Periodically, software engineers must provide estimates of their effort in developing new software. In the Journal of Empirical Software Engineering (Vol. 9, 2004), multiple regression was used to predict the accuracy of these effort estimates. The dependent variable, defined as the relative error in estimating effort, 

y = (Actual effort – Estimated effort)/(Actual effort)

was determined for each in a sample of n = 49 software development tasks. Eight independent variables were evaluated as potential predictors of relative error using stepwise regression. Each of these was formulated as a dummy variable, as shown in the table.

a. In Step 1 of the stepwise regression, how many different one-variable models are fit to the data?

b. In Step 1, the variable x₁ is selected as the “best” one variable predictor. How is this determined?

c. In Step 2 of the stepwise regression, how many different two-variable models (where x₁ is one of the variables) are fit to the data?

d. The only two variables selected for entry into the stepwise regression model were x₁ and x₈. The stepwise regression yielded the following prediction equation: 

ŷ = .12 - .28x₁ + .27x₈

Give a practical interpretation of the β-estimates multiplied by x₁ and x₈.

e. Why should a researcher be wary of using the model, part d, as the final model for predicting effort (y)?

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Company role of estimator: x1 = 1 if developer, 0 if project leader %3D Task complexity: x2 = 1 if low, 0 if medium/high Contract type: x3 = 1 if fixed price, O if hourly rate %3! Customer importance: x4 = 1 if high, 0 if low/medium Customer priority: xs = 1 or quality I if time-of-delivery, 0 if cost Level of knowledge: x6 = 1 if high, 0 if low/medium Participation: x7 = 1 if estimator participates in work, 0 if not Previous accuracy: xg = 1 if more than 20% accurate, 0 if less than 20% accurate