Question

Accuracy of software effort estimates. Refer to the Journal of Empirical Software Engineering (Vol. 9, 2004) study of the accuracy of new software effort estimates, Exercise 12.114 (p. 781). Recall that stepwise regression was used to develop a model for the relative error in estimating effort (y) as a function of company role of estimator (x₁ = 1 if developer, 0 if project leader) and previous accuracy (x₈ = 1 if more than 20% accurate, 0 if less than 20% accurate). The stepwise regression yielded the prediction equation $\hat{y}$= 0.12 - 0.28x₁+ 0.27x₈. The researcher is concerned that the sign of the estimated $\beta$ multiplied by x₁ is the opposite from what is expected. (The researcher expects a project leader to have a smaller relative error of estimation than a developer.) Give at least one reason why this phenomenon occurred.

Short answer

The estimated sign for $\beta$ for x₁ is positive (the developer has a larger relative error of estimation than a project leader) but the prediction equation estimated using step-wise regression is negative sign of x₁. A possible reason for the same could be the existence of multicollinearity in the model.

Step-by-step solution

Reason for opposite sign

The estimated sign for $\beta$ for x₁ is positive (the developer has a larger relative error of estimation than a project leader) but the prediction equation estimated using step-wise regression is negative sign of x₁. A possible reason for the same could be the existence of multicollinearity in the model.

Rationale behind opposite sign

Since there is high degree of correlation amongst relative error in estimating effort (y) and company role of estimator (x₁) the $\beta$ estimates will not be true parameter indicators and will be biased.