"This is too strange," is the thought that runs through your mind. The Harry Hines Medical Center's (HHMC) Board of Directors just informed you that it wants you to evaluate HHMC's managed care plan for professional astrologers. Apparently, the board thinks that the number of patient days used by astrologers in the plan might be influenced by the number of sunspots in a given month & wants you to investigate this question. The board collected the following eight months of data:
|
Month
|
Number of Sunspots
|
Patient Days
|
|
Jan
|
12
|
781
|
|
Feb
|
31
|
758
|
|
Mar
|
23
|
1,033
|
|
Apr
|
36
|
998
|
|
May
|
55
|
1,593
|
|
Jun
|
42
|
1,223
|
|
Jul
|
18
|
1,322
|
|
Aug
|
33
|
1,190
|
Returning to the office, you put the data into a MS-Excel spreadsheet and regress Patient Days (the dependent variable) on Number of Sunspots (the independent variable).
However, just as you start printing the results a power surge occurs -- somehow you suspected this might happen -- and you get the following (somewhat) garbled printout.
[A] Calculate the missing R-square statistic.
[B] What is the value of the correlation coefficient between sunspots & astrologer patient days?
[C] Calculate the missing t-statistic on the output for the coefficient of sunspots.
[D] Suppose the two-tail p-value = 0.105 for the t-statistic in the prior question. Using a Type-I error rate of 5%, is the coefficient of sunspots significantly different from zero?
(a) Explain your answer to part 'h' above using a picture.
(b) Calculate the missing F-Ratio.
[E] Assume that the F-Ratio = 5.99 in the prior question. Use the F-table in the back of the ook to find the upper the one-tail p-value?
a) Write the regression equation.
[E] What does the regression equation predict for the number of astrologer patient days given that the number sunspots is expected to be 40?
[F] What does the regression equation predict for the number of patient days given the number sunspots is zero? Explain why this is, or is not, a reasonable prediction.
[G] In the prior question, assume the missing t-statistic = 2.0 for the coefficient of sunspots. Use a t-test with df = 6 to test the null hypothesis that the coefficient is zero using a Type-I error rate of 5% (i.e., alpha = 0.05). Show all parts of the test & state your conclusion.