Regression Paper: MLB
Within this paper, we will be conducting a hypothesis test to answer the research question of whether the number of wins of a team can be explained linearly by the size of stadium, ERA, and stolen bases. To perform this test we will be using a given data set called Major League Baseball Data along with the Hypothesis test for independent groups. To get the calculations we need, we will input the data received into Mega Stat; the attach Appendixes show the results.
The 5 steps in Hypothesis Testing
Step 1: State the Hypothesis
As stated above this paper will be determining whether or not the number of wins can be determined linearly by the ERA, ...view middle of the document...
We take this information and look at the Appendix F on pg 786 of our text book and it shows the value being 2.98 (Doane & Seward, 2007). This table can also be seen in Appendix A of this paper.
Step 3: Set up the Decision Rule
We are going to test two decision rules in this hypothesis test. The first one would be the p-value approach where we reject the null if p-value is less than .05 (significance level), otherwise do not reject the null.
The second decision rule we are going to verify with the information gathered in this test is if the F value is greater than that of 2.98 we will reject the null hypothesis. By completing both tests we will show a stronger case that the null should be either rejected or accepted.
Step 4: Calculate the test statistic and the p-value
Using the mega stat to calculate our regression analysis we can see that the F- statistic is 9.37. The way we get this manually is by the following equation:
ESS symbolizes the sum of squares due to regression while RSS represents the explained sum of squares due to residual or error and degrees of freedom is denoted by df. So if we take the numbers computed by mega stat to show how to manually obtain the F-score it would be as followed:
F= (1768.197/3) / (1635.803/26) = 589.399/62.916 = 9.368
Finding the p-value manually is something of a challenge so for this paper we will go with the calculation of .002 found by Mega stat. The Mega stat calculations are as follows (the other calculations can be found in Appendix B):
| | | | | | |
ANOVA table | | | | | | |
Source | SS | df | MS | F | p-value | |
Regression | 1,768.19737679 | 3 | 589.39912560 | 9.37 | .0002 | |
Residual | 1,635.80262321 | 26 | 62.91548551 | | | |
Total | 3,404.00000000 | 29 | | | | |
| | | | | | |
Step 5: Draw conclusion
By looking at the p-value, it is safe to say that the null can be rejected seeing .002 is less than .05, which is the first decision rule. We can go further by showing that the F value of 9.37 is greater than that of the critical value of F which we found earlier to be 2.98. This also shows that we should reject the null and go to the alternative hypothesis.
After determining our confidence level and conducting our hypothesis tests, and determining that the p-value is near zero, we have come to the conclusion that we can safely reject the null...