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Fit a straight line to the following data with x as independent variable.
x 1965 1966 1967 1968 1969
y 125 140 165 195 200
straight line • 1.6k  views
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x $X_i$ $Y_i$ $X_i^2$ $X_iY_i$
1965 -2 125 4 -250
1966 -1 140 1 -140
1967 0 165 0 0
1968 1 195 1 195
1969 2 200 4 400
N=5 $\sum X_i=0$ $\sum Y_i = 825$ $\sum X_i^2=10$ $\sum X_iY_i=205$

The equations are:-

$\sum Y_i \;=\; Na + b \sum X_i \; \; \therefore 825=5a+b(0) \; \; a \;=\; \dfrac{825}{5} = 165 \\ \; \\ \; \\ \sum X_i Y_i \;=\; a \sum X_i + b \sum X_i^2 \\ \; \\ \; \\ \; \; \; \therefore 205=0a+10b \; \; \; \therefore b\;=\; \dfrac{205}{10} \;=\; 20.5$

The equation of straight line is $y=a+bX$

$\\ \; \\ \; \\ \therefore y=165+20.5X \; \; \; where X=x-1967$

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