# Regression - PowerPoint PPT Presentation

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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.

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Regression

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## Regression

-.04

.98

-.79

DATA

REGRESSION LINE

DATA

REGRESSION CURVE

### 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