In least squares regression, what do y and a represent?

Author:
Harold Averkamp, CPA, MBA

Here are the meanings of the components or symbols used in the least squares equation of y = a + bx:

y is the dependent variable, such as the estimated or expected total cost of electricity during a month. The amount of y is dependent upon the amounts of a and bx.

a is the estimated total amount of fixed electricity costs during the month. It is the value of y, when x is zero. If the total cost line intersects the y-axis at \$1,000 then it is assumed that the total fixed costs for a month are \$1,000.

b is the estimated variable cost per unit of x. It determines the slope of the total cost line. If b is \$5, this means that the variable cost portion of electricity is estimated to be \$5 for every unit of x.

x is the independent variable. For example, x could represent the known number of machine hours used in the month.

bx is the total variable cost of electricity. If the company’s electricity cost is estimated to be \$5 per unit of x, and x is 4,000 machine hours, then the total variable cost of electricity for the month is estimated to be \$20,000.

In our example the total estimated cost of electricity (y) in a month when x is 4,000 machine hours will be \$21,000.

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