๐ The goal is to find a function f-hat that can make predictions y hat from the data.
๐ We want to find the best fit line (F-hat) that minimizes the errors between predicted and actual labels.
๐ก Two options to find the best fit line are parametric and non-parametric methods.
๐ Parametric methods involve making assumptions about the shape or form of the data.
๐ Nonparametric methods do not make assumptions about the shape or form of the data.
๐ Estimating the function is simplified when assuming a linear form.
๐ Parametric methods simplify the estimation problem by using known parameters.
๐ Nonparametric methods do not assume a specific form for the data distribution.
๐ Parametric models may not accurately match the true form of the data.
Choosing a linear model for non-linear data results in poor predictions.
Using a parametric method involves expressing output based on a linear equation.
Estimating the beta values allows for predicting sales in the advertising dataset.
๐ Parametric methods use predetermined parameters to make predictions based on specific assumptions.
๐ Nonparametric methods do not make explicit assumptions about the shape or form of the data and seek to estimate it based on the data points.
๐ Nonparametric methods have the advantage of being able to accurately fit a wider range of possible functions.
๐ Parametric methods assume a certain shape for the data, which can result in inaccurate predictions if the actual data shape is different.
๐ Nonparametric methods do not make any assumptions about the shape of the data, resulting in better fitting models.
๐ However, nonparametric methods require a larger amount of data for accurate estimation.
๐ Parametric methods rely on predefined assumptions about the data, while nonparametric methods do not.
๐ Nonparametric methods may struggle to accurately estimate the response for observations not included in the training dataset.
๐ Having a large, clean dataset with minimal outliers and noise is crucial for accurately estimating the best line in nonparametric methods.
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