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.

Question

Camille Burgess

Business

10 August, 19:42

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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Answers (1)

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Kristin Mora · Answer 1

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.