**Regression Equation**

The regression equation is a mathematical formula that represents the relationship between two variables, usually denoted as y and x. It is used to predict the value of the dependent variable (y) based on the given independent variable (x).

The given regression equation is: 2x + 3y + 50 = 0

To find the value of byx, we need to rearrange the equation into the slope-intercept form (y = mx + b), where m represents the slope and b represents the y-intercept.

**Rearranging the Equation**

Let's rearrange the given equation to isolate y:

2x + 3y + 50 = 0
3y = -2x - 50
y = (-2/3)x - 50/3

From the rearranged equation, we can see that the slope (m) is equal to -2/3.

**Calculating byx**

The coefficient byx represents the partial regression coefficient of x, given that y is the dependent variable. It measures the change in the dependent variable (y) for a one-unit change in the independent variable (x), while holding all other variables constant.

In our regression equation, the coefficient of x is -2/3. Therefore, the value of byx is -2/3.

**Explanation**

The value of byx is determined by the slope of the regression equation. In this case, the slope is -2/3, which indicates that for every one-unit increase in x, the value of y decreases by 2/3 units.

It is important to note that the coefficient byx is a measure of the linear relationship between x and y, assuming all other variables are held constant. It quantifies the strength and direction of the relationship between the variables.

By calculating the value of byx, we can understand how changes in the independent variable (x) can impact the dependent variable (y) in a linear regression model. This information is useful for predicting values of y based on given values of x and understanding the overall relationship between the variables.