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# lec30v1_1up - Stat 104 Quantitative Methods for Economists...

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Stat 104: Quantitative Methods for Economists Class 30: Prediction with Regression 1

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Example square6 In the summer of 2006, gasoline prices soared to record levels in the United States, heightening motor vehicle customers’ concern for fuel economy. square6 Analysts at a major automobile company collected data on a variety of variables for a sample of 30 different cars and small trucks. Included among those data were the Environmental Protection Agency ( EPA)’ s highway mileage rating and the horsepower of each vehicle. square6 The analysts were interested in the relationship between horsepower ( x) and highway mileage ( y). 2
Scatter Plot 25 30 35 mpg 3 15 20 2 m 100 200 300 400 500 hp

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Regression Output 4 Interpretation?
It sure appears that there is a relationship between mpg and hp, but we need to explicitly test for this. 5 0 0 0 : 0 : 0 a H H β β = 0 1 1 : 0 : 0 a H H β β =

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If we are satisfied with how well the model fits the data, we can use it to make predictions for the y variable. Predict the mpg of a car with 200 hp Price = 31.16 - 0.0285(200) = 25.46 6 We can put a confidence interval on this number using s e : Price = 25.46 +/- 1.96 (3.55) = (18.5,32.42)
boxshadowdwn A regression on the basis of a random sample of a bunch of cars indicates that an additional 1 horsepower decreases the miles per gallon by 0.028. boxshadowdwn This effect is substantial and statistically significant. Reporting your results: 7 boxshadowdwn The regression line explains 30% of the variation in the selling price. boxshadowdwn A car with 200 hp is expected to have a mpg of 25.46.

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More Accurate Predictions square6 We have discussed bounding the predictions from the regression model using the formula ˆ 1.96( ) e Y s ± square6 This is actually an approximation-sort of a back of the envelope calculation. square6 In reality, the formulas are a bit more involved as we will now detail. 8
Suppose there is a final coming up in your economics class.

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lec30v1_1up - Stat 104 Quantitative Methods for Economists...

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