Consider the data set davis.data which, among other things gives the reported weight (repwt) and actual weight (weight) of some experimental subjects (reported weight is what they said they weighed). The idea here is that we would like to just ask people "How much do you weigh?" instead of actually having to weigh them. Thus in the model weight_i = β₀ + β₁repwt_i + ε_i we would hope that the slope β₁ would be equal to 1.

Of course, we don't expect the data to give a slope exactly equal to one, but we've mentioned the idea of an "eyeball confidence interval" -- take the slope and add and subtract twice the standard error, 2 being a stand-in for 1.96, and the whole thing is a t and not normal anyway, but the idea is that this should be "close enough for government work". You are free to use that kind of confidence interval in this problem. We'd like 1 to be in this confidence interval. If you want to be more pedantically correct, you can use the command confint (assuming you did something like my.mod = lm(...) you then enter confint(my.mod)).

1. Fit the model with weight as the y-variable and repwt as the x-variable.
2. Compute a 95% confidence interval for the repwt slope. Is 1 in the confidence interval?
3. Now plot the data. Notice anything odd? Which observation number is that? Look through the data by hand (with your eyeballs?) if you like. Assuming you typed plot(repwt,weight) you can type identify(repwt,weight) and click the point. Click some more points if you like. You'll have to right-click the plot and choose Quit to get the R prompt back. Turn in your plot and tell me what looks funny.
4. Re-compute the slope and intercept without the offending point (lm(...,subset=-5) will fit the model omitting observation 5, you can probably adapt this to your situation). Then re-compute the confidence interval. What happens?