The following data relate road width x and accident frequency y. Road width (in feet) was treated
Question:
Assume that Y is normally distributed with mean A + Bx and constant variance for all x and that the sample is random. Interpolate if necessary.
(a) Fit a least-squares line to the data, and forecast the accident frequency when the road width is 55 feet.
(b) Construct a 95 percent prediction interval for Y+, a future observation of Y, corresponding to x+ = 55 feet.
(c) Suppose that two future observations on Y, both corresponding to x+ = 55 feet, are to be made. Construct prediction intervals for both of these observations so that the probability is at least 95 percent that both future values of Y will fall into them simultaneously. If k predictions are to be made, such as given in part (d), each with probability 1 α, then the probability is at least 1 kα that all k future observations will fall into their respective intervals.
(d) Construct a simultaneous tolerance interval for the future value of Y corresponding to x+ = 55 feet with P = 0.90 and 1 α = 0.95.
Future value (FV) is the value of a current asset at a future date based on an assumed rate of growth. The future value (FV) is important to investors and financial planners as they use it to estimate how much an investment made today will be worth...
Step by Step Answer:
Introduction to Operations Research
ISBN: 978-1259162985
10th edition
Authors: Frederick S. Hillier, Gerald J. Lieberman