Here's what you'll find in this section:Inferences for Simple Linear Regression and Correlation
Regression analysis is a statistical tool that utilizes the relation
between two or more quantitative variables so that one variable (dependent
variable) can be predicted from the others (independent variables). For
example, if one knows the relationship between advertising expenditures and
sales, one can predict sales by regression analysis once the level of
advertising expenditures has been set. In this chapter, we specifically
consider the case when a single independent variable is used for predicting
the dependent variable and the dependent variable and the independent
variable are linearly related.
The model can be stated as: [ Y_i;=; _0 + _1 X_i + _i, i=1,2,..., n ; ] where
Recall the following notations:
We then have
In many situations, a general form for a % confidence interval for a parameter is [ ^ (critical value)SE(^ ), ] where is a sample statistic used to estimate , SE [the standard error of ] gives the variation of and the critical value is a value such as or . Thus, all we have to do is (1) find the formula for SE and (2) ``plug-in'' numbers into this general equation to get a confidence interval. The following confidence (prediction) intervals all follow this rule.
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