This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: ⇒ Set up times are not significantly different in the two systems while the per byte times (slopes) are different. 1432 ©2008 Raj Jain CSE567M Washington University in St. Louis Confidence Intervals for Predictions Confidence Intervals for Predictions ! This is only the mean value of the predicted response. Standard deviation of the mean of a future sample of m observations is: ! m =1 ⇒ Standard deviation of a single future observation: 1433 ©2008 Raj Jain CSE567M Washington University in St. Louis CI for Predictions (Cont) CI for Predictions (Cont) ! m = ∞ ⇒ Standard deviation of the mean of a large number of future observations at x p : ! 100(1 α )% confidence interval for the mean can be constructed using a t quantile read at n2 degrees of freedom. 1434 ©2008 Raj Jain CSE567M Washington University in St. Louis CI for Predictions (Cont) CI for Predictions (Cont) ! Goodness of the prediction decreases as we move away from the center. 1435 ©2008 Raj Jain CSE567M Washington University in St. Louis Example 14.5 Example 14.5 ! Using the disk I/O and CPU time data of Example 14.1, let us estimate the CPU time for a program with 100 disk I/O's. ! For a program with 100 disk I/O's, the mean CPU time is: 1436 ©2008 Raj Jain CSE567M Washington University in St. Louis Example 14.5 (Cont) Example 14.5 (Cont) ! The standard deviation of the predicted mean of a large number of observations is: ! From Table A.4, the 0.95quantile of the tvariate with 5 degrees of freedom is 2.015. ⇒ 90% CI for the predicted mean 1437 ©2008 Raj Jain CSE567M Washington University in St. Louis Example 14.5 (Cont) Example 14.5 (Cont) ! CPU time of a single future program with 100 disk I/O's: ! 90% CI for a single prediction: 1438 ©2008 Raj Jain CSE567M Washington University in St. Louis Visual Tests for Regression Assumptions Visual Tests for Regression Assumptions Regression assumptions: 1. The true relationship between the response variable y and the predictor variable x is linear. 2. The predictor variable x is nonstochastic and it is measured without any error. 3. The model errors are statistically independent. 4. The errors are normally distributed with zero mean and a constant standard deviation. 1439 ©2008 Raj Jain CSE567M Washington University in St. Louis 1. Linear Relationship: Visual Test 1. Linear Relationship: Visual Test ! Scatter plot of y versus x ⇒ Linear or nonlinear relationship 1440 ©2008 Raj Jain CSE567M Washington University in St. Louis 2. Independent Errors: Visual Test 2. Independent Errors: Visual Test 1. Scatter plot of ε i versus the predicted response ! All tests for independence simply try to find dependence. 1441 ©2008 Raj Jain CSE567M Washington University in St. Louis Independent Errors (Cont) Independent Errors (Cont) 2. Plot the residuals as a function of the experiment number 1442 ©2008 Raj Jain CSE567M Washington University in St. Louis 3. Normally Distributed Errors: Test 3. Normally Distributed Errors: Test ! Prepare a normal quantilequantile plot of errors....
View
Full Document
 Spring '13
 MRR
 Math, Linear Regression, Regression Analysis, Washington University, Raj Jain

Click to edit the document details