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Regression. Population Covariance and Correlation. Sample Correlation. Sample Correlation. -.04. .98. -.79. Linear Model. DATA. REGRESSION LINE. (Still) Linear Model. DATA. REGRESSION CURVE. Parameter Estimation. Minimize SSE over possible parameter values. - PowerPoint PPT Presentation
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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