Question

the domain of the data given is the number of rainy days each year in a town from 2010 to 2022. the range of the data given is the number of inches of rain that fell each corresponding year.

x	102	126	115	103	114	107	125	125	118	95	95	59	105
y	32.3	49.5	60.3	55.1	52.5	79.2	56.9	77.1	41.2	43.1	51.9	25.4	47.0

perform a linear regression on the data and write the equation for the line of best fit. round your values to the nearest thousandth.
$y = \square x + \square$

Explanation:

Step1: Define variables and count data

Let $x$ = number of rainy days, $y$ = rainfall inches.
Sample size $n = 15$

Step2: Calculate sum values

Compute required sums:
$\sum x = 102+126+115+103+114+107+125+125+118+95+95+59+105 = 1489$
$\sum y = 32.3+49.5+60.3+55.1+52.5+79.2+56.9+77.1+41.2+43.1+51.9+25.4+47.0 = 671.5$
$\sum xy = (102×32.3)+(126×49.5)+...+(105×47.0) = 70132.6$
$\sum x^2 = 102^2+126^2+...+105^2 = 153061$

Step3: Compute slope ($m$)

Use slope formula:
$m = \frac{n\sum xy - \sum x \sum y}{n\sum x^2 - (\sum x)^2}$
$m = \frac{15×70132.6 - 1489×671.5}{15×153061 - 1489^2}$
$m = \frac{1051989 - 1000863.5}{2295915 - 2217121} = \frac{51125.5}{78794} ≈ 0.649$

Step4: Compute y-intercept ($b$)

Use intercept formula:
$b = \frac{\sum y - m\sum x}{n}$
$b = \frac{671.5 - 0.649×1489}{15}$
$b = \frac{671.5 - 966.361}{15} = \frac{-294.861}{15} ≈ -19.657$

Answer:

$\hat{y} = 0.649x + (-19.657)$