Lecture7_Prediction_2012

# Lecture7_Prediction_2012 - Lecture 7 Stat102 2012...

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1 Lecture 7 Stat102 2012 • Estimating the conditional mean of y given x (Section 3.5.1), and CI s • Predicting an individual value of y given x (Section 3.5.2), and CI s • Some cautions in interpreting regression results (Section 3.7)

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2 Example; Car Prices • A used-car dealer wants to understand how odometer reading affects the selling price of used cars. • The dealer randomly selects 100 three-year old Ford Tauruses that were sold at auction during the past month. Each car was in top condition and equipped with automatic transmission, AM/FM cassette tape player and air conditioning. • carprices.JMP contains the price and number of miles on the odometer of each car.
3 13500 14000 14500 15000 15500 16000 Price 25000 35000 45000 Odometer Car Prices Linear Fit Price = 17067 - 0.0623 Odometer Summary of Fit RSquare 0.650 Root Mean Square Error e s = 303.1 Mean of Response y =14823 Observations 100 Moments Mean x =36009 Std Dev x s =6597 Std Err Mean 659 N 100 Note: 2 2 6597 4352409 x s 

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4 Two prediction problems a) The used-car dealer has an opportunity to bid on a lot of cars offered by a rental company. The rental company has very many Ford Tauruses, all equipped with automatic transmission, air conditioning and AM/FM cassette tape players. All of these cars have about 40,000 miles on the odometer. The dealer would like an estimate of the average selling price of all of these cars . b) The used-car dealer is about to bid on a 3-year old Ford Taurus equipped with automatic transmission, air conditioner and AM/FM cassette tape player and with 40,000 miles on the odometer. The dealer would like to predict the selling price of an individual car.
5 Prediction Problem (a): Prediction of the Mean for a Given x Goal is to estimate the conditional mean of selling price given odometer reading, x m =40,000. ie , estimate m Yx at x m =40,000. The estimate itself is just 01 ˆˆ m m y b b x    . For our example 17067 - 0.0623 17067 - 0.0623 40,000 14,575 m m yx  

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6 Assuming the ideal simple linear regression model holds, and if 2 e were known the variance of this estimate would be     2 22 2 1 1 m me x xx n n s      . This follows from a theoretical calculation like those in the notes for Lectures 3 & 5.
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## This note was uploaded on 04/04/2012 for the course STAT 102 taught by Professor Shaman during the Spring '08 term at UPenn.

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Lecture7_Prediction_2012 - Lecture 7 Stat102 2012...

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