### Analyze length on age for smallmouth bass in a northeastern MN lkae

smbass=read.table("http://www.stat.umn.edu/alr/data/wblake.txt",header=TRUE)

names(smbass)

[1] "Age"    "Length" "Scale" 


attach(smbass)

### construct scatter plot with regression line

plot(Length~Age)
regmod=lm(Length~Age)
abline(coef(regmod))

## inspect coefficients
summary(regmod)

Call:
lm(formula = Length ~ Age)

Residuals:
    Min      1Q  Median      3Q     Max 
-85.794 -19.499  -4.499  16.177  94.853 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)  65.5272     3.1974   20.49   <2e-16 ***
Age          30.3239     0.6877   44.09   <2e-16 ***
---

Residual standard error: 28.65 on 437 degrees of freedom
Multiple R-squared: 0.8165,     Adjusted R-squared: 0.8161 
F-statistic:  1944 on 1 and 437 DF,  p-value: < 2.2e-16 

### find 95% confidence and prediction intervals for
### length when age=4.5 

x=data.frame(Age=4.5)
 predict(regmod,x)
[1] 201.9847
 predict(regmod,x,interval="confidence")
          fit      lwr      upr
[1,] 201.9847 199.2677 204.7016
 predict(regmod,x,interval="prediction")
          fit      lwr      upr
[1,] 201.9847 145.6184 258.3509