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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 certain bivariate data the following information are available
XY
A.M.1317
S.D.32
Correlation coefficient between x and y is 0.6, estimate x when y = 15 and estimate y when x = 10.
✓

Answer

$\begin{aligned} & \text { Given, } \bar{x}=13, \bar{y}=17, \sigma_{\mathrm{x}}=3, \sigma_{\mathrm{y}}=2, \mathrm{r}=0.6 \\ & \mathrm{~b}_{\mathrm{yx}}=\frac{r \sigma_y}{\sigma_x}=0.6 \times \frac{2}{3}=0.4 \\ & \mathrm{~b}_{\mathrm{xy}}=\frac{r_{\sigma_x}}{\sigma_y}=0.6 \times \frac{3}{2}=0.9 \\ & \text { Regression equation of } \mathrm{Y} \text { on } \mathrm{X} \\ & (\mathrm{Y}-\bar{y})=\mathrm{b}_{\mathrm{yx}}(\mathrm{X}-\bar{x}) \\ & \mathrm{Y}-17=0.4(\mathrm{x}-13) \\ & \mathrm{Y}=0.4 \mathrm{x}+11.8 \\ & \text { When } \mathrm{x}=10 \\ & \mathrm{Y}=0.4(10)+11.8 \\ & =4+11.8 \\ & =15.8 \\ & \text { Regression equation of } \mathrm{X} \text { on } \mathrm{Y} \\ & (\mathrm{X}-\bar{x})=\mathrm{b}_{\mathrm{xy}}(\mathrm{Y}-\bar{y}) \\ & (\mathrm{X}-13)=0.9(\mathrm{y}-17) \\ & \mathrm{X}-13=0.9 \mathrm{y}-15.3 \\ & \mathrm{X}=0.9 \mathrm{y}-2.3 \\ & \text { When } \mathrm{y}=15 \\ & \mathrm{X}=0.9(15)-2.3 \\ & =13.5-2.3 \\ & =11.2\end{aligned}$

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