HW 16 Key

20:31 Wal-Mart.

20:31 a a.Scatterplot. Linear? No. It grows at a growing rate.

20:31 b b. Fit a linear trend. Interpret slope and intercept. Intercept (-379 billion) is extrapolation for time 0. Slope ($190 million) is constant rate of growth.

20:31 c c. Plot the residuals. Random variation or pattern? The data bends, with increasing seasonal variation.

20:31 d d. Scatterplot with log scale for y. Closer to linear but still a bit of a downward bend.

20:31 e e. Fit the equation for log y. Interpret the slope. The intercept of -241 million is extrapolation. Slope of.124 is annual percentage rate of growth.

20:31 f f. What pattern remains? Can you explain what’s happening? Some curvature with seasonal pattern (Q4).

20:31 g g. Which equation offers the better summary? What the basis for your choice? The transformed equation captures overall growth. It is not indicated by a higher r^2 (you can’t compare r^2 when transformed). Instead you should compare the fit of residual plots.

20:37 Cellular Phones in the United States. Cellular (or mobile) phones are everywhere these days, but it has not always been so. These data from CTIA, an organization representing the wireless communications industry, track the number of cellular subscribers in the United States. The data are semiannual, from 1985 through mid

20:37 a a.From what you have observed about the use of cellular telephones, what do you expect the trend in the number of subscribers to look like? I expect subscriptions to shoot exponentially upward with time.

20:37 b b. Create a scatterplot for the number of subscribers on the date of the measurement. Does the trend look as you would have expected? Yes it does.

20:37 c c. Fit a linear equation with the number of subscribers as the response and the date as the explanatory variable. What do the slope and intercept tell you, if you accept this equation’s description of the pattern in the data? The slope 12.7 million tells you that each year 12.7 million more subscribers join. The intercept tells you how many subscribers at 0 years, which doesn’t make sense.

20:37 d d. Create a scatterplot for the same data shown in the scatterplot done in part b, but for this plot, put the response on a log scale. Does the scatterplot suggest that a curve of the form: Estimated log (#subscribers)=b0+b1Date is a good summary? This doesn’t work either, as the graph just curves the other way.

20:37 e e. Create a scatterplot for the percentage change in the number of subscribers versus the year minus Does this plot suggest any problem with the use of the equation of the log of the number of subscribers on the date? What should this plot look like for a log equation as in part d to be a good summary? You would take the log of both according to Tukey’s bulging rule. % change ought to be constant, but in fact decreases.

20:37 f f. Summarize the curve in this scatterplot using a curve of the form: Estimated %age growth = b0+b1 1/(Date-1984) Is this curve a better summary of the pattern of growth in the domestic cellular industry? Yes, this is the most linear yet.

20:37 g g. What’s the interpretation of the estimated intercept b0 in the curve fit in part f? This is the expected growth in 1984, the baseline from which all percentage increases rise. The intercept is the long term rate of growth.

20:37 h h. Use the equation from part f to predict the number of subscribers in the next period. Do you think this will be a better estimate than that offered by the linear equation or logarithmic curve? 5.2% increase, which should be the best given our models.