Modeling Relationships of Multiple Variables with Linear Regression
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Stat Cheat Sheet
| Normality of Residuals The residuals should follow a normal distribution, with a mean of 0. Recall that a normal distribution is shaped like a bell—it is symmetric, and most points are in the middle, with fewer and fewer farther from the mean. Since the residuals measure where the points fall in relation to the line, asymmetric distribution of the residuals indicates that the same number of points fall above and below the line. Since a residual of 0 means a point is right on the line, a mean of 0 indicates the line is in the middle of the points. Once again, some are above and some are below. And the bell shape means that most are close to the line, and there are fewer points farther from the line. One way to check the normality of residuals is to save and plot residuals from the regression command. To do so for our multiple variable example Analyze Regression Linear Dependent: DMS397 (Births to Teenage Mothers as Percentage of All Births 2007) Independents: PVS519 (Poverty Rate 2008) EDS (Per Capita Spending on Education 2007) PVS546 Maximum Monthly TANF Benefit for Family of Three in 2007) DMS468 (Percent of Population Black 2008) Save Residuals: Check Unstandardized Continue OK This will create anew variable RES, which can be graphed using the Graph command (Figure 7.11). Graphs Chart Builder Gallery Histogram Drag Simple Histogram to Chart preview Drag RES from Variables list to X-axis? box [Hint:RES_1 will beat the bottom of the list!] Element Properties Display Normal Curve Apply OK As Figure 7.11 shows, the residuals form a reasonably normal distribution, which is a good indication that the regression is working well. Chapter 7 • Modeling Relationships of Multiple Variables with Linear Regression 179 Figure 7.11 Histogram of Normally Distributed Residuals Download 0.6 Mb. Share with your friends:
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