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Y X XP
Source: McClave & Sincich (2003) Using the model for prediction
If 3 TV ads are run prior to a sale, we expect
the mean number of cars sold to be:
y = 10 + 5(3) = 25 cars The 95% prediction interval estimate of the
number of cars sold in one particular week when 3
TV ads are run is:
25 + 8.28 = 16.72 to 33.28 cars
Here 8.28 4.66667 3.182 1 1/ 5 1/ 4 Residual Analysis: checking assumptions If the assumptions about the error term e appear
questionable, the hypothesis tests about the
significance of the regression relationship and the
interval estimation results may not be valid. The residuals provide the best information about e . Residual for Observation i ˆ
yi yi Much of the residual analysis is based on an
examination of graphical plots. Residual Plot Against x Residual ˆ
yy Good Pattern 0 x Residual Plot Against x Residual ˆ
yy Nonconstant Variance 0 x Simple linear regression summary
1. Hypothesize deterministic component 2. Estimate unknown model parameters 3. Specify probability distribution of random
error term and estimate standard deviation
of error 4. Confidence interval and testing. 5. Model validation—residual analysis. 6. Use model for prediction & estimation...
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This note was uploaded on 09/28/2011 for the course STAT METHO 33:623:385 taught by Professor Faridalizadeh during the Spring '11 term at Rutgers.
- Spring '11