Question

Regarding the standard error of the estimate,

a. give two interpretations of it.

b. identify another name used for it, and explain the rationale for that name.

c. which one of the three sums of squares figures in its computation?

Short answer

a)Interpretation 1:Roughly speaking the standard error of the estimate describes how far the predicted and observed values of the response variable differ on average.

Interpretation2: It provides an estimate for the common population standard deviation sigma is estimated.

b)The residual standard deviation is another name for the estimate's standard error.

c)The sum of squares due to error is the error (SSE) is used in its computation.

Step-by-step solution

Part a  Step 1: Given Information

Assume that the variables being considered to meet the assumptions for regression $n$inferences.

Part a Step 2: Explanation

Interpretation 1:Roughly speaking the standard error of the estimate describes how far the predicted and observed values of the response variable differ on average.

Interpretation2: It provides an estimate for the common population standard deviation $sigma$ is estimated.

Part b Step 1 : Given Information

Assume that the variables being considered to meet the assumptions for regression$n$inferences.

Part b Step 2 : Explanation

Sometimes the residual standard deviation is another name for the estimate's standard error. We can express the standard error of the estimate in terms of residuals

$S_e=\sqrt{\frac{SSE}{n-2}}$

$=\sqrt{\frac{\sum {\left(y_i-{\hat{y}}_i\right)}^2}{n-2}}$

$=\sqrt{\frac{\sum e_i^2}{n-2}}$

We can show that the sum of the residuals is always 0 , which, in term, implies that $\overline{e}=0$

As a result, the estimate's standard error is nearly identical to the residuals' standard deviation.

Part c Step 1 : Given Information

We have to find the three sums of squares figures in its computation.

Part c Step 2 : Explanation

The sum of squares due to error is the error (SSE) used in its computation.