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## PowerPoint Slideshow about ' Regression' - rafer

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Parameter Estimation

Minimize SSE over possible parameter values

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

Multiple Regression

Example: we could try to predict change in diameter

using both change in height as well as starting height

and 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

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)

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

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)

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

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