Cost Estimation and Forecasting

1
Cost Estimationand Forecasting

• Regression Problems?

2
Regression Problems

• Problems with the models specification
• Problems with the models assumptions

3
Models Specification

• The omission of relevant independent variables or
  the inclusion of irrelevant independent variables
  (Wrong regressors)
• The relation between the dependent and
  independent variable is not linear (nonlinearity)
• Two or more independent variables are
  approximately linearly related (multicolinearity)

4
Choosing the variables in the Model

• Forward selection
• Backward elimination
• Step-wise method

5
Models Assumptions

• Conduct what we call Residual Analysis
• A regression residual is defined as the
  difference between an observed y value and its
  corresponding predicted value

6
Residual Analysis

• Check for a misspecified model by plotting
  residuals against each independent variable in
  the model. A curvilinear trend detected in a
  plot implies that a quadratic term for the
  particular x variable will probably improve model
  adequacy.
• Check for unequal variances by plotting the
  residuals against the predicted values (y). Any
  patterns might reflect a heteroskedasticity
  problem

7
Residual Analysis Contd

• Check for non normal residuals by constructing a
  histogram for the residuals. If you detect
  extreme skewness in the data, you might want to
  use some kind of data transformation to stabilize
  these variances.
• Check for outliers by locating residuals that lie
  a distance of 3s or more above or below 0 on a
  residual plot versus (y). Before eliminating an
  outlier you should investigate its cause.

8
Residual Analysis Contd

• Check for correlated residuals by plotting the
  residual in time order. If you detect runs of
  positive and negative residuals, then an
  autocorrelation problem exists in the model.
  Propose addressing seasonality with indicator
  dummy variables or a time series model to account
  for the residual correlation.

9
Inference problems due to autocorrelation

• The data set contains less information than
  assumed because the observations are not
  independent.
• Therefore, the standard error/deviation estimates
  are smaller than they should be, so . . .
• Confidence intervals are too narrow
• Implying more precision than is warranted.
• We will tend to reject the null hypothesis too
  often.

10
Plot the regression residuals against a time
variable.
Residual Total
Month
11
For regression analysis using dummy variables,
refer to our discussion in the previous class