Introduction to Statistical Methods and Econometrics — Economics STD 12 — Question
Tamilnadu BoardEnglish MediumSTD 12EconomicsIntroduction to Statistical Methods and Econometrics5 Marks
Question
Explain Fit the Regression equation on [X on Y]?
✓
Answer
Fit regression equation $X$ on $Y$ and $Y$ on $X$ for the following data.
$\bar{X}=12, \bar{Y}=10, \sigma y =0.2, \sigma x =0.1 \text { and } r =0.85$
Solution:
The regression $X$ on $Y$ is
$( X -\bar{X}) r = r \times \frac{\sigma x}{\sigma y} \times( X -\bar{X})$
Given $\bar{X}=12, \bar{Y}=10$
$r=0.85, \sigma x=0.1 \text { and } \sigma y=0.2$
Then substituting the values in formula
$(X-12)=0.85 \times(0.1 / 0.2) \times(Y-10)$
$(X-12)=0.85 \times(0.5) \times(Y-10)$
$X=0.425 \times(Y-10)+12$
$X=0.425 Y-4.25+12$
$X=0.425 Y+7.75$
$Y \text { on } X$
$Y=0.425 Y+7.75$
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