Q. 4.87 - Elementary Statistics

Question

For regression analysis, $55 T=8291.0$ and $5 S R=7626.6$.

a. Obtain and interpret the coefficient of determination.

b. Determine SSE :

Step-by-Step Solution

Answer

a) 

$r^2=0.92(92.0\%)$

Interpretation: Since the value obtained above is closer to 1 then evidently the variation in the observed variable is explained by the regression.

b) $S S E=664.4$

Part (a) Step 1: Given Information

Given: 

$$\begin{gathered} SSE=8291.0 \\ SSR=7626.6 \end{gathered}$$

Part (a) Step 2: Explanation

The coefficient of determination can be calculated as;

$$\begin{gathered} r^2=\frac{SSR}{SST} \\ {r}^2=\frac{7626.6}{8291.0} \\ {r}^2=0.92(92.0\%) \end{gathered}$$

Interpretation: Since the value obtained above is closer to $1$ then evidently the variation in the observed variable is explained by the regression.

Part (b) Step 1: Given Information

To determine the value of SSE

Part (b) Step 2: Explanation

Given:

$$\begin{gathered} SST=8291.0 \\ SSR=7626.6 \end{gathered}$$

The Total Sum of Squares is equal to the Regression Sum of squares plus the error sum of squares.

That is,

$$\begin{gathered} S S T=S S R+S S E \\ S S E=S S T-S S R \\ S S E=8291.0-7626.6 \\ S S E=664.4 \end{gathered}$$