When simple linear regression is used to analyze a data set, we get total variation = 7492.4 and unexplained variation (SSE) = 888.96. What is the coefficient of determination? (round to 2 decimal places)
Question
When simple linear regression is used to analyze a data set, we get total variation = 7492.4 and unexplained variation (SSE) = 888.96. What is the coefficient of determination? (round to 2 decimal places)
Solution
To find the coefficient of determination, we need to calculate the explained variation (SSR) first. The formula for SSR is SSR = Total Variation - Unexplained Variation.
Given that the total variation is 7492.4 and the unexplained variation (SSE) is 888.96, we can substitute these values into the formula:
SSR = 7492.4 - 888.96
Calculating this, we get:
SSR = 6603.44
Now, we can calculate the coefficient of determination (R-squared) using the formula:
R-squared = SSR / Total Variation
Substituting the values we have:
R-squared = 6603.44 / 7492.4
Calculating this, we get:
R-squared ≈ 0.88
Therefore, the coefficient of determination is approximately 0.88.
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