Using $\bar x=3$, $\bar y=4$, $b_{yx}=0.6$ and $b_{xy}=1.0$ from Worked Example 4, write down the two regression line equations and verify that they intersect at $(\bar x,\bar y)$.

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**Step 1 — Write the regression line of $y$ on $x$.** $y-\bar y = b_{yx}(x-\bar x) \Rightarrow y-4 = 0.6(x-3) \Rightarrow y = 0.6x-1.8+4 = 0.6x+2.2$.

**Step 2 — Write the regression line of $x$ on $y$.** $x-\bar x = b_{xy}(y-\bar y) \Rightarrow x-3 = 1.0(y-4) \Rightarrow x=y-1$, which rearranges to $y=x+1$.

**Step 3 — Solve the two equations simultaneously.** Setting the two expressions for $y$ equal: $0.6x+2.2 = x+1 \Rightarrow 2.2-1 = x-0.6x \Rightarrow 1.2=0.4x \Rightarrow x=3$. Substituting back: $y=x+1=3+1=4$.

**Step 4 — Confirm this matches the known means.** The intersection point, $(3,4)$, is exactly $(\bar x,\bar y)=(3,4)$ — confirming, as the theory predicts, that both regression lines pass through the point of means. …

Q.Using $\bar x=3$ , $\bar y=4$ , $b_{yx}=0.6$ and $b_{xy}=1.0$ from Worked Example 4, write down the two regression line equations and verify that they intersect at $(\bar x,\bar y)$ .

Concept understanding — Regression Lines and Their Point of Intersection

Q.Using xˉ=3\bar x=3xˉ=3, yˉ=4\bar y=4yˉ​=4, byx=0.6b_{yx}=0.6byx​=0.6 and bxy=1.0b_{xy}=1.0bxy​=1.0 from Worked Example 4, write down the two regression line equations and verify that they intersect at (xˉ,yˉ)(\bar x,\bar y)(xˉ,yˉ​).

Concept understanding — Regression Lines and Their Point of Intersection

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Q.Using $\bar x=3$ , $\bar y=4$ , $b_{yx}=0.6$ and $b_{xy}=1.0$ from Worked Example 4, write down the two regression line equations and verify that they intersect at $(\bar x,\bar y)$ .

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