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--- r:linear_regression [2018/12/07 08:16] – [Multiple Regression] hkimscil
+++ r:linear_regression [2019/06/13 10:15] (current) – hkimscil
@@ Line 162: / Line 162: @@
 ====== Multiple Regression ======
+regression output table
 | anova(m)  | ANOVA table  |
 | coefficients(m) = coef(m)  | Model coefficients  |
@@ Line 200: / Line 201: @@
   * What is R<sup>2</sup>?
   * How many cars are involved in this test? (cf. df = 90)
+    * df + # of variables involved (3) = 93
+    * check 'str(Cars93)'
   * If I eliminate the R<sup>2</sup> from the above output, can you still identify what it is?
+</WRAP>
+<WRAP box info>The last question:
+  * If I eliminate the R<sup>2</sup> from the above output, can you still identify what it is?
+  * to answer the question, use the regression output table:
+R<sup>2</sup> = SS<sub>reg</sub>/SS<sub>total</sub> = 1 - SS<sub>res</sub>/SS<sub>total</sub>
+=
+<code>> anova(lm.model)
+Analysis of Variance Table
+Response: Cars93$MPG.city
+                  Df Sum Sq Mean Sq F value  Pr(>F)
+Cars93$EngineSize  1   1465    1465  100.65 2.4e-16 ***
+Cars93$Price       1    131     131    9.01  0.0035 **
+Residuals         90   1310      15
+---
+Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
+> sstotal = 1465+131+1310
+> ssreg <- 1465+131
+> ssreg/sstotal
+[1] 0.54921
+>
+> # or
+> 1-(deviance(lm.model)/sstotal)
+[1] 0.54932
+</code>
 </WRAP>
@@ Line 207: / Line 240: @@
   * $\hat{Y} = \widehat{\text{MPG.city}}$
-<WRAP box help>in the meantime,
+<WRAP box info>in the meantime,
 <code>> lm.beta(lm.model)
 Cars93$EngineSize      Cars93$Price
@@ Line 231: / Line 264: @@
 >
 </code>
+Beta coefficients are not equal to correlations among variables.
 </WRAP>