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

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The formula for the adjusted coefficient of determination is: $$R_{adj}^2 = 1 - \frac{(n-1)}{(n-k)}\frac{SSE}{SST}$$ where SSE is the sum of squared errors, SST is the total sum of squares, k is the number of predictors in the model, and n is the sample size. We are given that SSE = 100, k = 5, and n = 15. We need to find SST to calculate $R_{adj}^2$. The total sum of squares can be calculated as: $$SST = \sum_{i=1}^{n}(y_i - \bar{y})^2$$ where $y_i$ is the observed value of the dependent variable and $\bar{y}$ is the mean of the dependent variable. Since we don't have any information about the dependent variable, we need to assume that the model includes an intercept term. In this case, we can use the fact that SSE is equal to the sum of squared errors around the mean: $$SSE = \sum_{i=1}^{n}(y_i - \bar{y})^2$$ Therefore, we can calculate $\bar{y}$ as: $$\bar{y} = \frac{1}{n}\sum_{i=1}^{n}y_i$$ We don't have any information about the values of the independent variables, so we can't calculate the predicted values of the dependent variable or the residuals. However, we know that the multiple coefficient of determination is: $$R^2 = \frac{SSR}{SST}$$ where SSR is the sum of squared regression (also known as explained sum of squares). Since we don't have the values of the independent variables, we can't calculate SSR directly. However, we are given that: $$R² = R = \sqrt{R^2} = 0.995$$ This means that the model explains 99.5% of the variability in the dependent variable. Therefore, we can estimate SST as: $$SST = \frac{SSE}{1 - R^2} = \frac{100}{1 - 0.995^2} = 5025$$ Plugging in the values into the formula for $R_{adj}^2$, we get: $$R_{adj}^2 = 1 - \frac{(n-1)}{(n-k)}\frac{SSE}{SST} = 1 - \frac{14}{10}\frac{100}{5025} = 0.992$$ Therefore, the adjusted coefficient of determination is 0.992, which is closest to choice B).

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