Questions: In a regression analysis, if SST = 4500 and SSE = 1575, then the coefficient of determination is a. 45 b. 2.85 c. 65 d. 35

In a regression analysis, if SST = 4500 and SSE = 1575, then the coefficient of determination is a. 45 b. 2.85 c. 65 d. 35
Transcript text: In a regression analysis, if SST $=4500$ and SSE $=1575$, then the coefficient of determination is $\qquad$ a. 45 b. 2.85 c. 65 d. 35
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Solution

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Solution Steps

Step 1: Calculate SSR

To find the Sum of Squares due to Regression (SSR), we use the formula:

\[ SSR = SST - SSE \]

Given:

  • \( SST = 4500 \)
  • \( SSE = 1575 \)

Calculating SSR:

\[ SSR = 4500 - 1575 = 2925 \]

Step 2: Calculate Coefficient of Determination

The coefficient of determination (\( R^2 \)) is calculated using the formula:

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

Substituting the values:

\[ R^2 = \frac{2925}{4500} = 0.65 \]

Final Answer

The coefficient of determination is

\[ \boxed{R^2 = 0.65} \]

This indicates that approximately 65% of the variability in the dependent variable can be explained by the independent variable in the regression model.

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