From data (-4, 1), (-1, 2), (2, 7) and (3, 1), the regression line of y on x is obtained as y=a+bx, then what is the value of 2a+15b?

Explanation

The regression line y = a + bx always passes through the mean point (\bar{x}, \bar{y}). Here, \bar{x} = \frac{-4-1+2+3}{4} = 0 and \bar{y} = \frac{1+2+7+1}{4} = \frac{11}{4}. Substituting these gives \frac{11}{4} = a + b(0) \implies a = \frac{11}{4}. The slope is b = \frac{\sum xy - n\bar{x}\bar{y}}{\sum x^2 - n\bar{x}^2}. We have \sum xy = -4-2+14+3 = 11 and \sum x^2 = 16+1+4+9 = 30, so b = \frac{11}{30}. Thus, 2a + 15b = 2(\frac{11}{4}) + 15(\frac{11}{30}) = \frac{11}{2} + \frac{11}{2} = 11.

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