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

46

20

29

14

65

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 ofrandomnumbers, there really isnorelationship 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==0.10.

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

Part 1:

Repeat this process 20 timesand send me a table summarizing your results. It should look like this:

Trial #slopecorrelationp-value of slopesignificant?

1-.23-.130.43No

2.05.020.55No

...

20.11.120.25No

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?