Model Development

polynomial regression, each of which has its own advantages and disadvantages depending on the dataset and the relationship between the variables.

1. Simple Linear Regression:

   • Simple linear regression is a method to model the relationship between a single independent variable (predictor) and a dependent variable (response).
   • It assumes a linear relationship between the predictor and response variables.
   • The model equation is of the form: $�={�}_0+{�}_1�+�$, where $�$ is the dependent variable, $�$ is the independent variable, ${�}_0$ is the intercept, ${�}_1$ is the slope, and $�$ is the error term.
   • Simple linear regression is appropriate when there is a clear linear relationship between the variables.

2. Multiple Linear Regression:

   • Multiple linear regression extends simple linear regression to model the relationship between multiple independent variables and a single dependent variable.
   • It assumes a linear relationship between each predictor and the response variable, holding other predictors constant.
   • The model equation is of the form: $�={�}_0+{�}_1{�}_1+{�}_2{�}_2+\mathrm{.}\mathrm{.}\mathrm{.}+{�}_{�}{�}_{�}+�$, where $�$ is the dependent variable, ${�}_1,{�}_2,\mathrm{.}\mathrm{.}\mathrm{.},{�}_{�}$ are the independent variables, ${�}_0,{�}_1,{�}_2,\mathrm{.}\mathrm{.}\mathrm{.},{�}_{�}$ are the coefficients, and $�$ is the error term.

3. Polynomial Regression:

   • Polynomial regression is a form of regression analysis in which the relationship between the independent variable and the dependent variable is modeled as an $�$th degree polynomial.
   • It can capture non-linear relationships between variables better than linear regression.
   • The model equation is of the form: $�={�}_0+{�}_1�+{�}_2{�}^2+\mathrm{.}\mathrm{.}\mathrm{.}+{�}_{�}{�}^{�}+�$, where $�$ is the dependent variable, $�$ is the independent variable, ${�}_0,{�}_1,{�}_2,\mathrm{.}\mathrm{.}\mathrm{.},{�}_{�}$ are the coefficients, and $�$ is the error term.

These regression techniques are used to develop predictive models that can be used to estimate the price of a car based on relevant independent variables or features. Model evaluation techniques such as R-squared, mean squared error (MSE), and visualization are employed to assess the performance of the models and make informed decisions in prediction tasks.