7.4 Confidence Intervals for the Parameter Estimates

Note that the summary output gives you information that can be used to construct a confidence interval around both \(\hat{\beta}_0\) and \(\hat{\beta}_1\).

• What information do you need to construct the margin of error here?
• How would you find the reference distribution multiplier you need?

R has a function that makes it easy to get the confidence intervals for all of the estimated parameters, confint:

confint(lin.model)

##                   2.5 %     97.5 %
## (Intercept) -0.06552929 0.02082758
## Y.2012       0.86521184 1.04069116

You can deduce from the output of confint that the confidence level is assumed to be 0.95 by default, although any appropriate level can be specified using the level argument. For example, a 99% confidence interval is given by:

confint(lin.model, level=0.99)

##                   0.5 %     99.5 %
## (Intercept) -0.07995125 0.03524955
## Y.2012       0.83590605 1.06999696