7.6 Omnibus tests for “Goodness of Fit”

The summary output for a linear model includes key elements from the ANOVA table for the omnibus statistical tests that assess goodness of fit. Let’s look at it again here.

summary(lin.model)

## 
## Call:
## lm(formula = Y.2016 ~ Y.2012, data = election50)
## 
## Residuals:
##       Min        1Q    Median        3Q       Max 
## -0.079300 -0.022713  0.000465  0.019404  0.061641 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -0.02235    0.02148  -1.041    0.303    
## Y.2012       0.95295    0.04364  21.838   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.03152 on 48 degrees of freedom
## Multiple R-squared:  0.9086, Adjusted R-squared:  0.9066 
## F-statistic: 476.9 on 1 and 48 DF,  p-value: < 2.2e-16

• What are the ANOVA table test components shown here?
• Interpret the values of \(R^2\) and the \(F\)-statistic. What do they say about the goodness of fit?