Regression equations

Regression  equations are often used in statistics to evaluate whether or not there is a connection between two sets of data, one being a dependent variable and the other an independent variable. In statistical modeling, regression analysis is a set of statistical procedures used to assess the associations between a dependent variable and one or more independent variables. There are two most common types of regression  equations- multiple regression and simple linear regression equation. It is used to find out the value of one variable if we know the other variables and the relationship that exists between the two or, in a mathematical sense, the ratio between the two.

What is a regression equation?

Sometimes when we are at the ticket counter for a train ticket. Have you ever seen how a class like first-class second class determines the price? Like an AC department or First class has the highest ticket. So when two relations are observed, and the price is dependent on the other equation like the one equation is dependent on the other equation, we can determine the value variable if we know the view of the other and the relationship that exists between the two, this relationship between the two is known as regression  equations.

Types of regression  equations

There are two most common types of regression  equations

simple linear regression equation

As the name implies, one variable is reliant on the other, and if we know the connection or ratio between the two variables, we may get the value of the outcome variable. A product’s pricing, for example, is determined by its size.

multiple regression equation

A subset of multiple regression is linear regression. It’s a statistical method that combines multiple explanatory variables to predict the outcome of a response variable.

Formula of regression  equations

LINEAR regression  equations

Y= a + bX is the form of the equation.

A and b can be calculated by the next formulas

Where b = n∑xy−(∑x)(∑y)/n∑x2−(∑x)2

a= (∑y−b(∑x))/n

The dependent variable (the one plotted on the Y-axis), the independent variable (the one drawn on the X-axis), the line’s slope, and the y-intercept are all represented by the letters Y, X, and an.

multiple regression  equations

Y = m x₁ + m x₂+ mx₃+ b

Y= the dependent variable of the regression.

M = slope of the regression.

X₁=first independent variable of the regression.

The X₂=second independent variable of the regression.

The X₃=third independent variable of the regression.

B= constant.

The Use of regression  equations

• The idea of analyzing engine performance in cars using test data.
• Market research studies and consumer survey results analysis can both benefit from linear regression. In observational astronomy, linear regression is frequently utilized.
• In astronomical data analysis, a variety of statistical techniques and methodologies can be utilized, and there are entire libraries in languages like Python dedicated to astrophysical data analysis.
• Linear regression can also be used to examine the impact of marketing, pricing, and promotions on product sales.

What are the properties of linear regression  equations?

• The sum of squared discrepancies between observed and predicted values is reduced by the line.
• The regression line connects the mean values of the X and Y variables.
• The y-intercept of the linear regression is equal to the regression constant ( b₀).

The slope of the regression line equals the average change in the dependent variable (Y) for a unit change in the independent variable is the regression coefficient (b₀) (X).

Conclusion

Regression  equations are often used in statistics to evaluate whether or not there is a connection between two sets of data, one being a dependent variable and the other an independent variable. We use regression  equations to find out the value of one variable if we know the other variables and the relationship that exists between the two or, in a mathematical sense, the ratio between the two. In a regression equation, the slope is the essential variable since it informs you how much Y will change as X grows. The units for slope are normally the Y variable’s units divided by the X variable’s units. It’s the difference between Y and X divided by the difference between Y and X.