220 PART 5 Looking for Relationships with Correlation and Regression

»

» ^{Higher-weight participants have higher SBP, which is represented by the}

points near the upper-right part of the graph.

You can also tell that there aren’t any higher-weight participants with a very low

SBP, because the lower-right part of the graph is rather empty. But this relation-

ship isn’t completely convincing, because several participants in the lower weight

range of 70 to 80 kg have SBPs over 125 mmHg.

A correlation analysis (described in Chapter 15) will tell you how strong this type

of association is, as well as its direction (which is positive in this case). The results

of a correlation analysis help you decide whether or not the association is likely

due to random fluctuations. Assuming it is not, proceeding to a regression analy-

sis provides you with a mathematical formula that numerically expresses the

relationship between the two variables (which are weight and SBP in this example).

Interpreting the Output of

Straight-Line Regression

In the following sections, we walk you through the printed and graphical output

of a typical straight-line regression run. Its looks will vary depending on your

software. The output in this chapter was generated using R (see Chapter 4 to get

started with R). But regardless of the software you use, you should be able to pro-

gram the regression so the following elements appear on your output:»

» ^{A statement of what you asked the program to do (the code you ran for the}

regression)»

» ^{A summary of the residuals, including graphs that display the residuals and}

help you assess whether they’re normally distributed»

» ^{The regression table (providing the results of the regression model)»}

» ^{Measures of goodness-of-fit of the line to the data}

Seeing what you told the program to do

In the example data set, the SBP variable is named BPs, and the weight variable is

named wgt. In Figure 16-4, the first two lines produced by the statistical software

reprint the code you ran. The code says that you wanted to fit a linear formula

where the software estimates the parameters to the equation SBP = weight based on

your observed SBP and weight values. The code used was lm(formula = BPs ~ Wgt).