LectureTuesMarch.pptVIP

Lecture 17: Tues., March 16 Inference for simple linear regression (Ch. 7.3-7.4) R2 statistic (Ch. 8.6.2) Association is not causation (Ch. 7.5.3) Next class: Diagnostics for asssumptions of simple linear regression model (Ch. 8.2-8.3) Regression Goal of regression: Estimate the mean response Y for subpopulations X=x, Example: Y= catheter length required, X=height Simple linear regression model: Estimate and by least squares – choose to minimize the sum of squared residuals (prediction errors) Car Price Example 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. Inference for Simple Linear Regression Inference based on the ideal simple linear regression model holding. Inference based on taking repeated random samples ( ) from the same subpopulations ( ) as in the observed data. Types of inference: Hypothesis tests for intercept and slope Confidence intervals for intercept and slope Confidence interval for mean of Y at X=X0 Prediction interval for future Y for which X=X0 Ideal Simple Linear Regression Model Assumptions of ideal simple linear regression model There is a normally distributed subpopulation of responses for each value of the explanatory variable The means of the subpopulations fall on a straight-line function of the explanatory variable. The subpopulation standard deviations are all equal (to ) The selection of an observation from any of the subpopulations is independent of the selection of any other observation. Sampling Distributions of and See handout. See Display 7.7 Stan