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Global use of cell phones grew rapidly between 1989 and 2000. below is a scatterplot of the percentage of people in the world who are cell phone subscribers versus year for this time interval, along with the residual plot from a linear regression analysis. (a) is a linear model appropriate for these data? justify your answer. (b) below is a scatterplot of the natural logarithm of cell phone subscribers vs. year. this relationship is clearly more linear that the one above. does this suggest that the relationship between cell phone subscribers and year can be modeled by an exponential function or by a power function? explain. (c) computer output from the regression of ln (cell phone subscribers) vs. year is given below. use it to predict the percentage of people in the world who were cell phone subscribers in 2005. (d) comment on the reliability of this prediction.

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Answer:

Explanation:

A)

The regression equation is,

ln(Cell Phone Subscribers) = -820.894 + 0.411704 Year

or,

Percent of Cell Phone Subscribers = exp(--820.894 + 0.411704 Year)

For the year 2005,

Percent of Cell Phone Subscribers = exp(--820.894 + 0.411704 * 2005)

= 96.79%

B)

P-value for the significance of the slope is very low (0.000). Thus, the model is statistically significant and the prediction of the model is highly reliable.

Based on the information given, the linear model is not applicable for this data because the growth rate is increasing at a faster rate (exponential times),

It should be noted that since we are plotting the ln(function) v/s year, hence the relation between these will be an exponential relation

Based on the computer output from the regression given, the percentage will be:

y(2005) = -820.894 + 0.411784(2005) = 4.75%

Lastly, the model is not a feasible model since the exponential function will soon shoot more than 100%, hence the reliability of the model will be compromised.

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