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Regression Constant Calculator











Formula

The formula to calculate the regression constant (a) is:

a=(ΣYΣX2ΣXΣXY)(nΣX2(ΣX)2)

Where:

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).

Example Calculation

Example 1:

Step 1: Calculate the numerator:

ΣYΣX2ΣXΣXY=15012001002000=180000200000=20000

Step 2: Calculate the denominator:

nΣX2(ΣX)2=1012001002=1200010000=2000

Step 3: Calculate the regression constant:

a=200002000=10

Example 2:

Step 1: Calculate the numerator:

ΣYΣX2ΣXΣXY=18015001202400=270000288000=18000

Step 2: Calculate the denominator:

nΣX2(ΣX)2=1215001202=1800014400=3600

Step 3: Calculate the regression constant:

a=180003600=5