Question

2. Course Evaluation data consisted ofn- 32 MBA students for a basic statistics class. From the correlation matrix the following principle components were extracted 2 6 Variable Presentation Ability to stimulate interest Knowledge of material Interest in students Objectivity Overall evaluation of instructor0.5 eigenvalue 0.420.430.49 0.07 0.25 -0.57 0.410.37-0.66-0.25 -0.41-0.20 0.270.55 0.31 -0.67 -0.24 -0.13 0.400.45 0.43 0.12 0.65 0.11 0.41-0.33 0.13 0.67 0.51 0.02 0.26 0.18 0.12 0.15 0.78 3.20 .50 0.550.45 0.22 0.08 a. Interpret as many components as appear to explain appreciable proportions of the total variance, b. Reproduce the correlation matrix from which these principle components were extracted

Answer 1

la) Panipal Componets is bosed on finn whick vaa vartables mpst styorgly corelated with each Component, t'e> which these nurm bess ae Lange e โวา magnitude one needs to deteymine at what level the correlatton is Comsídeied signifrcant. This is a suhjeetve chotce Pci: Hijkly oelated wit "ovea valuatom of %2: Thts #3 highly negatively coyYelated uith knowledge Pc3: Th's ts stnorgly negattvely Coraelated uth abiLt Pck: Ths ts hig^ nejathvely corelated uith knowledge importance. eye a Correlation above 0-5 is vary from Pefson to Peson. instructos Thus thts depends on significant on how the fnstnuct evalvates the yesults. «f Materal . So it behaves inversely to knowlede to Stmulate imterest. of Matejlal and highlh ^ostve for objecthry and Posltfve With mteYest m students. and Positv wit ovefall evalvatton of instnuctox e: This highly nejatvely corvelated wthuenatin fpcb: This s neşa Pci esplains the mazimm vaytance whteh is close 15 hus fr aipose pci and peupfrce

using spect yal decompooftto f a matifx. The 0yia7mal matrix ahỉch yields eigen Valves Hence x can be found fvom the folowmą R Code. X1 = c Co.42,0.41, .24, .40, .41, 51) xu= cCo64,-o.as,-o-6も0-12 , О.6も-o-12 , o·02,0.73) (Xs %#xt(XsD | sum (X5"rs)+0.OS-(X6 ไ.* Xt(xsj the coryelation matix.