1.A plant distills liquid air to produce oxygen, nitrogen, and argon. The percentage of impurity in the oxygen is through to be linearly related to the amount of impurities in the air as measured by the "pollution count" in parts per million (ppm). A sample of plant operating data is shown below: (picture 1)

a.Calculate coefficient correlation between Purity and Pollution and interpret the result.

b.Fit a linear regression model to the data

c.Test for significance of regression.

d.Calculate estimation of variance for regression model.

2.An article in Industrial Quality Control (1956, pp. 5-8) describes an experiment to investigate the effect of glass type and phosphor type on the brightness of a television tube. The response measured is the current necessary (in micro amps) to obtain a specified brightness level. The data are shown in Table. Analyze the data and draw conclusions. (picture 2)

3.A process engineer is trying to improve the life of a cutting tool. He has run a 23 experiment using cutting speed (A), metal hardness (B), and cutting angle (C) as the factors. The data from two replicates are shown in Table (picture 3)

Purity (%) 93.3 92.0 92.4 91.7 94.0 Pollution count (ppm) 1.10 1.45 1.36 1.59 1.08 Purity (%) 93.1 93.2 92.9 92.2 91.3 90.1 Pollution count (ppm) 0.99 0.83 1.22 1.47 1.81 2.03 Replicate Picture 1 Run I II (1) 221 311 325 435 b 354 348 ab 552 472 C 440 453 Phosphor Type ac 406 377 be 605 500 Glass Type 1 2 3 abc 392 419 280 300 290 Picture 3 290 310 285 285 295 290 230 260 220 235 240 225 240 235 230 Picture 2