What’s the Linear Regression?
Linear regression is a statistical technique used to model the relationship between a dependent variable and one or more independent variables by fitting a linear equation to the data. The dependent variable is also known as the response variable, while the independent variables are also known as explanatory or predictor variables.
The goal of linear regression is to find the best fit line, which represents the linear relationship between the dependent and independent variables. This line is expressed as y = b0 + b1x1 + b2x2 + … + bnxn, where y is the dependent variable, x1, x2, …, xn are the independent variables, and b0, b1, b2, …, bn are the coefficients that represent the intercept and slopes of the line.
The process of finding the best fit line involves minimizing the sum of the squared differences between the predicted values of the dependent variable and the actual values. This is done using a technique called least squares estimation.
Linear regression can be used for various purposes, such as predicting future values of the dependent variable, identifying the strength and direction of the relationship between the dependent and independent variables, and testing hypotheses about the relationship between the variables.
In the context of linear regression, the terms p-value, coefficient, and R-squared value are commonly used to interpret and evaluate the model’s performance. Here is an explanation of each term:
P-value: The p-value is a measure of the statistical significance of the coefficient(s) of the independent variable(s) in the linear regression model. It indicates the probability of observing a coefficient as extreme as the one estimated in the model, assuming the null hypothesis that the coefficient is zero. In other words, a p-value less than the significance level (typically 0.05) suggests that there is strong evidence to reject the null hypothesis and conclude that the independent variable(s) has a significant impact on the dependent variable.
Coefficient: The coefficient represents the slope of the line in the linear regression equation. It indicates the change in the dependent variable for a one-unit change in the independent variable, while holding other independent variables constant. For example, if the coefficient for the variable “age” is 0.5, it means that for every one-year increase in age, the dependent variable increases by 0.5 units, all other things being equal.
R-squared value: The R-squared value is a measure of how well the linear regression model fits the data. It represents the proportion of the variation in the dependent variable that can be explained by the independent variables in the model. It ranges from 0 to 1, where 0 indicates that the model explains none of the variability in the dependent variable, and 1 indicates that the model explains all of the variability. A high R-squared value suggests that the model is a good fit for the data, while a low R-squared value suggests that the model is not a good fit and may need to be revised or improved.
