## Single Variable Regression

Probably the easiest place to start with regression analysis is with the case introduced about cost and schedule. In regression analysis, one or more of the variables must be the independent variable. The remaining data variable is the dependent variable. The simplest relationship among two variables, one independent and one dependent, is the linear equation of the form

Y = a * X + b where X is the independent variable, and the value of Y is dependent on the value of X. When we plot the linear equation we observe that the "curve" is a straight line. Figure 8-1 provides a simple illustration of the linear "curve" that is really a straight line. In Figure 8-1, the independent variable is time and the dependent variable is cost, adhering to the time-honored expression "time is money." Horizontal axis = Time IndepenileTit Variable T Figure 8-1: Linear Equation.

Those familiar with linear equations from the study of algebra recognize that the parameter

"a" is the slope of the line and has dimensions of "Y per X," as in dollars per week if Y were dimensioned in dollars and X were dimensioned in weeks. As such, project managers can always think of the slope parameter as a "density" parameter. t2] The "b" parameter is usually called the "intercept," referring to the fact that when X = 0, Y = b. Therefore, "b" is the intercept point of the curve with the Y-axis at the origin where X = 0.

Of course, X and Y could be deterministic variables (only one fixed value) or they could be random variables (observed value is probabilistic over a range of values). We recognize that the value of Y is completely forecasted by the value of X once the deterministic parameters "a" and "b" are known.

In Figure 8-2, we see a scatter of real observations of real cost and schedule data laid on the graph containing a linear equation of the form we have been discussing, C = a * T + b. Visually, the straight line (that is, the linear curve) seems to fit the data scatter pretty well. As project managers, we might be quite comfortable using the linear curve as the forecast of data values beyond those observed and plotted. If so, the linear equation becomes the "regression" curve for the observed data. Figure 8-2: Random

Horizontal axis = Time independent VariabEeT "Linear" Data. ## Project Management Made Easy

What you need to know about… Project Management Made Easy! Project management consists of more than just a large building project and can encompass small projects as well. No matter what the size of your project, you need to have some sort of project management. How you manage your project has everything to do with its outcome.

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