# Question

The following data relate road width x and accident frequency y. Road width (in feet) was treated as the independent variable, and values y of the random variable Y, in accidents per 108 vehicle miles, were observed.

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.

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.

## Answer to relevant Questions

The following data are observations y on a dependent random variable Y taken at various levels of an independent variable x. [It is assumed that E(Yi׀xi) = A + Bxi, and the Yi are independent normal random variables with ...You are using exponential smoothing to obtain monthly forecasts of the sales of a certain product. The forecast for last month was 2,083, and then the actual sales turned out to be 1,973. Obtain the forecast for next month ...Ivy University is planning to construct a new building for its engineering school. This project will require completing all of the activities in the above table. For most of these activities, a set of predecessor activities ...A transition matrix P is said to be doubly stochastic if the sum over each column equals 1; that is, If such a chain is irreducible, a periodic, and consists of M + 1 state, show that Consider the second version of the stock market model presented as an example in Sec. 29.2. Whether the stock goes up tomorrow depends upon whether it increased today and yesterday. If the stock increased today and ...Post your question

0