Q.The fitted regression line of Y on X is $\hat{y} = 23.2 - 1.2x$ and one of the observations used in fitting of the line is $(6, 17)$. Find the error in estimating Y for $X = 6$.

$\hat y(6)=23.2-1.2(6)=16$; error $=y-\hat y=17-16=1$.

The error of estimation (residual) for an observation is $e=y-\hat y$, where $\hat y$ is the value predicted by the regression line. At $x=6$: …

$\hat{y}(6)=23.2-1.2(6)=16$; error $=y-\hat{y}=17-16=\mathbf{1}$.

Given: regression line $\hat{y}=23.2-1.2x$; observed point $(x,y)=(6,17)$.

Step 1 — estimate $Y$ at $X=6$.

$\hat{y}=23.2-1.2(6)=23.2-7.2=16.$

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