{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Lecture 10_MultReg-2012-1

# Lecture 10_MultReg-2012-1 - Lecture 10 Multiple...

This preview shows pages 1–6. Sign up to view the full content.

1 Lecture 10: Multiple Regressions (Introduction) The Multiple Regression Model. Read Chap. 4.1 - Model description - Estimation of the coefficients - Interpretation of the coefficients in the multiple model vs. the simple regression model Inferences about the multiple regression coefficients - Chap 4.2 - Confidence intervals for the coefficients - Hypothesis tests for the coefficients Example : Gasoline Mileage for New Cars (2004)

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
2 General Description In multiple regression analysis, we consider more than one independent variable x 1 ,…, x K . We are interested in the conditional mean of y given x 1 ,…, x k -- μ Y x 1 ,.., x K We assume this mean is a linear function of each variable. The coefficients are fit to the data using least-squares Thus, the coefficient b i for x i measures the (linear) effect of changing x i while holding all other variables constant. This is often described as the effect of variable x i after “controlling” for the other variables in the model. The analysis can also be used to predict the value of a new y at chosen values of x 1 ,…, x K .
3 Example: Gas Mileage A team charged with designing a new automobile is concerned about the gas mileage that they should aim to achieve. They want to aim for the average value that their competitors would achieve for such a car. We’ll use Y = MPG-City . The new car is planned to have the following characteristics: horsepower – 225; weight – 4000 lbs; seating – 5 adults; length - 180 To estimate what the average competitor would achieve for such a vehicle they gathered data on all car models in 2004. The data includes information for each model about gas mileage and about the 4 variables: horsepower, weight, seating, & length. Here are some lines of the data:

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
4 Selected Automobile Data Make/Model MPG City MPG Hwy HP WT (1000) Seats Length Width Displ Cyl Acura_RL 18 24 225 3.898 5 196.6 71.6 3.5 6 Acura_TL 20 28 270 3.575 5 189.3 72.2 3.2 6 Acura_TSX 23 32 200 3.318 5 183.3 69.4 2.4 4 Acura_RSX 25 34 160 2.771 4 172.2 67.9 2 4 Buick_Century 20 30 175 3.342 6 194.6 72.7 3.1 6 Buick_LeSabre 20 29 205 3.567 5 200 73.5 3.8 6 Chevrolet_Blazer 16 21 190 3.591 5 176.8 67.8 4.3 6 Chevrolet_Cavalier 24 34 140 2.676 5 180.9 67.9 2.2 4 Chevrolet_Corvette 18 25 350 3.214 2 179.7 73.6 5.7 8 There are 43 car Makes in the data, with a total of 242 Make/Model entries. We viewed 20 Make/Models as “not ordinary”, and will exclude them from future analyses. Thus our analysis only holds for “ordinary” car types.
5 Answer s via Simple Regression We could use simple regression to derive 4 separate prediction equations. Each could give a predicted value corresponding to their respective design parameter, x . {See demonstration in Lecture.} The following table shows the coefficients of the 4 resulting linear prediction equations, and the corresponding Prediction of Y at each of the given values of our design parameters.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 24

Lecture 10_MultReg-2012-1 - Lecture 10 Multiple...

This preview shows document pages 1 - 6. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online