Please explain steps to solution:

For Upper Mahanadi Basin, the mean monthly rainfall, air temperature, precipitable water, pressure, geo-potential height at 925 mb and wind speed at 925 mb are presented for the year 1971

How many principal components are enough for explaining 90% of total variance of the data set? (Ans. The first principal component explains 97% of variability.)

Month Precipitation (mm) Air Precipitable Pressure (mb) Geo-potential Wind Temperature water (kg/m) height (m) speed (C) (m/s) 20.1 18.65 962.88 788.11 33.98 22.61 17.81 960.73 770.48 27.96 26.52 14.9 961.25 778.71 22.81 1 9.51 2 15.42 3 8.72 4 29.55 31.5 24.61 955.72 731.13 17.91 5 36.77 33.25 29.84 953.51 712.47 12.12 6 375.43 26.94 50.06 950.38 678.67 11.82 7 331.02 24.52 950.7 681.07 13.80 52.71 50.57 8 312.48 23.84 952.33 695.3 13.32 9 103.19 23.9 955.3 9.26 44.11 38.7 10 104.47 0.54 22.43 20.06 959.04 964.97 722.38 755.85 806.14 797.28 11 15.81 2.21 22.69 23.47 12 0.00 19.11 11.15 964 Calculate the principal components for the data set. How many principal components are enough for explaining 95% of total variance of the data set? [Marks 8] Month Precipitation (mm) Air Precipitable Pressure (mb) Geo-potential Wind Temperature water (kg/m) height (m) speed (C) (m/s) 20.1 18.65 962.88 788.11 33.98 22.61 17.81 960.73 770.48 27.96 26.52 14.9 961.25 778.71 22.81 1 9.51 2 15.42 3 8.72 4 29.55 31.5 24.61 955.72 731.13 17.91 5 36.77 33.25 29.84 953.51 712.47 12.12 6 375.43 26.94 50.06 950.38 678.67 11.82 7 331.02 24.52 950.7 681.07 13.80 52.71 50.57 8 312.48 23.84 952.33 695.3 13.32 9 103.19 23.9 955.3 9.26 44.11 38.7 10 104.47 0.54 22.43 20.06 959.04 964.97 722.38 755.85 806.14 797.28 11 15.81 2.21 22.69 23.47 12 0.00 19.11 11.15 964 Calculate the principal components for the data set. How many principal components are enough for explaining 95% of total variance of the data set? [Marks 8]