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GATE 2023 EE – Question 35

Engineering Mathematics · Probability and Statistics: Sampling theorems, Mean, Median, Mode, Standard Deviation, Discrete and Continuous distributions, Correlation and Regression analysis · 1 mark · Numerical answer

Three points in the $x$-$y$ plane are $(-1,0.8)$, $(0,2.2)$ and $(1,2.8)$. The value of the slope of the best fit straight line in the least square sense is _____________ (Round off to 2 decimal places).

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Correct answer: 0.99 to 1.01

Explanation

The mean of $x$ is 0 and the mean of $y$ is 1.933. Slope $=\dfrac{\sum(x-\bar x)(y-\bar y)}{\sum(x-\bar x)^2}=\dfrac{\sum xy}{\sum x^2}=\dfrac{-0.8+0+2.8}{2}=1.00$.