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Answer the following on regression and correlation.
Given that the observations are (9,-4), (10, -3), (11,-1), (13,1), (14,3), (15,5), (16,8), find the…
Given that the observations are $(9,-4), (10, -3), (11,-1), (13,1), (14,3), (15,5), (16,8)$, find the two lines of regression. Estimate the value of $y$ when $x = 13.5$.
Answer
Answer
Mean of x: 88/7
Mean of y: 9/7
Regression coefficient of y on x: 475/292
Regression coefficient of x on y: 475/794
Line of y on x: y = (475/292)x - 1399/73
Line of x on y: x = (475/794)y + 9371/794
Estimate: y = 1633/584 when x = 13.5
$n = 7$, $\bar{x} = \frac{88}{7}$, $\bar{y} = \frac{9}{7}$.
$b_{yx} = \frac{475}{292} \approx 1.627$, $b_{xy} = \frac{475}{794} \approx 0.598$.
Line of $y$ on $x$: $y - \frac{9}{7} = \frac{475}{292}\left(x - \frac{88}{7}\right)$, i.e. $y = \frac{475}{292}x - \frac{1399}{73}$.
Line of $x$ on $y$: $x = \frac{475}{794}y + \frac{9371}{794}$.
At $x = 13.5$: $y = \frac{475}{292}(13.5) - \frac{1399}{73} = \frac{1633}{584} \approx 2.80$.
Hence the estimated $y$ is $\approx 2.80$.