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98 Part II: Using Different Types of Regression to Make Predictions

Checking the Fit of the Multiple

Regression Model

Before you run to your boss in triumph saying you’ve slam-dunked the
question of how to estimate plasma TV sales, you first have to make sure
all your i’s are dotted and all your t’s are crossed, as you do with any other
statistical procedure. In this case, you have to check the conditions of the
multiple regression model. These conditions mainly focus on the residuals
(the difference between the estimated values for y and the observed values of
y from your data). If the model is close to the actual data you collected, you
can feel somewhat confident that if you were to collect more data, it would
fall in line with the model as well, and your predictions should be good.

In this section, you see what the conditions are for multiple regression and
specific techniques statisticians use to check each of those conditions. The
main character in all this condition-checking is the residual.

Noting the conditions

The conditions for multiple regression concentrate on the error terms,
or residuals. The residuals are the amount that’s left over after the model
has been fit. They represent the difference between the actual value of y
observed in the data set and the estimated value of y based on the model.
Following are the conditions for the residuals of the multiple regression
model; note that all conditions need to be met in order to give the go-ahead
for a multiple regression model:

✓ They have a normal distribution with a mean of zero.
✓ They have the same variance for each fitted (predicted) value of y.
✓ They’re independent (meaning they don’t affect each other).

Plotting a plan to check the conditions

It may sound like you have a ton of things to check here and there, but
luckily, Minitab gives you all the info you need to know in a series of four
graphs, all presented at one time. These plots are called the residual plots,
and they graph the residuals so that you can check to see whether the
conditions from the previous section are met.

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