A statistical program is recommended. Sherry is a production manager for a small manufacturing shop and is interested in developing a predictive model to estimate the time to produce an order of a given size—that is, the total time to produce a certain quantity of the product. Suppose she has collected data in the following table on the total time (in minutes) to produce 30 different orders of various quantities. Quantity Total Time (minutes) 105 172 125 189 135 221 141 323 149 248 171 317 190 372 204 185 206 250 240 177 255 397 277 227 299 228 335 369 371 490
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
| Quantity | Total Time (minutes) |
|---|---|
| 105 | 172 |
| 125 | 189 |
| 135 | 221 |
| 141 | 323 |
| 149 | 248 |
| 171 | 317 |
| 190 | 372 |
| 204 | 185 |
| 206 | 250 |
| 240 | 177 |
| 255 | 397 |
| 277 | 227 |
| 299 | 228 |
| 335 | 369 |
| 371 | 490 |
| Quantity | Total Time (minutes) |
|---|---|
| 388 | 351 |
| 392 | 428 |
| 400 | 412 |
| 421 | 545 |
| 439 | 443 |
| 439 | 320 |
| 455 | 587 |
| 458 | 483 |
| 480 | 513 |
| 486 | 423 |
| 493 | 403 |
| 506 | 700 |
| 586 | 593 |
| 589 | 456 |
| 665 | 643 |
#1) Develop the estimated regression equation. (Let x = quantity, and let y = total time (in minutes). Round your numerical values to four decimal places.) ŷ =
#2) Find the value of the test statistic (round to two decimal places). Find the p-value (round to three decimal places).
#3) Did the estimated regression equation provide a good fit? (Round your numerical answer to four decimal places.) Since r2 =_______. is (less than OR at least .55), the estimated regression equation (did not provide OR did provide) a good fit.
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