Please have Excel pick a random number between 0 and 9 (with the function =Randbetween (0, 9).

By dragging and copying, create 5 rows of two columns of random numbers. It should look like this, for example (of course everyone's numbers, being random, will be different):

X Y

4 6

2 0

2 9

1 4

6 5

Then ask Excel to run the linear regression between these two columns and generate a p-value for testing the significance of the linear relationship between X and Y. Use a significance level (alpha) of 10%.

Since these are pairs of random numbers, there really is no relationship between X and Y. So if a p-value is less 0.10 that is because a Type I error has occurred. The Probability(of making the Type I error)=alpha=α=0.10.

P(Type I error)=P(rej H0 |H0 is true)=alpha=0.10.

Part 1: Repeat this process 20 times and send me a table summarizing your results. It should look like this:

Trial # slope             correlation        p-value of slope        significant?

 1        -.23               -.13                            0.43                          No

 2         .05                .02                            0.55                           No

...

 20      .11                 .12                            0.25                           No

Part 2: Then, do one last regression simulation, this time using 2000 pairs of random numbers (by dragging the first line down to row 2001). Use Excel to make a graph of the scatter diagram and the straight line that best fits the last set of 2000 pairs. Have Excel calculate the slope, intercept, correlation, p-value.

Report on all your findings and interpret what you saw (among the twenty (20) repeats). The report should answer the following eight questions:

Part 3: How does the number (%) of significant p-values correspond to the theory of a Type I error? 

Part 4: What was the average slope?

Part 5: What was the average intercept?

Part 6: Explain why the numbers from Parts 4 and 5 make sense.

Part 7: How do you explain the results you got for the 2000 pairs? (Discuss the slope, intercept, correlation, p-value.)

Part 8: If there are 100 students doing this assignment (using 2000 pairs) using an alpha (significance level) of 10% how many of the students are expected to report a significant intercept?

Part 9: Calculate the 95% prediction interval of y when x=5 using the 2000 pairs.

Part 10: Explain the result you got in Part 9.  Even though the sample size is so large (2000 pairs) why is the 95% prediction interval so wide and therefore practically useless?