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Chapter 12 Inference on the Least-squares Regression Line; ANOVA
12.1 Inference about the Least-squares Regression Line
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The standard error of the estimate, se , is found using the formula
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EXAMPLE Computing the Standard Error
Determine the standard error of the drilling data. The data is given on the next slide.
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EXAMPLE Verifying the Normality of the Residuals
Verify that the residuals for the drilling data are normal.
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Step 1. A claim is made regarding the linear relation between a response variable, y, and a predictor variable, x. The claim is used to determine the null and alternative hypothesis. The hypothesis can be structured in one of three ways.
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Step 3. Compute the test statistic
which follows Student’s t-distribution with n – 2 degrees of freedom.
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Step 4: Compare the critical value with the test statistic:
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EXAMPLE Testing for a Linear Relation
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Confidence Intervals for the Slope of the Regression Line
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EXAMPLE Confidence Interval for Slope
Construct a 95% confidence interval for the slope of the least-squares regression line for the drilling data.
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