Regression

Population Covariance and Correlation

Sample Correlation

Sample Correlation

.98 -.04 -.79

Linear Model

DATA

REGRESSION LINE

(Still) Linear Model

DATA

REGRESSION CURVE

Parameter Estimation

Minimize SSE over possible parameter values

Fitting a linear model in R

Fitting a linear model in R

Intercept parameter is significant at .0623 level

Fitting a linear model in R

Slope parameter is significant at .001 level, so reject

Fitting a linear model in R

Residual Standard Error:

Fitting a linear model in R

R-squared is the correlation squared, also % of variation explained by the linear regression

Create a Best Fit Scatter Plot

Add X and Y Labels

Inspect Residuals

Multiple Regression

Example: we could try to predict change in diameterusing both change in height as well as starting heightand Fertilizer

Multiple Regression

• All variables are significant at .05 level • The Error went down and R-squared went up (this is good)• Can even handle categorical variables