In a multiple regression model,the following statistics are given: SSE = 100,R² = 0.995,k = 5,and n = 15.Then,the coefficient of determination adjusted for degrees of freedom is: A)0.992 B)0.900 C)0.955 D)0.855

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Quizplus · Accepted Answer

The adjusted coefficient of determination is calculated using the formula: $R^2_{adj} = 1 - [(1-R^2)(\frac{n-1}{n-k-1})]$, where $R^2$ is the coefficient of determination, $n$ is the sample size, and $k$ is the number of predictors. Given $R^2 = 0.995$, $n = 15$, and $k = 5$, we first calculate $R^2_{adj}$ as follows: $R^2_{adj} = 1 - [(1-0.995)(\frac{15-1}{15-5-1})] = 1 - [0.005(\frac{14}{10})] = 1 - 0.007 = 0.993$. The closest option to this calculated value is 0.992, hence option A is correct.

In a Multiple Regression Model,the Following Statistics Are Given: SSE