Question

The following table shows the mean and standard deviation of the marks of Mathematics and Physics scored by the students in a school

	Mathematics	Physics
Mean	$84$	$81$
Standard Deviation	$7$	$4$

The correlation coefficient between the given marks is $0.86$. Estimate the likely marks in Physics if the marks in Mathematics are $92$.

Answer 1

$\overline{x}=84,\overline{y}=81$
${\sigma }_x=7,{\sigma }_y=4$
$r=0.86$
$\therefore b_{yx}=r.\frac{{\sigma }_y}{{\sigma }_x}$
$=0.86\times \frac{4}{7}=0.49$

$\therefore$ Regression equation of y on x

$y-\overline{y}=b_{yx}(x-\overline{x})$
$y-81=0.49(x-84)$
$y-81=0.49x-41.16$
$\Rightarrow y=0.49x+39.84$

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

Hence, the likely marks in Physics are $\mathrm{84.92.}$