With the use of regression, you may calculate how the dependent variable will change when the independent variable or variables change.

By a line to the observed data, regression models describe the relationship between variables. While logistic and nonlinear regression models employ a curved line, linear regression methods do not.

Regression models are useful for a variety of tasks:

- assessing how an independent variable affects a dependent variable
- predicting the dependent variable’s future values based on past observations of both variables

###### Simple Linear Regression: What Is It?

A straight line can be used in simple linear regression to establish the link between two variables. Finding the slope and intercept, which both define the line and reduce regression errors, is the first step in drawing the line.

One x variable and one y variable make up simple linear regression’s most basic version. Because it cannot be predicted by the dependent variable, the x variable is the independent variable. The fact that the y variable is contingent on the prediction you make makes it the dependent variable.

y = Î²0 +Î²1x+Îµ is the formula used for simple linear regression.

y is the dependent variable’s (y) expected value for any given value of the independent variable (x).

When x is 0, the projected value of y is known as the intercept, or B0.

The regression coefficient, or B1, indicates how much we anticipate y to change as x rises.

The independent variable is x. ( the variable we expect is influencing y).

The estimation error, or the range of our regression coefficient estimate, is expressed as e.

While simple linear regression creates a line that corresponds to your data, it does not ensure that the line is adequate.

For instance, if your data points are relatively distant from one another and show an upward trend, simple linear regression would produce a line that slopes downward, which is inconsistent with your data.

###### Comparison of Multiple and Simple Linear Regression

Multiple linear regression is preferable than basic linear regression when predicting the result of a complex process. However, it is not required to use sophisticated algorithms for straightforward issues.

The relationship between two variables in straightforward relationships can be precisely captured by a straightforward linear regression. But you need to go from basic to multiple regression when working with more complicated relationships that demand more thought.

Multiple independent variables are used in a multiple regression model. It is able to match curved and non-linear connections since it is not constrained by the same issues as the simple regression equation.

###### Simple Linear Regression Assumptions

Linearity

There should be a linear relationship between x and y. It implies that while one value rises, the other rises in lockstep with it. This linearity should be seen in the scatterplot.

Regardless of mistakes

Verifying that your data are free of inaccuracies is crucial. Your model might have issues if there is a relationship between the residuals and the variable. Examine a scatterplot of “residuals vs fits” to verify the independence of errors; there shouldn’t be any indication of a relationship.

Standard Deviation

Additionally, it is crucial to verify that your data are delivered appropriately. To do this, look at the residuals’ histogram; it should be about regularly distributed. The majority of your observations should be close to 0 or 1 (the max/min values), as shown by the histogram. It will assist you in ensuring the accuracy and dependability of your model.

Difference Equality

It is crucial to verify that the variances in your data are equal. To do this, check for any outliers or points that appear to be far apart or in disagreement on a scatterplot (you can also use statistics software like Minitab or Excel). if certain points have considerable volatility as compared to the others, or if there are outliers.