Question

1. a company’s social media manager tracked the length in seconds and the number of likes received for each video. the table shows the data for several videos. a linear function can be used to model this relationship. which function best models the data in the table? a. $y = -277.4x + 84.2$ b. $y = 84.2x - 277.4$ c. $y = 74.4x + 118.6$ d. $y = 118.6x + 74.4$ \

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length of video (seconds)	15	22	41	45	60	35	30	48	\
number of likes	1,235	1,756	2,943	3,266	5,233	2,467	2,111	3,687

Explanation:

Step1: Identify variables

Let $x$ = video length (seconds), $y$ = number of likes.

Step2: Calculate regression slope

Use formula:
$$m=\frac{n\sum xy - \sum x \sum y}{n\sum x^2 - (\sum x)^2}$$
First compute sums:
$\sum x = 15+22+41+45+60+35+30+48 = 296$
$\sum y = 1235+1756+2943+3266+5233+2467+2111+3687 = 22698$
$\sum xy = (15×1235)+(22×1756)+(41×2943)+(45×3266)+(60×5233)+(35×2467)+(30×2111)+(48×3687) = 920093$
$\sum x^2 = 15^2+22^2+41^2+45^2+60^2+35^2+30^2+48^2 = 12274$
$n=8$
Substitute:
$$m=\frac{8×920093 - 296×22698}{8×12274 - 296^2}=\frac{7360744 - 6718608}{98192 - 87616}=\frac{642136}{10576}≈74.4$$

Step3: Calculate regression intercept

Use formula:
$$b=\frac{\sum y - m\sum x}{n}$$
Substitute values:
$$b=\frac{22698 - 74.4×296}{8}=\frac{22698 - 22022.4}{8}=\frac{675.6}{8}≈118.6$$

Step4: Form linear function

Combine slope and intercept: $y=mx+b$

Answer:

C. $y = 74.4x + 118.6$