Question
Download Solution PDFIt is given that X̅ = 10, Y̅ = 90, σX = 3, σY = 12 and rXY = 0.8. The regression equation of X on Y is
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
Regression equation: Let x and y be two variables, then equation is given as:
\(\frac{{{\rm{x}} - {\rm{\bar x}}}}{{{{\rm{\sigma }}_{\rm{x}}}}} = {\rm{r}}\left[ {\frac{{{\rm{y}} - {\rm{\bar y}}}}{{{{\rm{\sigma }}_{\rm{y}}}}}} \right]\)
Calculation:
Given: x̅ = 10, y̅ = 90, σx = 3, σy = 12 and rxy = 0.8
So, regression equation is given as,
\(\frac{{{\rm{x}} - {\rm{\bar x}}}}{{{{\rm{\sigma }}_{\rm{x}}}}} = {\rm{r}}\left[ {\frac{{{\rm{y}} - {\rm{\bar y}}}}{{{{\rm{\sigma }}_{\rm{y}}}}}} \right]\)
\(\Rightarrow \frac{{{\rm{x}} - 10}}{3} = 0.8\left[ {\frac{{{\rm{y}} - 90}}{{12}}} \right]\)
⇒ x - 10 = 0.2 × {y - 90}
⇒ x = 0.2y - 18 + 10
⇒ x = 0.2y - 8
⇒ X = 0.2Y - 8Last updated on Jun 18, 2025
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