Question

The following table shows the number of subscribers of a cable company for recent years.

Years	2013	2014	2015	2016	2017
Subscribers in thousands	26	36	45	115	135

a) Find the correlation coefficient for the recorded data of subscriptions.

b) Predict the number of subscribers for the year 2018.

Answer 1

Question (a)

The regression output is as follow

Subscribers SUMMARY OUTPUT Years 2013 26 2014 36 2015 45 2016 115 Regression Statistics Multiple R 0.94121282 R Square 0.885881573 Adjusted R Square 0.847842098 Standard Error 19.46192865 Observations 5 2017 135 ANOVA df SS MS F Significance F 0.016958626 1 8820.9 8820.9 23.28848015 Regression Residual Total 3 378.7666667 1136.3 9957.2 4 Coefficients t Stat Lower 95% Intercept Years -59774.1 29.7 Standard Error 12401.12352 6.154402218 -4.82005521 4.825813937 P-value 0.017013872 0.016958626 -99240.00974 10.1139454 Upper 95% -20308.19026 49.2860546

The correlation coefficient is the Multiple R value from the regression statistic section in the above output

so correlation coefficient = 0.941213 rounded to 6 decimal places

Question (b)

The regression equation is

$\hat{y}$ = 29.7 * x + (-59774.1)

Where $\hat{y}$ is the predicted number of subsribers

and x is the year

Given x = 2018

$\hat{y}$ = 29.7 * 2018 + (-59774.1)

$\hat{y}$ = 59934.6 - 59774.1

$\hat{y}$ = 160.5

So the predicted number of subscribers for the year 2018 = 160.5

= 161 rouded up to nearest integer