Researchers wondered whether the size of a person\'s brain was related to the in

Question

Researchers wondered whether the size of a person's brain was related to the individual's mental capacity. They selected a sample of 3 females and 3 males and measured their MRI counts and IQ scores. The data is reported on the right. Females Males MRI IQ MRI IQ 856 comma 473 141 1 comma 001 comma 121 141 866 comma 664 132 935 comma 493 144 790 comma 620 135 965 comma 355 132 Treat the MRI count as the explanatory variable. Compute the linear correlation coefficient between MRI count and IQ for both the males and the females. Do you believe that MRI count and IQ are linearly related? The linear correlation coefficient for females is nothing . The linear correlation coefficient for males is nothing . (Round to three decimal places as needed.)

Explanation / Answer

We would use the below formula for correlation: -

n(Exy)-(Ex)(Ey)/ÖnEx^2-(Ex)^2* nEy^2-(Ey)^2

Females: -

3(341896041)-(2513757)(408)/ Ö3*2109732473025-(2513757)^2*3*55530-(408)^2

0.0663 (Almost no correlation)

Males: -

3(403295913)-(2901969)(417)/ Ö3*2809300685715-(2901969)^2*3*58041-(417)^2

-0.1895 (Negative correlation)

FEMALES MRI (x) IQ (y) x^2 y^2 xy 856473 141 7.33546E+11 19881 120762693 866664 132 7.51106E+11 17424 114399648 790620 135 6.2508E+11 18225 106733700 2513757 408 2109732473025.00 55530 341896041 MALES MRI (x) IQ (y) x^2 y^2 xy 1001121 141 1.00224E+12 19881 141158061 935493 144 8.75147E+11 20736 134710992 965355 132 9.3191E+11 17424 127426860 2901969 417 2809300685715.00 58041 403295913

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