Enter the sum of Y values, sum of X values, sum of XY products, sum of X squared, and the number of data points into the calculator to determine the regression constant (a) for a linear regression equation.
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Regression Constant Formula
The following formula is used to calculate the regression constant (a):
a = (ΣY * ΣX² - ΣX * ΣXY) / (n * ΣX² - (ΣX)²)
Variables:
- a is the regression constant
- ΣY is the sum of Y values
- ΣX is the sum of X values
- ΣXY is the sum of the products of X and Y values
- ΣX² is the sum of X values squared
- n is the number of data points
To calculate the regression constant, use the formula above by plugging in the values for ΣY, ΣX, ΣXY, ΣX², and n.
What is a Regression Constant?
The regression constant (a) is the y-intercept of the linear regression line. It represents the point where the regression line crosses the Y-axis. In the context of a linear regression equation y = ax + b, the constant is the value of y when x equals zero. It is a crucial part of the linear regression model as it provides a starting point for the predicted relationship between the independent variable (x) and the dependent variable (y).
How to Calculate the Regression Constant?
The following steps outline how to calculate the Regression Constant (a).
- First, determine the sum of Y values (ΣY).
- Next, determine the sum of X values (ΣX).
- Then, calculate the sum of the products of X and Y values (ΣXY).
- Calculate the sum of X values squared (ΣX²).
- Determine the number of data points (n).
- Use the formula to calculate the regression constant (a).
- After inserting the variables and calculating the result, check your answer with the calculator above.
Example Problem :
Use the following variables as an example problem to test your knowledge.
Sum of Y values (ΣY) = 50
Sum of X values (ΣX) = 20
Sum of XY products (ΣXY) = 220
Sum of X squared (ΣX²) = 90
Number of data points (n) = 5
