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GATE 2022 CE (CE1) – Question 49

Engineering Mathematics · Probability and Statistics: Random variables, Poisson and Normal distributions, linear regression · 2 marks · Numerical answer

For observations x=(5,2,4,3), y=(16,10,13,12), the fitted model is y=a+bx with a=6.1. Find b (one decimal).

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Correct answer: 1.89 to 1.91

Explanation

A fitted least-squares line passes through $(\bar x,\bar y)$. Here $\bar x=(5+2+4+3)/4=3.5$ and $\bar y=(16+10+13+12)/4=12.75$.

Since a=6.1, $b=(12.75-6.1)/3.5=\mathbf{1.9}$. The covariance-over-variance calculation gives the same slope.