In the regression equation y = a + b x, what does 'a' represent?

In the regression equation y = a + b x, what does 'a' represent?

• A. The fixed cost component (intercept)
• B. The variable cost per unit
• C. The total cost at maximum output
• D. The coefficient of determination (R-squared)

Answer: (A)

The constant term in a linear equation is the intercept—it’s the value of the dependent variable when the independent variable is zero. In a cost model where y is total cost and x is activity level, this intercept represents fixed costs, because these costs do not change with the level of activity. So the parameter a is the fixed cost component. The slope, b, is the variable cost per unit, since it multiplies x to adjust cost as activity increases. The remaining options don’t describe this constant term: the variable cost per unit is the slope, the total cost at maximum output depends on a specific x value, and the coefficient of determination (R-squared) is a measure of how well the line fits the data, not a parameter of the equation.

The constant term in a linear equation is the intercept—it’s the value of the dependent variable when the independent variable is zero. In a cost model where y is total cost and x is activity level, this intercept represents fixed costs, because these costs do not change with the level of activity. So the parameter a is the fixed cost component.

The slope, b, is the variable cost per unit, since it multiplies x to adjust cost as activity increases. The remaining options don’t describe this constant term: the variable cost per unit is the slope, the total cost at maximum output depends on a specific x value, and the coefficient of determination (R-squared) is a measure of how well the line fits the data, not a parameter of the equation.