lec30v1_1up

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 s In the summer of 2006, gasoline prices soared to record levels in the United States, heightening motor vehicle customers’ concern for fuel economy. s Analysts at a major automobile company collected data n a variety of variables for a sample of 30 different cars 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. s The analysts were interested in the relationship between horsepower ( x) and highway mileage ( y). 2
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Scatter Plot 25 30 35 mpg 3 15 20 100 200 300 400 500 hp
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Regression Output 4 Interpretation?
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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 = 0 1 1 : 0 : 0 a H H =
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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 rice = 1.16 .0285(200) 5.46 6 Price = 31.16 - 0.0285(200) = 25.46 We can put a confidence interval on this number using s e : Price = 25.46 +/- 1.96 (3.55) = (18.5,32.42)
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b 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. his ffect ubstantial nd tatistically ignificant Reporting your results: 7 b This effect is substantial and statistically significant. b The regression line explains 30% of the variation in the selling price. b A car with 200 hp is expected to have a mpg of 25.46.
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More Accurate Predictions s We have discussed bounding the predictions from the regression model using the formula ˆ 1.96( ) e Y s ± s This is actually an approximation-sort of a back of the envelope calculation.
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This note was uploaded on 03/27/2012 for the course STATS 104 taught by Professor Michaelparzen during the Fall '11 term at Harvard.

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

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