Slope Coefficient Calculator

Formula

The formula to calculate the Slope Coefficient is:

\[ B1 = \frac{\sum{(x_i - \bar{x})(y_i - \bar{y})}}{\sum{(x_i - \bar{x})^2}} \]

Where:

\(B1\) is the slope coefficient
\(x_i\) is the value of the independent variable in the \(i\)-th observation
\(\bar{x}\) is the mean value of the independent variable
\(y_i\) is the value of the dependent variable in the \(i\)-th observation
\(\bar{y}\) is the mean value of the dependent variable

What is a Slope Coefficient?

A slope coefficient is a key parameter in a regression analysis that represents the change in the dependent variable resulting from a one-unit change in the corresponding independent variable. It is the value that appears next to the independent variable in the equation of a regression line. The slope coefficient indicates the direction (positive or negative) and the strength of the relationship between the variables.

Example Calculation 1

Let's assume the following values:

Independent Variable Values (xi) = [1, 2, 3, 4, 5]
Dependent Variable Values (yi) = [2, 4, 5, 4, 5]

Using the formula:

\[ B1 = \frac{\sum{(x_i - \bar{x})(y_i - \bar{y})}}{\sum{(x_i - \bar{x})^2}} = 0.6 \]

The Slope Coefficient is 0.6.

Example Calculation 2

Let's assume the following values:

Independent Variable Values (xi) = [2, 3, 5, 7, 9]
Dependent Variable Values (yi) = [1, 2, 3, 4, 5]

Using the formula:

\[ B1 = \frac{\sum{(x_i - \bar{x})(y_i - \bar{y})}}{\sum{(x_i - \bar{x})^2}} = 0.55 \]

The Slope Coefficient is 0.55.