Statistics Question

Question

The data below represents the number of hits on your web site over 10 months. 

x 1 2. 3. 4 5. 6. 7. 8. 9. 10

y 22. 39 70. 126. 227. 408. 735. 1322. 2380. 4285

1. Use your answers from parts a and b to find an exponential model and a power model to represent this data by hand.
2. Use the regression feature on your calculator to find an exponential model and a power model to represent this data.
3. Use your answer from parts c and d to make the best estimate for the number of hits your web site will have in 12 months.

Answer 1

1. You need to plot for exponential model, x vs. log(y), and for the power model, log(x) vs log(y). In this case, log is the natural log.
2. For the exponential, note that since you're plotting x vs. log(y), the calculator will give you a relation for log(y) = a*x + b, so what you do is raise each side to the power of e, giving you which is your exponential model.

Then for your polynomial power model, you have log(y) = a*log(x) + b from the calculator, so your model is given by

3. So for 12 months, use the model for which the regression produces the best correlation value "r", and plug in 12 for x.