Enter the values of the independent and dependent variables, along with their mean values, into the calculator to determine the slope coefficient.

Slope Coefficient Formula

The following formula is used to calculate the slope coefficient in a regression analysis.

B1 = Σ[(xi - x̄)(yi - ȳ)] / Σ[(xi - x̄)^2]

Variables:

  • B1 is the slope coefficient
  • xi is the value of the independent variable in the i-th observation
  • x̄ is the mean value of the independent variable
  • yi is the value of the dependent variable in the i-th observation
  • ȳ 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.

How to Calculate Slope Coefficient?

The following steps outline how to calculate the Slope Coefficient.

  1. First, calculate the mean value of the independent variable (x̄).
  2. Next, calculate the mean value of the dependent variable (ȳ).
  3. Next, for each observation, calculate the difference between the independent variable value (xi) and the mean value of the independent variable (x̄), and the difference between the dependent variable value (yi) and the mean value of the dependent variable (ȳ).
  4. Next, square each difference obtained in the previous step.
  5. Next, multiply each pair of differences obtained in step 3 (xi – x̄) and (yi – ȳ).
  6. Next, sum up all the products obtained in the previous step.
  7. Finally, divide the sum of the products obtained in step 6 by the sum of the squared differences obtained in step 4.
  8. The result obtained in step 7 is the Slope Coefficient (B1).

Example Problem:

Use the following variables as an example problem to test your knowledge:

xi = [2, 4, 6, 8, 10]

yi = [5, 7, 9, 11, 13]

x̄ = 6

ȳ = 9

Using the formula B1 = Σ[(xi – x̄)(yi – ȳ)] / Σ[(xi – x̄)^2], calculate the Slope Coefficient (B1).