Sample slides from "Getting Started with R" course, run in collaboration with PRISMTC http://www.prismtc.co.uk/f106-r-starter-course-1/

1. © 2012 Heather Turner
Part II
Using R for Data Analysis
49 / 90

2. © 2012 Heather Turner
Simple Linear Regression
A simple linear model is fitted using lm
> model1 <- lm(wt ~ gestation, data = infant)
> model1
Call:
lm(formula = wt ~ gestation, data = infant)
Coefficients:
(Intercept) gestation
-10.0642 0.4643
Specific components of the model fit can be extracted,
for example using coef, deviance, fitted or residuals
> deviance(model1)
[1] 339092.1
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3. © 2012 Heather Turner
Model Summary
> summary(model1)
Call:
lm(formula = wt ~ gestation, data = infant)
Residuals:
Min 1Q Median 3Q Max
-49.394 -11.125 0.071 10.106 57.353
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -10.06418 8.32220 -1.209 0.227
gestation 0.46426 0.02974 15.609 <2e-16 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 16.66 on 1221 degrees of freedom
(13 observations deleted due to missingness)
Multiple R-squared: 0.1663, Adjusted R-squared: 0.1657
F-statistic: 243.6 on 1 and 1221 DF, p-value: < 2.2e-16
51 / 90

4. © 2012 Heather Turner
Diagnostics
> layout(matrix(1:4, nrow = 2))
> plot(model1)
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−60−202060
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Residuals vs Fitted
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−3 −1 0 1 2 3
−3−113
Theoretical Quantiles
Standardizedresiduals
Normal Q−Q
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0.00.51.01.5
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Scale−Location
261
5571100
0.00 0.02 0.04
−2024
Leverage
Standardizedresiduals
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Cook's distance
0.5
Residuals vs Leverage
261
870
1200
52 / 90

5. © 2012 Heather Turner
Multiple Regression
Here we add key maternal characteristics. Dummy
variables are automatically created for each level of
race with white as the reference
> (model2 <- lm(wt ~ gestation + wt.1 + ht +
+ parity + race, data = infant))
Call:
lm(formula = wt ~ gestation + wt.1 + ht + parity + race, data = infant)
Coefficients:
(Intercept) gestation wt.1 ht
-79.48027 0.44183 0.09081 0.99258
parity racemexican raceblack raceasian
0.86424 7.70791 -6.56544 -3.68222
racemixed race
-0.56133
53 / 90

6. © 2012 Heather Turner
Sequential Anova
The significance of each addition to the model can be
assessed using sequential anova, aka Type I ANOVA
> anova(model2)
Analysis of Variance Table
Response: wt
Df Sum Sq Mean Sq F value Pr(>F)
gestation 1 66615 66615 255.9291 < 2.2e-16 ***
wt.1 1 8382 8382 32.2039 1.751e-08 ***
ht 1 6060 6060 23.2815 1.585e-06 ***
parity 1 1567 1567 6.0189 0.0143 *
race 4 10076 2519 9.6781 1.061e-07 ***
Residuals 1163 302715 260
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘
54 / 90

7. © 2012 Heather Turner
Type II Tests
Type II tests are provide by the Anova function from the
car package
> library(car); Anova(model2)
Anova Table (Type II tests)
Response: wt
Sum Sq Df F value Pr(>F)
gestation 55567 1 213.4810 < 2.2e-16 ***
wt.1 3052 1 11.7238 0.0006386 ***
ht 5469 1 21.0132 5.054e-06 ***
parity 2847 1 10.9393 0.0009702 ***
race 10076 4 9.6781 1.061e-07 ***
Residuals 302715 1163
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘
55 / 90