Question

State Math SAT scores. Refer to the simple linear regression relating y = 2014 Math SAT scores to x = 2010 Math SAT scores, Exercise 11.19 (p. 654). A portion of the SPSS printout of the analysis is shown below.

a. Locate the values of SSE, ${\mathbf{s}}^{\mathbf{2}}$, and s on the SPSS printout.

b. Give a practical interpretation of the value of s.

Short answer

1. SSE is 12249.3817, s² is 249.996 and s is 15.811
2. Preferable if it is small.

Step-by-step solution

Introduction

The standard error shows how far the population mean is expected to deviate from the sample mean. It indicates how much the sample mean would change if you repeated a research with new samples from the same population.

Finding SSE, s2 , and s.

a.

From the given table we get,

SSE = 12249.3817

$\begin{array}{rcl}{\mathrm{s}}^2& =& \mathrm{MSE}\\ & =& 249.996\end{array}$

Thus, the standard error of estimation is: S = 15.811

Therefore, SSE is 12249.3817, ${\mathbf{s}}^{\mathbf{2}}$is 249.996 and s is 15.811.

Provide a practical interpretation of s.

b.

The variable ‘s’ depicts the range of predicted values. If the model is a good fit, it is small.