They appear significant for TOT but less so for AMI. For example, the effects of PR and DIAP seem borderline. That covariance needs to be taken into account when determining if a predictor is jointly contributing to both models. The main takeaway is that the coefficients from both models covary. You can verify this for yourself by running the following code and comparing the summaries to what we got above. These are exactly the same results we would get if modeled each separately. Notice the summary shows the results of two regressions: one for TOT and one for AMI. Residual standard error: 292.4 on 11 degrees of freedom
Lm(formula = AMI ~ GEN + AMT + PR + DIAP + QRS, data = ami_data) Residual standard error: 281.2 on 11 degrees of freedom The following code reads the data into R and names the columns. We’ll use the R statistical computing environment to demonstrate multivariate multiple regression. The predictors are as follows:ĪMT, amount of drug taken at time of overdose TOT is total TCAD plasma level and AMI is the amount of amitriptyline present in the TCAD plasma level. There are two responses we want to model: TOT and AMI. This data come from exercise 7.25 and involve 17 overdoses of the drug amitriptyline (Rudorfer, 1982). To get started, let’s read in some data from the book Applied Multivariate Statistical Analysis (6th ed.) by Richard Johnson and Dean Wichern. However, because we have multiple responses, we have to modify our hypothesis tests for regression parameters and our confidence intervals for predictions. It regresses each dependent variable separately on the predictors. You may be thinking, “why not just run separate regressions for each dependent variable?” That’s actually a good idea! And in fact that’s pretty much what multivariate multiple regression does. This allows us to evaluate the relationship of, say, gender with each score. For example, we might want to model both math and reading SAT scores as a function of gender, race, parent income, and so forth. Multivariate Multiple Regression is the method of modeling multiple responses, or dependent variables, with a single set of predictor variables.
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