Reduction Techniques

Q$\mathrm{.}12\mathrm{.}2$ Consider input data on Table $12\mathrm{.}1$Q on baby weight at birth as dependent variable to be affected by the parameters for each of the class or group in AHC of Q$\mathrm{.}12\mathrm{.}1$ and establish the following trial models: $($i$)$ Linear multiple regression; $($ii$)$ power$-$law model of chapter $5$ and $($iii$)$ Quadratic multiple regression model; and $($iv$)$ compare all the simulated models with respect to goodness of fit, $R^2$ values and mean square error $($MSE$).$

Q$\mathrm{.}12\mathrm{.}3$ Repeat problem $12\mathrm{.}1$ using Principal Component Analysis, PCA; as a factor reduction technique and compare results with AHC.

Q$\mathrm{.}12\mathrm{.}4$ Outline the step by step method of sensitivity analysis application in factor reduction as discussed in Section $12\mathrm{.}3$ using data of Table $5\mathrm{.}12$ for Q$5\mathrm{.}2,$ that is$,$ carry out sensitivity analysis for $x_1$ and $x_2$ and drop the less sensitive of the two independent variables.

Q$\mathrm{.}12\mathrm{.}5$ Repeat Q$\mathrm{.}12\mathrm{.}4$ using input data from Table $9\mathrm{.}13$ for Q$\mathrm{.}9\mathrm{.}6.$ In this case use $S_1$ as dependent variable while $S_2,S_3$ and $S_4$ as independent variables. Arrange the three independent variables in order of most to least sensitivity$.$

Table $12\mathrm{.}1$Q: Input data on mother's physical observations & heavy metals in the blood for exercise $12\mathrm{.}1$

$\backslash$table$[[$ID$,$M$.$A$,$M$.$H$,$M$.$W$,$M$.$BMI,Aq$10$a$,$LBW$,$GA@D$,$GWG$,$Pb$,$Cd$,$Mn$,$Zn$,$Al$,$Cu$],[$M$1,34,1\mathrm{.}53,80,34\mathrm{.}2,5,2,36,11,0\mathrm{.}005,0\mathrm{.}021,0\mathrm{.}058,0\mathrm{.}88,0\mathrm{.}024,0\mathrm{.}86],[$M$2,34,1\mathrm{.}58,81,32\mathrm{.}4,2,2,39,10,0\mathrm{.}005,0\mathrm{.}023,0\mathrm{.}063,0\mathrm{.}94,0\mathrm{.}019,0\mathrm{.}87],[$M$3,30,1\mathrm{.}66,81,29\mathrm{.}4,2,2,40,6,0\mathrm{.}005,0\mathrm{.}019,0\mathrm{.}072,0\mathrm{.}73,0\mathrm{.}022,0\mathrm{.}91],[$M$4,40,1\mathrm{.}7,94,32\mathrm{.}5,4,2,39,4,0\mathrm{.}005,0\mathrm{.}018,0\mathrm{.}033,0\mathrm{.}69,0\mathrm{.}024,0\mathrm{.}88],[$M$5,26,1\mathrm{.}6,80,31\mathrm{.}3,2,2,30,5,0\mathrm{.}005,0\mathrm{.}014,0\mathrm{.}062,0\mathrm{.}79,0\mathrm{.}026,0\mathrm{.}79],[$M$6,20,1\mathrm{.}4,70,35\mathrm{.}7,0,2,40,5,0\mathrm{.}005,0\mathrm{.}016,0\mathrm{.}067,0\mathrm{.}83,0\mathrm{.}021,0\mathrm{.}83],[$M$7,29,1\mathrm{.}58,95,38\mathrm{.}1,1,2,39,10,0\mathrm{.}01,0\mathrm{.}017,0\mathrm{.}068,0\mathrm{.}59,0\mathrm{.}028,0\mathrm{.}84],[$M$8,40,1\mathrm{.}56,85,34\mathrm{.}9,4,2,39,6,0\mathrm{.}01,0\mathrm{.}019,0\mathrm{.}069,0\mathrm{.}64,0\mathrm{.}027,0\mathrm{.}89],[$M$9,33,1\mathrm{.}52,85,36\mathrm{.}8,5,2,38,4,0\mathrm{.}01,0\mathrm{.}021,0\mathrm{.}072,0\mathrm{.}71,0\mathrm{.}024,0\mathrm{.}87],[$M$10,36,1\mathrm{.}56,83,34\mathrm{.}1,5,2,37,4,0\mathrm{.}01,0\mathrm{.}035,0\mathrm{.}059,0\mathrm{.}82,0\mathrm{.}025,0\mathrm{.}91],[$M$11,19,1\mathrm{.}5,65,28\mathrm{.}9,1,2,38,4,0\mathrm{.}005,0\mathrm{.}033,0\mathrm{.}061,0\mathrm{.}95,0\mathrm{.}026,0\mathrm{.}93],[$M$12,34,1\mathrm{.}57,76,30\mathrm{.}8,3,2,40,3,0\mathrm{.}005,0\mathrm{.}038,0\mathrm{.}077,0\mathrm{.}97,0\mathrm{.}024,0\mathrm{.}95],[$M$13,34,1\mathrm{.}56,80,32\mathrm{.}9,3,2,38,13,0\mathrm{.}005,0\mathrm{.}039,0\mathrm{.}078,0\mathrm{.}83,0\mathrm{.}023,0\mathrm{.}84],[$M$14,34,1\mathrm{.}61,96,37\mathrm{.}0,1,2,38,15,0\mathrm{.}005,0\mathrm{.}036,0\mathrm{.}073,1\mathrm{.}11,0\mathrm{.}021,0\mathrm{.}86],[$M$15,36,1\mathrm{.}65,70,25\mathrm{.}7,3,2,38,7,0\mathrm{.}005,0\mathrm{.}035,0\mathrm{.}074,1\mathrm{.}05,0\mathrm{.}022,0\mathrm{.}85]]$