**A Strategy for Developing Multiple Linear Regression (MLR) Models**

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**1.** Hypothesize the model and state the LINE assumptions:

## · If you have a few predictors, start with the first-order (main effect) linear model; otherwise use the best subsets and stepwise regression methods to select a few alternative models.

## · LINE assumptions are:

1. L: Model is linear in terms of the parameters;

2. I: Errors are distributed independently;

3. N: Errors are distributed normally;

4. E: Errors have equal variance.

**2.** Fit the model to data; that is, obtain the model parameter estimates using the LSE method.

**3.** Check the validity of LINE assumptions by performing residual analysis:

## · Obtain standardized residuals.

## · Check for normality assumption by using:

1. Normal probability plot (NPP) of standardized residuals

2. Histogram (comment if it is bell-shaped or skewed)

3. Shapiro-Wilk test (or Ryan-Joiner test)

## · Check for constant (equal) error variance assumption by using:

1. Standardized residuals versus fitted values plot

2. If there are replications, Bartlett test (or F test for two groups) if normality assumption holds; Levene test otherwise

## · Check for independence of errors assumption by using:

1. Observation order (run order or time) versus standardized residuals

2. Durbin-Watson (D-W) test