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Question

The following table shows the mean and standard deviation of the marks of Mathematics and Physics scored by the students in a school
MathematicsPhysics
Mean8481
Standard Deviation74
The correlation coefficient between the given marks is 0.86. Estimate the likely marks in Physics if the marks in Mathematics are 92.

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Solution

¯¯¯x=84,¯¯¯y=81
σx=7,σy=4
r=0.86
byx=r.σyσx
=0.86×47=0.49

Regression equation of y on x

y¯¯¯y=byx(x¯¯¯x)
y81=0.49(x84)
y81=0.49x41.16
y=0.49x+39.84

Putting x=92,
y=45.08+39.84=84.92

Hence, the likely marks in Physics are 84.92.

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