Estimating Setup Time

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. She has collected the data on the total time to produce 30

different orders of various quantity in the file Setup.

Quantity Total Time

105 173

125 188

135 222

141 324

149 249

171 318

190 371

204 185

206 250

240 176

255 396

277 226

299 227

335 368

371 490

388 352

392 429

400 411

421 545

439 442

455 588

458 484

480 512

486 422

493 404

506 700

586 592

589 457

665 642

a) Develop a scatter diagram (scatter plot) with quantity as the independent variable. Be sure to

label the graph and the axes.

b) Compute the sample data correlation coefficient. Comment on the form, direction, and the

strength of the relationship.

c) Test for a significance of the positive correlation. Use = 0.05. [Report the hypotheses, t-test

statistic, either the p-value or the test or the critical value, state your decision and conclusion.]

d) Develop the estimated regression equation. Interpret the slope and the y-intercept.

e) Use the estimated regression equation to predict the total time to produce the order of size

240. What is the residual for this observation?

f) Report the standard error of the estimate, . Interpret its value.

g) Report the coefficient of determination. Interpret the meaning of the value.

h) Report a 95% confidence interval for the slope coefficient.

i) Test for a significance of the positive slope. Use = 0.05. [Report the hypotheses, t-test

statistic, either the p-value or the test or the critical value, state your decision and conclusion.]

j) Test for the overall significance of the model. Use = 0.05. [Report the hypotheses, F-test

statistic, either the p-value, state your decision and conclusion.]