Residulas §

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Notes and Ideas: §

Defination:

• Residuals in a statistical or machine learning model are the differences between observed and predicted values of data. They are a diagnostic measure used when assessing the quality of a model. They are also known as errors
• is an estimation of =0 . unbiased
• Note:
  1. is an unbiased estimator of
  2. Sampling distribution of :

     • Normally distributed

Out of Sample Error: given (new data)

properties: Sampling distribution of :

• Normally Distribution

Use :

• Residuals are importatant when determining the quality of a model. We can examine residuals in terms of their mahnitude and/ or whether they form a parttern
• Where the residuals are all 0, the model predicts perfectly. THe further residuals are from 0, the less accurate the model. In the case of Linear Regression, the greater the sum of squared residucals, the smaller the r-squared tatistic, all else being equal
• Where the average residual is not 0, it implies that the model is systematically biased(i.e., consistently over-or under-predicting)

Residual plot:

• In the case of simple linear regression (regression with 1 predictor), we set the predictor as the x-axis and the residual as the y-axis
• In the case of multiple linear regression (regression with >1 predictor), we set the fitted value as the x-axis and the residual as the y-axis

Residcual function:

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Properties: §

1. mean of the residuals should be 0
2. Variance of e
3. Non-independence, Scine
4. is normally distributed
5. For simple linear regression(2D):

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TAGS §

#linear_regression