The Graduate Management Admission Test (GMAT) has four sections: analytical writ

Question

The Graduate Management Admission Test (GMAT) has four sections: analytical writing, integrated reasoning, quantitative and verbal sections. Suppose that a researcher collected GMAT score data and calculated the covariance matrix across sections.

Find the pair of two sections that have the largest correlation coefficient.

Integrated reasoning and quantitative

Analytical writing and quantitative

Analytical writing and integrated reasoning

Analytical writing and verbal

Quantitative and verbal

Analytical Writing Integrated Reasoning Quantitative Verbal Analytical Writing 0.81 Integrated Reasoning 0.324 1.44 Quantitative 1.44 2.4 16 Verbal 1.62 0.36 2.4 9

Explanation / Answer

Standard deviation for

a) Analytical writing = sqrt(0.81)=0.9

b) IR = 1.2

c) Quantitative = sqrt(16)=4

d) Verbal = sqrt(9)=3

Correlation coefficient is given by covariance/standard deviationA * Standard deviationB

IR and quantitative = 2.4/(1.2*4) = 0.5

Analytical and quantitative= 0.81/0.9*4 = 0.225

Analytical and IR - 0.324/(0.9*1.2)=0.3

analytical and verbal= 1.62/(3*0.9) =0.6

Quant and verbal = 2.4/(4*3)=0.2

Hence, analytical writing and verbal is the correct answer.

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