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