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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)1 Mark
Question
If for a bivariate data $\bar{x}=10, \bar{y}=12, \mathrm{v}(\mathrm{x})=9, \sigma_{\mathrm{y}}=4$ and $\mathrm{r}=0.6$. Estimate $\mathrm{y}$ when $\mathrm{x}=5$.
✓

Answer

Given, $V(x)=9$
$
\begin{aligned}
& \therefore \sigma_{\mathrm{x}}=3 \\
& \mathrm{~b}_{\mathrm{yx}}=\frac{r \cdot \sigma_y}{\sigma_x} \\
& =0.6 \times \frac{4}{3} \\
& =0.8
\end{aligned}
$
$\therefore$ Regression equation of $\mathrm{Y}$ on $\mathrm{X}$ is
$
\begin{aligned}
& (y-\bar{y})=b_{y x}(x-\bar{x}) \\
& (y-12)=0.8(5-10) \\
& y-12=0.8(-5) \\
& y-12=-4 \\
& y=8
\end{aligned}
$

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