Correlation, Outliers & Correlation Coefficients

Q1. For the information given in the table below, calculate the standardized value of a new observation: x = [12.0 0.78 190.2].
a. Does the standardized observation indicate that any of the measured variables may be an outlier (and explain how you know)?

b. If so, which one?

For the remainder of the questions, suppose you have 1000 observations of 6 process variables as predictors. The eigenvalues of the correlation matrix of the data are λ = 4.58, 1.03, 0.21, 0.15, 0.029, and 0.001.

c. What is the condition number of the predictor matrix for linear regression if we include all 6 process variables?

d. What is the minimum regularization parameter (α) needed to have a well-conditioned matrix in ridge regression?

e. If these data are transformed to the PC space, how many PCs will we need to explain at least 95% of the information?

Q2. If the table below gives the correlation coefficients of the six predictors with the output, indicate which variables you would include in a linear regression model and explain why?

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