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Question: Determine the equation of the regression line and plot the line on the scatter plot for the data.
x28753641
y68415723



A ) y′ = 2.893 + 0.357x ; Graph 1
B ) y′ = 0.357 + 2.893x ; Graph 3
C ) y′ = 2.893 - 0.357x ; Graph 2
D ) y′ = - 0.357 + 2.893x ; Graph 4

Steps to derive

1 Make a table with values for x, y, x2, xy.


2 Regression line equation is y′ = a + bx
a = (Σy)(Σx2)-(Σx)(Σxy)n(Σx2)-(Σx)2
b = n(Σxy)-(Σx)(Σy)n(Σx2)-(Σx)2

3 a = 2.893, b = 0.357
 [Substitute the values and simplify.]

4 Therefore, the equation of the regression line y′ = a + bx is y′ = 2.893 + 0.357x.

5 Draw a scatter plot for the data and plot the line.




Hence the right answer is Option A

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