Question

what is the equation of the line of best fit for the following data? round the slope and y-intercept of the line to three decimal places.

x	y
7	7
10	12
12	14
13	18

a. $y=-1.526x+1.383$
b. $y=-1.526x-1.383$
c. $y=1.383x-1.526$
d. $y=1.383x+1.526$

Explanation:

Step1: Calculate $\sum x, \sum y, \sum xy, \sum x^2$

First, list the data points: $(4,5), (7,7), (10,12), (12,14), (13,18)$
$\sum x = 4+7+10+12+13 = 46$
$\sum y = 5+7+12+14+18 = 56$
$\sum xy = (4×5)+(7×7)+(10×12)+(12×14)+(13×18) = 20+49+120+168+234 = 591$
$\sum x^2 = 4^2+7^2+10^2+12^2+13^2 = 16+49+100+144+169 = 478$
$n=5$ (number of data points)

Step2: Compute slope $m$

Use formula $m=\frac{n\sum xy - \sum x \sum y}{n\sum x^2 - (\sum x)^2}$

$$\begin{align*} m&=\frac{5×591 - 46×56}{5×478 - 46^2}\\ &=\frac{2955 - 2576}{2390 - 2116}\\ &=\frac{379}{274}\\ &\approx1.383 \end{align*}$$

Step3: Compute y-intercept $b$

Use formula $b=\frac{\sum y - m\sum x}{n}$

$$\begin{align*} b&=\frac{56 - 1.383×46}{5}\\ &=\frac{56 - 63.618}{5}\\ &=\frac{-7.618}{5}\\ &\approx-1.526 \end{align*}$$

Step4: Form line equation

Line of best fit is $y=mx+b$

Answer:

C. $y = 1.383x - 1.526$