Section II 206 Sample Examination Four subscribers. 2. Every ten years since 192

Question

Section II 206 Sample Examination Four subscribers. 2. Every ten years since 1920, a magazine has announced to the public its number of These numbers are given in the table below. Years since Number of Subscribers 443 1920 1134 9436 1940 20 1950 30 17450 1960 40 15907 91747 77139 1990 2000 80 1178498 A regression analysis is performed using Yeans since 1920 the independent variable and as logarithm function of subscribers as the dependent variable, where log denotes the with base 10. The following computer output and residual plot are obtained. Coef SE Coef

Explanation / Answer

(a)

The R2 value is very close to 1, which means that the model predicts a very strong linear relationship between the two variables.

Also, the residual plot shows that the errors are randomly distributed, which suggests that the model is appropriate.

(b)

The regression equation as visible from the regression result is:

log(number of subscribers) = 0.0315783*(Years since 1920) + 3.364928

(c)

For the year 2030, the value of variable (years since 1920) = 2030-1920 = 110

So, from the regression equation we have:

log(no. of subscribers) = 0.0315783*(110) + 3.364928 = 6.838541

So, number of subscribers = 10^6.838541 = 6895106.84

(d)

This prediction is not valid because it is made outside the valid prediction region by extrapolating the regression line. This is not valid.

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