08-regression-part2-handout

08-regression-part2-handout - STA 3024: Regression Douglas...

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Unformatted text preview: STA 3024: Regression Douglas Whitaker Department of Statistics 12 March 2012 Douglas Whitaker (Department of Statistics) STA 3024: Regression 12 March 2012 1 / 45 Upcoming Statistics Courses Summer STA 4321 - Introduction to Probability (Mathematical Statistics I) MTWRF 2nd Period (Summer A) STA 4322 - Introduction to Statistics Theory (Mathematical Statistics II) MTWRF 2nd Period (Summer B) Fall STA 4321 - Introduction to Probability (Mathematical Statistics I) MWF 1st or 2nd Period STA 4210 - Regression Analysis MWF 2nd Period Douglas Whitaker (Department of Statistics) STA 3024: Regression 12 March 2012 2 / 45 Douglas Whitaker (Department of Statistics) STA 3024: Regression 12 March 2012 3 / 45 Douglas Whitaker (Department of Statistics) STA 3024: Regression 12 March 2012 4 / 45 Before Spring Break... The last thing we did was this: X Y 4 5 5 9 9 10 12 13 14 17 y i = α + βx i + e i ˆ y i = 2 . 123 + 0 . 986 x i Douglas Whitaker (Department of Statistics) STA 3024: Regression 12 March 2012 5 / 45 Scatterplot Douglas Whitaker (Department of Statistics) STA 3024: Regression 12 March 2012 6 / 45 Scatterplot with Regression Line Douglas Whitaker (Department of Statistics) STA 3024: Regression 12 March 2012 7 / 45 Computer Output (Note: This output was shown in class but a bit later on. We used it to get the 0.1887 for the SE for ˆ β when making a confidence interval for β .) Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 2.1176 1.8135 1.168 0.3273 x 0.9866 0.1887 5.230 0.0136 *--- Signif. codes: 0 ’***’ 0.001 ’**’ 0.01 ’*’ 0.05 ’.’ 0.1 Douglas Whitaker (Department of Statistics) STA 3024: Regression 12 March 2012 8 / 45 Regression: Interpretations But now that we have these numbers, what do we do? We tested to see if the model was significant (F and t tests). We could make confidence intervals for β in the usual way. But how do we actually interpret these numbers? Douglas Whitaker (Department of Statistics) STA 3024: Regression 12 March 2012 9 / 45 Interpreting the slope The way we interpret the slope ( ˆ β ) is: for a one unit increase in x we expect that the average value of y will increase by ˆ β ....
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This note was uploaded on 03/20/2012 for the course STA 3024 taught by Professor Ta during the Spring '08 term at University of Florida.

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08-regression-part2-handout - STA 3024: Regression Douglas...

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