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Questions: 1. Consider the data given in Activity 3 (task already completed by you titled "Multi Linear Regression - Exercise")(Attached) once again and augment the data by the dummy variable “cooling tower” as given in Table 6 (Attached) 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. Use residual analysis and R2 to check your model.  State which variables are important in predicting the cost of constructing an LWR plant. State a prediction equation that can be used to predict ln(C). Does adding CT improve R2? If so, by what amount? 2. Consider the data in Table 5 (Attached). Evaluate the correlation between the two scores and state if there seems to be any association between the two. Find the probability of upgrading for each division of the sample by the Bayes’ theorem. Find the probability of upgrading for each division of the sample by the naïve version of the Bayes’ theorem. Compare your results in parts b and c and explain the difference or indifference based on observed probabilities.