The R program
In this chapter we will mainly be using the lung data set so we will use the attach function.
attach(lung)
Regression equation from regressing ffev1a on fheight, bottom of p. 126.
First we create the variable ffev1a = ffev1/100.
ffev1a <- ffev1/100
lm1 <- lm(ffev1a ~ fheight, lung)
summary(lm1)
<output omitted>
Coefficients:
Value Std. Error t value Pr(>|t|)
(Intercept) -4.0867 1.1520 -3.5475 0.0005
fheight 0.1181 0.0166 7.1065 0.0000
Descriptive statistics, middle of p. 127.
subset.male <- data.frame(fage, fheight, ffev1a)
apply(subset.male, 2, mean)
apply(subset.male, 2, stdev)
apply(subset.male, 2, range)
fage fheight ffev1a
40.13333 69.26 4.093267
fage fheight ffev1a
6.889995 2.779189 0.6507523
fage fheight ffev1a
[1,] 26 61 2.50
[2,] 59 76 5.85
Regression equation from regressing ffev1a on fheight and fage, bottom p. 128.
lm2 <- lm(ffev1a ~ fage+fheight, lung)
summary(lm2)
Residuals:
Min 1Q Median 3Q Max
-1.347 -0.3414 0.009172 0.3717 1.419
Coefficients:
Value Std. Error t value Pr(>|t|)
(Intercept) -2.7607 1.1377 -2.4265 0.0165
fage -0.0266 0.0064 -4.1828 0.0000
fheight 0.1144 0.0158 7.2454 0.0000
Residual standard error: 0.5348 on 147 degrees of freedom
Multiple R-Squared: 0.3337
F-statistic: 36.81 on 2 and 147 degrees of freedom, the p-value is 1.094e-013
Correlation of Coefficients:
(Intercept) fage
fage -0.2786
fheight -0.9738 0.0561
Covariance matrix, middle p. 133.
subset2 <- data.frame(fage, fheight, fweight, ffev1a)
var(subset2, na.method="omit")
fage fheight fweight ffev1a
fage 47.472036 -1.0751678 -3.649217 -1.3876197
fheight -1.075168 7.7238926 34.695436 0.9122322
fweight -3.649217 34.6954362 573.797808 2.0671647
ffev1a -1.387620 0.9122322 2.067165 0.4234785
Correlation matrix, top p. 134.
cor(subset2, na.method="omit")
fage fheight fweight ffev1a
fage 1.00000000 -0.05614863 -0.02211064 -0.3094823
fheight -0.05614863 1.00000000 0.52116447 0.5043960
fweight -0.02211064 0.52116447 1.00000000 0.1326111
ffev1a -0.30948231 0.50439596 0.13261112 1.0000000
Table 7.1, p. 138.
Anova table corresponding to the regression of ffev1a on fheight and fage.
aov2 <- aov(ffev1a ~ fage+fheight, lung)
summary(aov2)
Df Sum of Sq Mean Sq F Value Pr(F)
fage 1 6.04351 6.04351 21.13149 9.165832e-006
fheight 1 15.01346 15.01346 52.49544 2.300000e-011
Residuals 147 42.04133 0.28600
Table 7.5, p. 150.
Regressing fev1a on age and height for the subsets of males only.
apply(subset.male, 2, mean)
apply(subset.male, 2, stdev)
male.lm <- lm(ffev1a ~ fage+fheight, lung)
summary(male.lm)
fage fheight ffev1a
40.13333 69.26 4.093267
fage fheight ffev1a
6.889995 2.779189 0.6507523
Coefficients:
Value Std. Error t value Pr(>|t|)
(Intercept) -2.7607 1.1377 -2.4265 0.0165
fage -0.0266 0.0064 -4.1828 0.0000
fheight 0.1144 0.0158 7.2454 0.0000
Residual standard error: 0.5348 on 147 degrees of freedom
Multiple R-Squared: 0.3337
F-statistic: 36.81 on 2 and 147 degrees of freedom, the p-value is 1.094e-013
Table 7.5, p. 150.
Regressing fev1a on age and height for the subsets of females only.
mfev1a <- mfev1/100
subset.female <- data.frame(mage, mheight, mfev1a)
apply(subset.female, 2, mean)
apply(subset.female, 2, stdev)
female.lm <- lm(mfev1a ~ mage+mheight, lung)
summary(female.lm)
mage mheight mfev1a
37.56 64.09333 2.973133
mage mheight mfev1a
6.714184 2.469537 0.4874136
Coefficients:
Value Std. Error t value Pr(>|t|)
(Intercept) -2.2112 0.8961 -2.4676 0.0147
mage -0.0200 0.0050 -3.9630 0.0001
mheight 0.0926 0.0137 6.7565 0.0000
Residual standard error: 0.413 on 147 degrees of freedom
Multiple R-Squared: 0.2915
F-statistic: 30.24 on 2 and 147 degrees of freedom, the p-value is 1e-011
Table 7.5, p. 150.
Regressing fev1a on age and height for both males and females using the data set lung.long.
apply(lung.long, 2, mean)
apply(lung.long, 2, stdev)
lm.all <- lm(fev1a ~ age+height, lung.long)
summary(lm.all)
age height fev1a
38.84667 66.67667 3.5332
age height fev1a
6.912484 3.685657 0.8025856
Coefficients:
Value Std. Error t value Pr(>|t|)
(Intercept) -6.7370 0.5633 -11.9601 0.0000
age -0.0186 0.0044 -4.1860 0.0000
height 0.1649 0.0083 19.7853 0.0000
Residual standard error: 0.5275 on 297 degrees of freedom
Multiple R-Squared: 0.5709
F-statistic: 197.6 on 2 and 297 degrees of freedom, the p-value is 0
Unless you plan to continue to use the data set lung is a good idea to detach it.
detach(lung)