1.Consider the data given in table 4. Augment the data by the dummy variable "cooling tower" as given in Table 6.

a.Build a multiple regression model to predict ln (C) by taking S and N or their natural logarithms, as well as CT, as the independent variables. Make sure to check for multicollinearity.

b.Use residual analysis and R² to check your model.

c.State which variables are important in predicting the cost of constructing an LWR plant.

d.State a prediction equation that can be used to predict ln(C).

e.Does adding CT improve R²? If so, by what amount?

2. Consider the data in Table 5 once more.

a.Evaluate the correlation between the two scores and state if there seems to be any association between the two.

b.Find the probability of upgrading for each division of the sample by the Bayes' theorem.

c.Find the probability of upgrading for each division of the sample by the nave version of the Bayes' theorem.

d.Compare your results in parts b and c and explain the difference or indifference based on observed probabilities.

Please provide your work in detail and include in-text citations.

Results on the Tests Taken by Employees Table 4 Table 6 Group Test Test 2 Cooling Tower Data in Constructing Light Water Reactors 90 85 Data Concerning Construction of Light Water Reactors 96 38 91 81 Plant C Plant S N CT 1 0 95 78 460.05 687 14 2 92 85 2 452.99 1,065 3 93 87 3 443.22 1,065 98 84 652.32 1,065 12 92 5 642.23 1.065 12 6 345.39 514 3 272.37 822 317.21 457 457.12 822 10 690.19 792 11 350.63 560 12 402.59 790 13 412.18 530 14 495.58 1,050 15 394.36 850 16 423.32 778 17 712.27 845 17 18 289.66 530 OOOOOOOOOOOOOOOOOOOOHHHHHHHH HH HH HHHH HH HMM P P HOHHOOHHOHOHOOHOOOOHOOHOOOH 10 881.24 1.090 20 490.88 1,050 8 21 567.79 913 15 22 665.99 828 20 23 621.45 786 18 24 608.8 821 3 25 473.64 538 10 26 697.14 1,130 21 27 207.51 745 8 28 288.48 821 29 284.88 886 11 30 280.36 886 11 31 217.38 745 8 32 32 270.71 886 11