Question

16 multiple choice 1 point the table below shows the number of new subscribers to a streaming service each year since 2015. new subscribers year subscribers (in millions) 2015 4.5 2016 6.1 2017 7.2 2018 9.0 2019 10.3 using a linear line - of - best - fit model, approximately what is the predicted number of new subscribers for the year 2022? 15.9 million 17.1 million 14.7 million 13.0 million

Explanation:

Step1: Assign \(x = 0\) to 2015

Let \(x\) represent the number of years since 2015. So for 2015 (\(x = 0\)), subscribers \(y=4.5\); 2016 (\(x = 1\)), \(y = 6.1\); 2017 (\(x=2\)), \(y = 7.2\); 2018 (\(x = 3\)), \(y=9.0\); 2019 (\(x = 4\)), \(y = 10.3\).

Step2: Calculate the slope \(m\)

The formula for the slope \(m=\frac{n\sum(xy)-\sum x\sum y}{n\sum(x^{2})-(\sum x)^{2}}\), where \(n = 5\).
\(\sum x=0 + 1+2 + 3+4=10\), \(\sum y=4.5+6.1 + 7.2+9.0+10.3=37.1\), \(\sum(xy)=0\times4.5+1\times6.1+2\times7.2+3\times9.0+4\times10.3=0 + 6.1+14.4+27+41.2 = 88.7\), \(\sum(x^{2})=0^{2}+1^{2}+2^{2}+3^{2}+4^{2}=0 + 1+4+9+16 = 30\).
\(m=\frac{5\times88.7-10\times37.1}{5\times30 - 10^{2}}=\frac{443.5-371}{150 - 100}=\frac{72.5}{50}=1.45\).

Step3: Calculate the \(y -\)intercept \(b\)

Using the formula \(b=\frac{\sum y-m\sum x}{n}\), \(b=\frac{37.1-1.45\times10}{5}=\frac{37.1 - 14.5}{5}=\frac{22.6}{5}=4.52\).
The linear equation is \(y = 1.45x+4.52\).

Step4: Predict for 2022

For 2022, \(x=2022 - 2015=7\).
Substitute \(x = 7\) into \(y=1.45x + 4.52\), \(y=1.45\times7+4.52=10.15+4.52=14.67\approx14.7\).

Answer:

14.7 million