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Confidence Intervals for Slope and Intercept Parameters

In the last section, we calculated the best fit line for a sample of data. However, these data are subject to random sampling error. This means that someone else could come later, perform the same experiment (x-values), and get different experimental results (y-values).

Therefore, our data are random variables, and the slope and y-intercept we calculate using those data are also random variables, chosen from distributions around the true (population) slope and y-intercept.

The true relationship between x and y is written y = b x + a. How close are the random variables a and b to the population parameters b and a?