Regression analysis For Example 11.6 in notes:

> x<-c(38.2, 40.0, 42.5, 43.4, 44.6, 44.9, 45.0, 45.4,46.0,47.3,47.3,48.0,49.1,50.5,51.6)

> y<-c(8.9,13.0,4.7,-2.4,12.5,18.4,6.6,13.5,8.5,15.3,18.9,6.0,10.4, 15.9,17.1)

> plot(y,x)

> cor(y,x)

[1] 0.3832905

> d<-data.frame(cbind(y,x)) %% Creating a data frame object

> d

y x

1 8.9 38.2

2 13.0 40.0

3 4.7 42.5

4 -2.4 43.4

5 12.5 44.6

6 18.4 44.9

7 6.6 45.0

8 13.5 45.4

9 8.5 46.0

10 15.3 47.3

11 18.9 47.3

12 6.0 48.0

13 10.4 49.1

14 15.9 50.5

15 17.1 51.6

> regout=lm(y~1+x,d) %% first part is the formula, second part is the data frame to be used, see more about formulas in page 50 of the R-intro file

> qqnorm(regout$res)

> qqline(regout$res)

> plot(x,regout$fitted)

> coef(regout) %%%%%%%%%%%%% more operations on the fitted model in more about formulas in page 53 of the R-intro file

(Intercept) x

-16.9910445 0.6173818

> beta<-coef(regout)

> beta

(Intercept) x

-16.9910445 0.6173818

> deviance(regout) %%gives RSS

[1] 412.6025

> formula(regout)

y ~ 1 + x

> plot(regout)

Hit <Return> to see next plot:

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> reg.aov<-aov(y~x,d)

> summary(reg.aov)

Df Sum Sq Mean Sq F value Pr(>F)

x 1 71.05 71.05 2.2387 0.1585

Residuals 13 412.60 31.74

> summary(regout)

Call:

lm(formula = y ~ 1 + x, data = d)

Residuals:

Min 1Q Median 3Q Max

-12.203 -3.557 1.956 2.775 7.671

Coefficients:

Estimate Std. Error t value Pr(>|t|)

(Intercept) -16.9910 18.8662 -0.901 0.384

x 0.6174 0.4126 1.496 0.158

Residual standard error: 5.634 on 13 degrees of freedom

Multiple R-Squared: 0.1469, Adjusted R-squared: 0.08129

F-statistic: 2.239 on 1 and 13 DF, p-value: 0.1585

>