What is the value of the residual standard error for the regression? Answer to two decimal places.

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BlackTom AI · Accepted Answer

The question asks for the value of the residual standard error for the regression, to two decimal places.

First, note that no answer options are provided in this item, so there is nothing to compare against or evaluate as correct/incorrect.

Understanding residual standard error (RSE): it is an estimate of the standard deviation of the residuals (the left-out variation not explained by the regression). In ordinary least squares regression, RSE is computed as:
RSE = sqrt(SSE / (n - p - 1))
where SSE is the sum of squared residuals, n is the number of observations, and p is the number of predictors (excluding the intercept).

To compute RSE, you need concrete values: SSE, n, and p. Without the dataset or the regression output (SSE and the degrees of freedom), you cannot perform the calculation.

Common steps if the data were available:
- Obtain the regression output or the residuals from the fitted model.
- Compute SSE by summing the squared residuals: sum(residual_i^2).
- Determine n, the total number of observations, and p, the number of predictors in the model (including or excluding the intercept depending on the convention; the formula typically uses the count of parameters estimated, excluding the intercept when using n - p - 1).
- Plug these into RSE = sqrt(SSE / (n - p - 1)) and round to two decimals.

If you have the regression results and the numbers SSE, n, and p, you would substitute them into the formula and obtain a numerical value such as 243.71 after rounding to two decimals. Without those values, however, the exact figure cannot be confirmed here.

Potential pitfalls:
- Confusing the residual standard error with the standard error of a particular coefficient; they are different quantities with different interpretations.
- Miscounting the degrees of freedom (n - p - 1) if you miscount the number of predictors or whether the intercept is included.
- Using SSE instead of the mean squared error in the numerator; MSE is SSE divided by its degrees of freedom, but RSE uses SSE directly under a square root with the same dof term in the denominator.

In summary, to determine a numeric value like 243.71, you must have SSE, n, and p from the fitted regression. With those, you would compute RSE as sqrt(SSE / (n - p - 1)) and round to two decimals.

BUSI_V 291 202 2024W2 Sample Final Exam (Canvas)

What is the value of the residual standard error for the regression? Answer to two decimal places.

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