Statistics 350 Review Today Today Review Simple Linear

Statistics 350 Review

Today • Today: Review

Simple Linear Regression • Simple linear regression model: • Yi= • Distribution of errors for i=1, 2, …, n

Simple Linear Regression • In practice, do not know the values of the ’s nor 2 • Use data to estimate model parameters giving estimated regression equation • Want to get the “line of best fit”…what does this mean?

Apartment Example

Least Squares • Estimation via least squares: Q= • Know how to derive • For simple linear regression and multiple linear regression • Related simplified models are fair game

Properties • Know properties of estimators and also residuals • Example: sum of residuals is • Show estimates of regression parameters are unbiased • How do you use the estimated regression line (function)?

Maximum likelihood • Know how to derive MLE for regression parameters and variance

Inference • Interested in making inference about regression parameters are the function • Example: • Inference about i: • Prediction intervals: • Confidence intervals:

Inference • Interested in making inference about regression parameters are the function • Example: • Inference about i: • Simultaneous Inference:

Inference • Prediction intervals: • Confidence intervals:

ANOVA • Know/understand ANOVA approach • ANOVA decomposition: • Hypotheses

Residual Diagnostics • Motivation • Plots • Remedial Measures…when to transform X or Y

Diagnostics • Could also do a Lack of Fit Test

Multiple regression • Derivations, inference • R 2 and adjusted R 2 • Extra sums of squares: • Multi-collinearity • Model Building: • Criteria and all sub-sets • Automatic methods

Final Steps • Model Validation: • Partial Regression Plots:

Exam