In today’s topic i have gone through
Linear regression between two predictor variables:
Linear regression between two predictor variables is known as simple linear regression. In simple linear regression, we seek to establish a linear relationship between two variables: a dependent variable (the one we want to predict) and an independent variable (the one we use to make predictions). The goal is to find a linear equation that best describes the relationship between these two variables.
The general form of a simple linear regression equation is:
Y=a+bX+ε
Where:
Y is the dependent variable (the variable you want to predict).
X is the independent variable (the predictor variable).
a is the intercept (the value of Y when X is 0).
b is the slope (the change in Y for a one-unit change in X).
ε represents the error term (the part of Y that is not explained by the linear relationship with X).
The goal in simple linear regression is to estimate the values of a and b that best fit the data. This is typically done using a method called least squares regression, where the values of a and b are chosen to minimize the sum of the squared differences between the observed values of Y and the values predicted by the equation.
Once you have estimated the values of a and b, you can use the equation to make predictions for Y based on values of X that were not in original dataset.
Linear model:
A linear model is a statistical technique that assumes a linear relationship between one or more independent variables and a dependent variable. It’s used for prediction and modeling. Examples include simple linear regression (one predictor) and multiple linear regression (multiple predictors). Other variations like logistic regression are used for binary outcomes, while Poisson regression is for count data. These models are widely used in various fields for data analysis and prediction.
Correlation with predictor variables:
Interactions between predictor variables mean that the effect of one predictor on the outcome depends on the value of another predictor. Correlation between predictor variables measures how they relate to each other. High correlations can complicate regression analysis. Handling interactions and addressing high correlations are essential for accurate modeling.