It’s a 95% CI, presumably for the expected value of the conditional (on age) population mean. It looks correct, given the sample size and variance, what issue do you see with it?
To expand a little: you get a 95% ci by taking the expected value ±SE*1.96 . The SE you get for a normal distribution by taking the sample SD and dividing that by the sqrt of the sample size. So if you take a standard normal distribution, the SE for a sample size of 9 would be 1/3 and for a sample size of 100 it would be 1/10, etc. This is much tighter than the population distribution, but that’s because youre estimating just the population mean, not anything else.
Capturing structured variance in the data then should increase the precision of your estimate of the expected value, because you’re removing variance from the error term and add it into the other parts of your model (cf. the term analysis of variance).
wtf is up with that confidence interval(?) though
It’s a 95% CI, presumably for the expected value of the conditional (on age) population mean. It looks correct, given the sample size and variance, what issue do you see with it?
To expand a little: you get a 95% ci by taking the expected value ±SE*1.96 . The SE you get for a normal distribution by taking the sample SD and dividing that by the sqrt of the sample size. So if you take a standard normal distribution, the SE for a sample size of 9 would be 1/3 and for a sample size of 100 it would be 1/10, etc. This is much tighter than the population distribution, but that’s because youre estimating just the population mean, not anything else.
Capturing structured variance in the data then should increase the precision of your estimate of the expected value, because you’re removing variance from the error term and add it into the other parts of your model (cf. the term analysis of variance).