CHAPTER 17 More of a Good Thing: Multiple Regression 243

this example, neither the Age coefficient (p = 0.126) nor the Weight coeffi-

cient (p = 0.167) is statistically significantly different from zero.»

» ^{Model fit statistics: These are calculations that describe how well the model}

fits your data overall.

• ^{Residual standard error: In this example, the Residual standard error:}

(bottom of output) indicates that the observed-minus-predicted residuals

have a standard deviation of 11.23 mmHg.

• ^{Multiple r2: This refers to the square of an overall correlation coefficient}

for the multivariate fit of the model, and is listed under Multiple R-squared.

• ^{F statistic: The F statistic and associated p value (on the last line of the}

output) indicate whether the model predicts the outcome statistically

significantly better than a null model. A null model contains only the

intercept term and no predictor variables at all. The very low p value

(0.0088) indicates that age and weight together predict SBP statistically

significantly better than the null model.

Checking out optional output to request

Depending on your software, you may also be able to request several other useful

calculations from the regression to be included:»

» ^{Predicted values for the dependent variable for each participant. This can be}

output either as a listing, or as a new variable placed into your data file.»

» ^{Residuals (observed minus predicted value) for each participant. Again, this}

can be output either as a listing, or as a new variable placed into your data file.

Deciding whether your data are suitable

for regression analysis

Before drawing conclusions from any statistical analysis, you need to make sure

that your data fulfill assumptions on which that analysis was based. Two assump-

tions of ordinary linear regression include the following:»

» ^{The amount of variability in the residuals is fairly constant, and not dependent}

on the value of the dependent variable.»

» ^{The residuals are approximately normally distributed.}