Linear Regression Model Overview

A function that takes a single input variable, in this case, the degree of the polynomial.

The function that calculates the gradient of the quadratic function, 2x, representing the instantaneous slope at any point on the function's curve.

A hyperparameter that controls the size of the step taken in each iteration of the gradient descent algorithm, determining how quickly the algorithm approaches the minimum point of a function.

A method used to assess the performance of a model, indicating how much of the variation in the dependent variable is explained by the independent variable.

The error or discrepancy between the predictions made by a machine learning model and the actual values of the data.

Incorrect or biased assumptions made during the training process of a machine learning model, leading to systematic errors in its predictions.

Unknown parameters or coefficients in a linear regression model that represent the impact of each independent variable on the dependent variable. They are estimated based on the data.

Polynomial representation in linear regression, where X3 is derived by squaring the first input variable X1. Higher-order terms allow capturing non-linear relationships.

Interaction terms in linear regression, where X3 is obtained by multiplying X1 and X2. These terms capture the combined effect of two variables.

Transformation of a quantitative input variable in linear regression, where X3 is computed by taking the logarithm of X1. This transformation can linearize the relationship.

A technique used to represent qualitative input variables in linear regression by creating dummy variables for each category or level of the variable. This allows the model to capture the effects of different categories.

A relationship that approximates a straight line between the predictor variable X and the response variable Y, a fundamental assumption in simple linear regression analysis.

Β0 represents the intercept, which is the value of the response variable when the predictor variable is zero, while Β1 represents the slope, which quantifies the rate of change in the response variable for every one-unit increase in the predictor variable.

The hat symbol represents estimation, indicating that the values are estimated based on the available data. It is used to differentiate estimated values from the true unknown parameters.

The goal is to find the best fit line by finding values of β0 and β1 that minimize the sum of squared differences between the actual data points and the predicted values.

sales ≈ β0 + β1 × TV + β2 × TV^2. The model now includes a quadratic term for TV, allowing for a curved relationship between sales and TV expenditure.

sales ≈ β0 + β1 × TV + β2 × Radio + β3 × TV × Radio. The model now includes an interaction term, allowing for a combined effect of TV and Radio on sales.

sales ≈ β0 + β1 × log(TV). This transformation changes the relationship between sales and TV expenditure by considering the logarithm of TV. It can often linearize the relationship.