3. Followings are information taken from a principal component analysis based on correlation matrix for random...

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3. Followings are information taken from a principal component analysis based on correlation matrix for random variables of ozone, radiation, temperature and wind speed at 11 observation stations. Mean: Variance: x' = (3.25, 184.80, 77.79, 9.94) s = (0.7928, 8308.74, 90.82, 12.67) Eigen values: = ' (2.416, 0.889, 0.482, 0.211) Correlation matrix: R = 1.000 0.422 0.422 1.000 0.753 0.294 -0.599 -0.127 -0.497 1.000 0.753 -0.599 0.294 -0.127 1.000 -0.497 Eigen vector matrix: G = -0.596 0.009 0.154 0.788 -0.335 -0.872 -0.307 -0.183 -0.553 0.107 0.624 -0.541 0.476 -0.479 0.702 0.228 (a) Determine equation for first principal component and its proportion of variation. (b) Is the principal component analysis based on correlation matrix reasonable? Give reason. (c) List out variation for each random variable that contributes to the first principal component. Give interpretation. (d) If only the first principal component is used for further analysis, determine residuals for correlation matrix (difference between correlation matrix of data and correlation matrix estimated based on first principal component). 3. Followings are information taken from a principal component analysis based on correlation matrix for random variables of ozone, radiation, temperature and wind speed at 11 observation stations. Mean: Variance: x' = (3.25, 184.80, 77.79, 9.94) s = (0.7928, 8308.74, 90.82, 12.67) Eigen values: = ' (2.416, 0.889, 0.482, 0.211) Correlation matrix: R = 1.000 0.422 0.422 1.000 0.753 0.294 -0.599 -0.127 -0.497 1.000 0.753 -0.599 0.294 -0.127 1.000 -0.497 Eigen vector matrix: G = -0.596 0.009 0.154 0.788 -0.335 -0.872 -0.307 -0.183 -0.553 0.107 0.624 -0.541 0.476 -0.479 0.702 0.228 (a) Determine equation for first principal component and its proportion of variation. (b) Is the principal component analysis based on correlation matrix reasonable? Give reason. (c) List out variation for each random variable that contributes to the first principal component. Give interpretation. (d) If only the first principal component is used for further analysis, determine residuals for correlation matrix (difference between correlation matrix of data and correlation matrix estimated based on first principal component).