 60% of the variation in the dependent variable can be explained by the variation in the independent variable.

Step-by-step explanation:

The information provided is:

SSR = 30

SSE = 20

Compute the total sum of squares as follows:

SST = SSR + SSE

       = 30 + 20

       = 50

The coefficient of determination R² specifies the percentage of the variance in the dependent-variable (Y) that is forecasted or explained by linear regression and the forecaster variable (X, also recognized as the independent-variable).

The coefficient of determination R² can be computed as follows:

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

     [tex]=\frac{30}{50}\\\\=0.60[/tex]

The coefficient of determination value is 0.60 or 60%.

This value implies that 60% of the variation in the dependent variable can be explained by the variation in the independent variable.

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