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
4 17
6 12
8 9
11 4
13 3

a. $y=-22.105x+1.560$
b. $y=1.560x-22.105$
c. $y=-1.560x+22.105$
d. $y=22.105x-1.560$

Explanation:

Step1: Calculate $\sum x, \sum y$

$\sum x = 4+6+8+11+13 = 42$
$\sum y = 17+12+9+4+3 = 45$

Step2: Calculate $\sum xy, \sum x^2$

$\sum xy = (4×17)+(6×12)+(8×9)+(11×4)+(13×3) = 68+72+72+44+39 = 295$
$\sum x^2 = 4^2+6^2+8^2+11^2+13^2 = 16+36+64+121+169 = 406$

Step3: Find slope $m$

Use formula $m=\frac{n\sum xy - \sum x \sum y}{n\sum x^2 - (\sum x)^2}$, $n=5$
$m=\frac{5×295 - 42×45}{5×406 - 42^2}=\frac{1475 - 1890}{2030 - 1764}=\frac{-415}{266}≈-1.560$

Step4: Find y-intercept $b$

Use formula $b=\frac{\sum y - m\sum x}{n}$
$b=\frac{45 - (-1.560)×42}{5}=\frac{45 + 65.52}{5}=\frac{110.52}{5}≈22.105$

Step5: Form line equation

Line form: $y=mx+b$

Answer:

C. $y = -1.560x + 22.105$