> lactgpa = lm(GPA ~ ACT, data = actgpa)

> summary(lactgpa)

Call:
lm(formula = GPA ~ ACT, data = actgpa)

Residuals:
     Min       1Q   Median       3Q      Max 
-0.78010 -0.22341  0.05116  0.17520  0.51488 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)  1.11263    0.34120   3.261  0.00331 ** 
ACT          0.08702    0.01290   6.747  5.6e-07 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 

Residual standard error: 0.2918 on 24 degrees of freedom
Multiple R-Squared: 0.6548,	Adjusted R-squared: 0.6404 
F-statistic: 45.52 on 1 and 24 DF,  p-value: 5.6e-07 


> actscores = data.frame(ACT = c(19:33))

> predict(lactgpa, newdata = actscores, interval = "confidence")
        fit      lwr      upr
1  2.766097 2.543730 2.988464
2  2.853121 2.652810 3.053433
3  2.940146 2.760647 3.119644
4  3.027170 2.866757 3.187583
5  3.114194 2.970451 3.257937
6  3.201219 3.070799 3.331639
7  3.288243 3.166694 3.409792
8  3.375267 3.257130 3.493405
9  3.462292 3.341643 3.582941
10 3.549316 3.420579 3.678053
11 3.636340 3.494891 3.777790
12 3.723365 3.565694 3.881035
13 3.810389 3.633954 3.986824
14 3.897413 3.700395 4.094432
15 3.984438 3.765530 4.203346

> predict(lactgpa, newdata = actscores, interval = "prediction")
        fit      lwr      upr
1  2.766097 2.124064 3.408129
2  2.853121 2.218390 3.487852
3  2.940146 2.311673 3.568619
4  3.027170 2.403880 3.650460
5  3.114194 2.494985 3.733404
6  3.201219 2.584966 3.817472
7  3.288243 2.673806 3.902680
8  3.375267 2.761496 3.989038
9  3.462292 2.848032 4.076551
10 3.549316 2.933417 4.165215
11 3.636340 3.017659 4.255022
12 3.723365 3.100775 4.345955
13 3.810389 3.182784 4.437994
14 3.897413 3.263714 4.531113
15 3.984438 3.343595 4.625280