# Lesson 36: More Regression

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### Introduction

In the previous lesson, we learned that one of the primary uses of an estimated regression line:

$\hat{y}=\hat{\alpha}+\hat{\beta}(x-\bar{x})$

is to determine whether or not a linear relationship exists between the predictor x and the response y. In that lesson, we learned how to calculate a confidence interval for the slope parameter β as a way of determining whether a linear relationship does exist. In this lesson, we'll learn learn two other primary uses of an estimated regression line:

(1) If we are interested in knowing the value of the mean response E(Y) = μY for a given value x of the predictor, we'll learn how to calculate a confidence interval for the mean E(Y) = μY.

(2) If we are interested in knowing the value of a new observation Yn+1 for a given value x of the predictor, we'll learn how to calculate a prediction interval for the new observation Yn+1.