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Linear Regression (p-2) — Maths (commerce) STD 12 Commerce / Arts — Question

Maharashtra BoardEnglish MediumSTD 12 Commerce / ArtsMaths (commerce)Linear Regression (p-2)3 Marks
Question
For bivariate data.
$
\bar{x}=53, \bar{x}=28, b_{y x}=-1.2, b_{x y}=-0.3
$
Find,
(i) Correlation coefficient between $\mathrm{X}$ and $\mathrm{Y}$.
(ii) Estimate $Y$ for $X=50$
(iii) Estimate $X$ for $Y=25$
✓

Answer

$
\begin{aligned}
& \text { (i) } r^2=b_{y x} \cdot b_{x y} \\
& r^2=(-1.2)(-0.3) \\
& r^2=0.36 \\
& r= \pm 0.6
\end{aligned}
$
Since, $b_{y x}$ and bxy are negative, $r=-0.6$
(ii) Regression equation of $\mathrm{Y}$ on $\mathrm{X}$ is
$
\begin{aligned}
& (Y-\bar{y})=b_{y x}(X-\bar{x}) \\
& Y-28=-1.2(50-53) \\
& Y-28=-1.2(-3) \\
& Y-28=3.6 \\
& Y=31.6
\end{aligned}
$
(iii) Regression equation of $\mathrm{X}$ on $\mathrm{Y}$ is
$
\begin{aligned}
& (X-\bar{x})=b_{x y}(Y-\bar{y}) \\
& (X-53)=-0.3(25-28) \\
& X-53=-0.3(-3) \\
& X-53=0.9 \\
& X=53.9
\end{aligned}
$

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