Page 137 - Applied Statistics with R

8.4. CONFIDENCE INTERVALS FOR SLOPE AND INTERCEPT 137

legend = c("t, df = 1", "t, df = 10", "Standard Normal"),
lwd = 2, lty = c(3, 2, 1), col = c("darkorange", "dodgerblue", "black"))

Normal vs t Distributions

0.4 Distributions
t, df = 1
0.3 t, df = 10
Standard Normal
Density 0.2

0.1

0.0

-4 -2 0 2 4

x

8.4 Confidence Intervals for Slope and Intercept

Recall that confidence intervals for means often take the form:

EST ± CRIT ⋅ SE

or

EST ± MARGIN

where EST is an estimate for the parameter of interest, SE is the standard error
of the estimate, and MARGIN = CRIT ⋅ SE.
Then, for and we can create confidence intervals using
0
1
1 2 ̄
̂
̂
̂
± /2, −2 ⋅ SE[ ] ± /2, −2 ⋅ √ +
0
0
0