Question

find the equation for the least squares regression line of the data described below. victoria is a pr agent for an up-and-coming band. she wants to convince the band members that being active on social media is good for their careers. she claims that a large social media following typically translates into ticket sales. to prove her point, victoria looked up information about several successful bands. she compared the number of social media followers (in millions), x, to the average number of hours it takes these bands to sell out a concert, y. followers (in millions) hours 1.0 37 2.0 69 3.5 59 5.5 41 9.6 16 round your answers to the nearest thousandth. y = x +

Explanation:

Step1: Calculate sums for regression

$n=5$, $\sum x = 1.0 + 2.0 +3.5 +5.5 +9.6 = 21.6$, $\sum y = 37 +69 +59 +41 +16 = 222$,
$\sum xy = (1.0*37)+(2.0*69)+(3.5*59)+(5.5*41)+(9.6*16) = 37 +138 +206.5 +225.5 +153.6 = 760.6$,
$\sum x^2 = 1.0^2 +2.0^2 +3.5^2 +5.5^2 +9.6^2 =1 +4 +12.25 +30.25 +92.16 = 139.66$

Step2: Compute slope $m$

$$ m = \frac{n\sum xy - \sum x \sum y}{n\sum x^2 - (\sum x)^2} = \frac{5*760.6 - 21.6*222}{5*139.66 - (21.6)^2} = \frac{3803 - 4795.2}{698.3 - 466.56} = \frac{-992.2}{231.74} \approx -4.281 $$

Step3: Compute intercept $b$

$$ b = \frac{\sum y - m\sum x}{n} = \frac{222 - (-4.281*21.6)}{5} = \frac{222 + 92.47}{5} = \frac{314.47}{5} \approx 62.894 $$

Answer:

$y = -4.281x + 62.894$