Multi Linear Regression: Prediction of Speed of Vehicle(MPG)

 

What is Multiple Linear Regression?

Multiple Linear Regression is a statistical technique used to model the relationship between one dependent variable (also known as the outcome or response variable) and two or more independent variables (also known as predictors or explanatory variables). It extends simple linear regression, which involves only one predictor, to include multiple predictors.

Prediction Equation

$y$$=$${\beta }_{}$$0_{}$$+$${\beta }_{}$$1_{}$$x_{}$$1_{}$$+$${\beta }_{}$$2_{}$$x_{}$$2_{}$$+$${\beta }_{}$$3_{}$$x_{}$$3_{}$$+$$\dots$$+$${\beta }_{}$$n_{}$$x_{}$$n_{}$$+$$ϵ$

• Where:

  • $\mathrm{y\; is\; the\; dependent\; variable\; (the\; variable\; we\; are\; trying\; to\; predict).}$

• β0​ is the y-intercept (the predicted value of y when all x values are 0).
• ${\mathrm{<span\; style="font-size:\; medium;"><br></span>}}_{}$
• β1​,β2​,…,βn​ are the coefficients (the change in $y$ for a one-unit change in the respective $x$ variable).

• $x1​,x2​,…,xn​ are the independent variables (the predictors).$

• ϵ is the error term (the difference between the actual and predicted values).

Example in Context

For your cars dataset, if we want to predict MPG (Miles Per Gallon) based on the features HP (Horse Power), VOL (Volume), SP (Speed), and WT (Weight), the prediction equation would look like this:

$\text{MPG}$$=$${\beta }_{}$$0_{}$$+$${\beta }_{}$$1_{}$$\cdot$$\text{HP}$$+$${\beta }_{}$$2_{}$$\cdot$$\text{VOL}$$+$${\beta }_{}$$3_{}$$\cdot$$\text{SP}$$+$${\beta }_{}$$4_{}$$\cdot$$\text{WT}$$+$$ϵ$

Explanation in Short

• Multiple Linear Regression: A method to predict a dependent variable using multiple independent variables.

• Prediction Equation: An equation that includes the intercept, coefficients for each predictor, and an error term to estimate the dependent variable.

• The goal is to find, the values of 
• $\beta_0, \beta_1, \ldots, \beta_n$, that minimize the error term $\epsilon$, thereby providing the best linear fit to the data.

Multi Linear Regression: Prediction of Speed of Vehicle(MPG)

To predict the fuel efficiency (MPG) of cars using multiple linear regression, we will analyze the relationships between MPG and other car attributes such as horsepower (HP), volume (VOL), speed (SP), and weight (WT).

Go through the following Jupyter Notebook

Download Cars dataset from here (Cars)