What is the regression equation in regression analysis?

The regression equation in regression analysis is a mathematical formula that represents the relationship between the independent variable(s) and the dependent variable. It is used to predict the value of the dependent variable based on the values of the independent variable(s). The general form of a regression equation is:

Y = a + bX

Where:
- Y is the dependent variable
- X is the independent 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)

In multiple regression analysis, where there are multiple independent variables, the regression equation takes the form:

Y = a + b1X1 + b2X2 + ... + bnXn

Where:
- Y is the dependent variable
- X1, X2, ..., Xn are the independent variables
- a is the intercept
- b1, b2, ..., bn are the coefficients for each independent variable

```
y = a + bx
```

where:

- y is the dependent variable
- x is the independent variable
- a is the y-intercept
- b is the slope