Given the following points in the plane, find the slope of the least squares line: (1, 2), (2, 1), (3, 3), and (5, 13) round your answer to two decimal places, if necessary.
A) 2.94
B) 2.89
C) 2.83
D) 2.77

Question

Quizplus · Accepted Answer

The slope (m) of the least squares line can be calculated using the formula $m = \frac{n(\sum xy) - (\sum x)(\sum y)}{n(\sum x^2) - (\sum x)^2}$, where n is the number of points, $x$ and $y$ are the coordinates of the points. For the given points (1, 2), (2, 1), (3, 3), and (5, 13):- $n = 4$- $\sum x = 1 + 2 + 3 + 5 = 11$- $\sum y = 2 + 1 + 3 + 13 = 19$- $\sum xy = (1\cdot2) + (2\cdot1) + (3\cdot3) + (5\cdot13) = 2 + 2 + 9 + 65 = 78$- $\sum x^2 = (1)^2 + (2)^2 + (3)^2 + (5)^2 = 1 + 4 + 9 + 25 = 39$Plugging these values into the slope formula:$m = \frac{4(78) - (11)(19)}{4(39) - (11)^2} = \frac{312 - 209}{156 - 121} = \frac{103}{35} \approx 2.94$Therefore, the slope of the least squares line, rounded to two decimal places, is approximately 2.94.

Given the Following Points in the Plane, Find the Slope