r:linear_regression
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r:linear_regression [2018/06/15 08:32] – [e.g. 3] hkimscil | r:linear_regression [2019/06/13 10:15] (current) – hkimscil | ||
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Does the model fit the data well? | Does the model fit the data well? | ||
* **Plot the residuals** and check the regression diagnostics. | * **Plot the residuals** and check the regression diagnostics. | ||
+ | * see [[https:// | ||
Does the data satisfy the assumptions behind linear regression? | Does the data satisfy the assumptions behind linear regression? | ||
* Check whether the diagnostics confirm that a linear model is reasonable for your data. | * Check whether the diagnostics confirm that a linear model is reasonable for your data. | ||
Line 146: | Line 147: | ||
</ | </ | ||
+ | <WRAP info> | ||
+ | What about beta coefficient? | ||
+ | |||
+ | < | ||
+ | |||
+ | < | ||
+ | EngineSize | ||
+ | -0.7100032 | ||
+ | > cor(MPG.city, | ||
+ | [1] -0.7100032 | ||
+ | > | ||
+ | </ | ||
====== Multiple Regression ====== | ====== Multiple Regression ====== | ||
+ | regression output table | ||
| anova(m) | | anova(m) | ||
| coefficients(m) = coef(m) | | coefficients(m) = coef(m) | ||
Line 184: | Line 198: | ||
F-statistic: | F-statistic: | ||
</ | </ | ||
- | Questions: | + | <WRAP box help>Questions: |
* What is R< | * What is R< | ||
* How many cars are involved in this test? (cf. df = 90) | * How many cars are involved in this test? (cf. df = 90) | ||
+ | * df + # of variables involved (3) = 93 | ||
+ | * check ' | ||
* If I eliminate the R< | * If I eliminate the R< | ||
+ | </ | ||
+ | <WRAP box info>The last question: | ||
+ | * If I eliminate the R< | ||
+ | * to answer the question, use the regression output table: | ||
+ | |||
+ | R< | ||
+ | = | ||
+ | |||
+ | < | ||
+ | Analysis of Variance Table | ||
+ | |||
+ | Response: Cars93$MPG.city | ||
+ | Df Sum Sq Mean Sq F value Pr(> | ||
+ | Cars93$EngineSize | ||
+ | Cars93$Price | ||
+ | Residuals | ||
+ | --- | ||
+ | Signif. codes: | ||
+ | |||
+ | > sstotal = 1465+131+1310 | ||
+ | > ssreg <- 1465+131 | ||
+ | > ssreg/ | ||
+ | [1] 0.54921 | ||
+ | > | ||
+ | > # or | ||
+ | > 1-(deviance(lm.model)/ | ||
+ | [1] 0.54932 | ||
+ | </ | ||
+ | |||
+ | |||
+ | </ | ||
Regression formula: | Regression formula: | ||
* $\hat{Y} = -2.99 * EngineSize + -0.15 * Price + 33.35$ | * $\hat{Y} = -2.99 * EngineSize + -0.15 * Price + 33.35$ | ||
* $\hat{Y} = \widehat{\text{MPG.city}}$ | * $\hat{Y} = \widehat{\text{MPG.city}}$ | ||
+ | |||
+ | <WRAP box info>in the meantime, | ||
+ | < | ||
+ | Cars93$EngineSize | ||
+ | | ||
+ | > cor(MPG.city, | ||
+ | [1] -0.7100032 | ||
+ | > cor(EngineSize, | ||
+ | [1] 0.5974254 | ||
+ | > cor(MPG.city, | ||
+ | [1] -0.5945622 | ||
+ | > | ||
+ | </ | ||
+ | Or . . . . | ||
+ | < | ||
+ | > temp | ||
+ | . . . . | ||
+ | |||
+ | > cor(temp) | ||
+ | | ||
+ | MPG.city | ||
+ | EngineSize -0.7100032 | ||
+ | Price -0.5945622 | ||
+ | > | ||
+ | </ | ||
+ | Beta coefficients are not equal to correlations among variables. | ||
+ | </ | ||
< | < | ||
Line 469: | Line 543: | ||
Residuals 99 240.84 | Residuals 99 240.84 | ||
</ | </ | ||
- | |||
- | < | ||
- | Analysis of Variance Table | ||
- | |||
- | Model 1: happiness ~ age + gender | ||
- | Model 2: happiness ~ age + gender + friends | ||
- | Model 3: happiness ~ age + gender + friends + pets | ||
- | Res.Df | ||
- | 1 97 233.97 | ||
- | 2 96 209.27 | ||
- | 3 95 193.42 | ||
- | --- | ||
- | Signif. codes: | ||
- | </ | ||
- | |||
- | * Model 0: SS< | ||
- | * Model 1: SS< | ||
- | * Model 2: SS< | ||
- | * SS< | ||
- | * FF(1,96) = 12.1293, pp = 0.0007521 (after adding friends) | ||
- | * Model 3: SS< | ||
- | * SS< | ||
- | * FF(1,95) = 7.7828, pp = 0.0063739 (after adding pets) | ||
< | < | ||
Line 506: | Line 557: | ||
Multiple R-squared: | Multiple R-squared: | ||
F-statistic: | F-statistic: | ||
+ | </ | ||
+ | < | ||
summary(m2) | summary(m2) | ||
Line 521: | Line 573: | ||
Multiple R-squared: | Multiple R-squared: | ||
F-statistic: | F-statistic: | ||
+ | </ | ||
+ | < | ||
summary(m3) | summary(m3) | ||
Line 539: | Line 593: | ||
</ | </ | ||
+ | |||
+ | |||
+ | < | ||
+ | > lm.beta(m3) | ||
+ | age genderMale | ||
+ | -0.14098154 -0.04484095 | ||
+ | </ | ||
+ | |||
+ | < | ||
+ | anova(m0, | ||
+ | Analysis of Variance Table | ||
+ | |||
+ | Model 1: happiness ~ 1 | ||
+ | Model 2: happiness ~ age + gender | ||
+ | Model 3: happiness ~ age + gender + friends | ||
+ | Model 4: happiness ~ age + gender + friends + pets | ||
+ | Res.Df | ||
+ | 1 99 240.84 | ||
+ | 2 97 233.97 | ||
+ | 3 96 209.27 | ||
+ | 4 95 193.42 | ||
+ | --- | ||
+ | Signif. codes: | ||
+ | </ | ||
+ | |||
+ | * Model 0: SS< | ||
+ | * Model 1: SS< | ||
+ | * Model 2: SS< | ||
+ | * SS< | ||
+ | * F(1,96) = 12.1293, p value = 0.0007521 (after adding friends) | ||
+ | * Model 3: SS< | ||
+ | * SS< | ||
+ | * F(1,95) = 7.7828, p value = 0.0063739 (after adding pets) | ||
+ | |||
+ | |||
{{https:// | {{https:// |
r/linear_regression.1529019178.txt.gz · Last modified: 2018/06/15 08:32 by hkimscil