SE-280 Dr. Mark L. Hornick 1 Prediction Intervals

SE-280 Dr. Mark L. Hornick 2 Review: PROBE’s regression calculations give us estimates (projections) for size (A+M LOC)…

SE-280 Dr. Mark L. Hornick 3 …and time

SE-280 Dr. Mark L. Hornick 4 But just how good are these estimates??? Off by 5%, 10%, 50%, 100%, 500%? Does it matter? Do you want to bet: Your weekends? Your reputation? Your JOB?

SE-280 Dr. Mark L. Hornick 5 Which of the following regression projections would you trust more?

SE-280 Dr. Mark L. Hornick 6 Example A 10 data points Correlation = Estimated Object LOC Actual Total LOC

SE-280 Dr. Mark L. Hornick 7 Example B 25 data points Correlation = Estimated Object LOC Actual Total LOC

A Prediction Interval calculation computes the bounds on the likely error of an estimate Range UPI = estimated A+M LOC + Range LPI = estimated A+M LOC - Range UPI LPI Projection (Estimate) Strictly speaking, the UPI/LPI "lines" are parabolas, and Range varies. Range

SE-280 Dr. Mark L. Hornick 9 If you had this kind of information about your estimates, how would you use it? Suppose your time projection said that a project would take 8 weeks. But, your prediction interval has a range of 3 weeks How should you make your plan? What should you tell management?

SE-280 Dr. Mark L. Hornick 10 If you had this kind of information about your estimates, how would you use it? Suppose your time projection said that a project would take 8 weeks. But, your prediction interval has a range of 3 weeks How should you make your plan? What should you tell management? 3 3

SE-280 Dr. Mark L. Hornick 11 If you had this kind of information about your estimates, how would you use it? Suppose your time projection said that a project would take 8 weeks How should you make your plan? What should you tell management? What if the range was 6 weeks? 6 6

SE-280 Dr. Mark L. Hornick 12 The prediction interval is based on the t distribution. 70% limits (area) Regression- projected value Range Lower prediction interval limit (LPI) Upper prediction interval limit (UPI)

SE-280 Dr. Mark L. Hornick 13 Prediction Interval Usage Range within which data is likely to fall Assuming variation is this estimate is similar to that in prior estimates PSP uses 70% and 90% limits Computes range in which actual value will likely fall 70% of the time 90% of the time Helps to assess planning quality

To get the prediction interval, we must calculate the range: Text, page 128; may have error in formula (n instead of d), depending on textbook revision. Note: this is for one independent variable.

For multiple regression, the range calculation is just extended a little.

The  ("sigma") value is computed in the following way. x i,j = previous independent variable values y i = previous dependent variable (estimate) values n= number of previous estimates m= number of independent variables d= n-(m+1) [degrees of freedom]  j = regression coefficients calculated from previous data Same for one independent variable. Alternate form:

The range formula requires us to find the integration limit that yields the correct integral value. For a 70% interval, we want p = 0.70 Question: what integration limit “t” gives this value? -tt Two-sided integral value = p We have to search (try t values) in order to find out. For a 90% interval, we want p = 0.90

When thinking about searching for the desired integral value, it may be helpful to plot the integral of the t-distribution function. Hint: create a "function object" that calculates the two-sided p integral, given a specified t value.

SE-280 Dr. Mark L. Hornick 19 The calculation needed is the reverse of that used in the significance calculation, since we are seeking "t" instead of "p". t p For a specified "p" (integral) value, we want to find the corresponding "t" (integration limit). How should we do the search?

In the significance calculation, we calculated "p" for a given "t"; now we are seeking "t" that will give us a desired "p". t p For a specified "p" (2-sided integral) value, we want to find the corresponding "t" (integration limit). How should we do the search?

The textbook's suggests a state-machine approach that requires the function to be monotonic (pg. 246). The sign of the error (desired versus actual "p") tells you whether to increase or decrease the trial "t" value to get closer to the desired answer. p t The increase/decrease step size is halved when changing search direction.

An alternative search method brackets the answer and bisects the interval.

How does the interval bisection method work? t p error (+) error (-)