estimate the simple linear regression equation.

The idea is to find the line that gets closest to all of the points in the sample. So the algorithm to estimate the equation of a line for a given set of data is called least squares estimation. So there must be some underlying algorithm that would consistently yield the same answer for these data, and for other data sets across different computer packages. Whether I use R, Stata, Excel, SPSS, etc, I should get the same answer regardless of what computer package I use. But it shouldn't matter what package I use. And it was estimated from individual arm circumference and height data, using a computer package. And this was estimated, I used a computer to estimate this.

It was equal to 2.7, the intercept, plus the slope 0.16 times x1, the height measurement. So for example, when relating arm circumference to height, using a random sample of 150 Nepalese children who were less than 12 months old, the resulting regression equation was y hat, the estimated mean arm circumference given a value of height, x1. So in the last section, we showed the results from several simple linear regression models. And that's akin to creating the confidence interval for a single population mean, the mean of the outcome y for all population values with a predictor value of zero, an x-value of zero. Similarly, we can do the same thing to create a confidence interval for a regression intercept. We take the estimated slope, and add and subtract to estimated standard errors. And the approach is business as usual, just like we did for mean differences in term one. Because as we've seen, each of the slopes has a mean difference interpretation. So what we'll review is that creating confidence intervals for linear regression slopes essentially means creating confidence intervals for mean differences.

And the approach we'll take will look incredibly similar to everything you did regarding confidence intervals and p-values in term one. So in this section, we'll account for the uncertainty in our estimates, our estimated slopes and intercepts, by creating confidence intervals and getting p-values for hypothesis tests.

Estimate the simple linear regression equation.