Question

For this exercise, round all regression parameters to three decimal places.

The following table shows the number, in millions, of cell phone subscribers C in the United States at the end of the given year t.

Year	Subscribers (millions)
2010	296.3
2011	316
2012	326.5
2013	335.6
2014	355.4

(a) Plot the data points. (Let t be years since 2010 and C be the number of cell phone subscribers, in millions.)

(b) Use exponential regression to construct an exponential model for the subscriber data. (Let t be years since 2010 and C be the number of cell phone subscribers, in millions.)

C = 294.404 × 1.031^t

C = 301.243 × 1.035^t

    

C = 298.914 × 1.043^t

C = 288.712 × 1.043^t

C = 304.289 × 1.041^t

(c) Add the graph of the exponential model to the plot in part (a).

(d) What was the yearly percentage growth rate from the end of 2010 through the end of 2014 for cell phone subscribership? (Use the model found in part (b). Round your answer to one decimal place.)
%

(e) In 2014 an executive had a plan that could make money for the company, provided that there would be at least 380 million cell phone subscribers by the end of 2016. Solely on the basis of an exponential model for the data in the table, would it be reasonable for the executive to implement the plan? (Use the model found in part (b).)

Yes, the model predicts at least 380 million.No, the model predicts less than 380 million.    

Answer 1

(a) To plot the data points we will use R software.

R software codes

>t=c(2010,2011,2012,2013,2014)

>C=c(296.3,316,326.5,335.6,355.4)

>plot(t,C, xlab="Year",ylab="Number of cellphone subscribers(in million)", col="red")

Data vectors t and C are created respectively for Year and Number of cellphone subscribers (in million). plot() function is used to plot the data points.

R software output

Observe the above plot. All the points are scattered around the straight line which indicates that there is a strong positive linear relationship between Year and Number of cellphone subscribers i.e. Number of cellphone subscribers increase as the year increases from 2010 to 2014.

Please note that, as per the HOMEWORKLIB RULES I can solve only one part. Please post remaining part as a seperate question so that we can help you.

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