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Regression

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.

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Regression

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  1. Regression

  2. Population Covariance and Correlation

  3. Sample Correlation

  4. Sample Correlation -.04 .98 -.79

  5. Linear Model DATA REGRESSION LINE

  6. (Still) Linear Model DATA REGRESSION CURVE

  7. Parameter Estimation Minimize SSE over possible parameter values

  8. Fitting a linear model in R

  9. Fitting a linear model in R Intercept parameter is significant at .0623 level

  10. Fitting a linear model in R Slope parameter is significant at .001 level, so reject

  11. Fitting a linear model in R Residual Standard Error:

  12. Fitting a linear model in R R-squared is the correlation squared, also % of variation explained by the linear regression

  13. Create a Best Fit Scatter Plot

  14. Add X and Y Labels

  15. Inspect Residuals

  16. Multiple Regression Example: we could try to predict change in diameter using both change in height as well as starting height and Fertilizer

  17. 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

  18. Regression w/ Machine Learning point of view

  19. Regression w/ Machine Learning point of view Music Year Timbre (90 attributes) http://archive.ics.uci.edu/ml/datasets/YearPredictionMSD • Let’s “train” (fit) different models to a training data set • Then see how well they do at predicting a different “validation” data set (this is how ML competitions on Kaggle work)

  20. Regression w/ Machine Learning point of view • Create a random sample of size 10000 from original 515,345 songs • Assign first 5000 to training data set, second 5000 are saved for validation

  21. Regression w/ Machine Learning point of view • Fit linear model and generalized boosting regression model (other popular choices include random forests and neural networks) • The period after the tilde denotes we will use all 91 variables for training, the –V1 throws out V1 (since this is what we’re predicting)

  22. Regression w/ Machine Learning point of view • Next we make predictions for the validation data set • We compare the models by calculating the sum of squares error (SSE) for each model

  23. Regression w/ Machine Learning point of view

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