The formula to calculate the regression constant (a) is:
a=(ΣY⋅ΣX2−ΣX⋅ΣXY)(n⋅ΣX2−(ΣX)2)
Where:
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 1:
Step 1: Calculate the numerator:
ΣY⋅ΣX2−ΣX⋅ΣXY=150⋅1200−100⋅2000=180000−200000=−20000
Step 2: Calculate the denominator:
n⋅ΣX2−(ΣX)2=10⋅1200−1002=12000−10000=2000
Step 3: Calculate the regression constant:
a=−200002000=−10
Example 2:
Step 1: Calculate the numerator:
ΣY⋅ΣX2−ΣX⋅ΣXY=180⋅1500−120⋅2400=270000−288000=−18000
Step 2: Calculate the denominator:
n⋅ΣX2−(ΣX)2=12⋅1500−1202=18000−14400=3600
Step 3: Calculate the regression constant:
a=−180003600=−5