Intercept when the slope is negative

Question

A line predicts the number of typos per page (y) from hours of proofreading (x). The slope is b = -3, and the averages are \bar{x} = 6, \qquad \bar{y} = 12. Find the intercept.

Accepted Answer

Use the fact that the line passes through the point of averages: a = \bar{y} - b \, \bar{x}. The slope is negative here, so be careful with signs. Subtracting a negative number turns into adding: a = 12 - (-3) 	imes 6 = 12 - (-18) = 12 + 18 = 30. The intercept is 30, and the line is \hat{y} = 30 - 3x. That makes sense: with a downward slope, the line has to start high (at x = 0) and fall as proofreading hours increase. Check: at x = 6, 30 - 3 	imes 6 = 30 - 18 = 12 = \bar{y}. The single most common mistake here is dropping the double negative. Write out -(-3)	imes 6 = +18 explicitly and it…

Intercept when the slope is negative

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