PSY-520 Graduate Statistics Topic 5– Benchmark – Correlation and Regression Project
PSY-520 Graduate Statistics
Topic 5– Benchmark – Correlation and Regression Project
Directions: Use the following information to complete the questions below. While APA format is not required for the body of this assignment, solid academic writing is expected, and documentation of sources should be presented using APA formatting guidelines, which can be found in the APA Style Guide, located in the Student Success Center.
Player # | Players Age (x) | Batting Averages (y) | XY | X^2 | Y^2 |
1 | 26 | 338 | 8788 | 676 | 14244 |
2 | 24 | 318 | 7632 | 576 | 101124 |
3 | 33 | 318 | 10494 | 1089 | 101124 |
4 | 33 | 316 | 10428 | 1089 | 99856 |
5 | 25 | 315 | 7875 | 625 | 99225 |
6 | 41 | 315 | 12915 | 1681 | 99225 |
7 | 24 | 312 | 7488 | 576 | 97344 |
8 | 29 | 307 | 8903 | 841 | 94249 |
9 | 34 | 304 | 10336 | 1156 | 92416 |
10 | 28 | 302 | 8428 | 784 | 91204 |
11 | 28 | 301 | 8428 | 784 | 90601 |
12 | 37 | 300 | 11100 | 1369 | 90000 |
13 | 34 | 289 | 10132 | 1156 | 88804 |
14 | 32 | 296 | 9472 | 1024 | 87616 |
15 | 39 | 295 | 11505 | 1521 | 87025 |
16 | 24 | 294 | 7056 | 576 | 86436 |
17 | 24 | 294 | 7056 | 576 | 8646 |
18 | 30 | 293 | 8790 | 900 | 85849 |
19 | 38 | 289 | 10982 | 1444 | 83521 |
20 | 34 | 288 | 9792 | 1156 | 82944 |
21 | 36 | 287 | 10332 | 1296 | 82369 |
22 | 32 | 287 | 9184 | 1024 | 82369 |
23 | 33 | 286 | 9438 | 1089 | 81796 |
24 | 31 | 285 | 8835 | 961 | 81225 |
25 | 28 | 284 | 7952 | 784 | 80656 |
26 | 31 | 284 | 8804 | 961 | 80656 |
27 | 29 | 278 | 8062 | 841 | 77284 |
28 | 26 | 276 | 7126 | 676 | 76176 |
29 | 29 | 275 | 7975 | 841 | 75625 |
30 | 22 | 274 | 6028 | 484 | 75076 |
31 | 24 | 274 | 6576 | 576 | 75076 |
32 | 31 | 273 | 8463 | 961 | 74529 |
33 | 23 | 271 | 6233 | 529 | 73441 |
34 | 29 | 271 | 7859 | 841 | 73441 |
35 | 26 | 270 | 7020 | 676 | 72900 |
36 | 29 | 268 | 7772 | 841 | 71824 |
37 | 37 | 268 | 9916 | 1369 | 71824 |
38 | 26 | 267 | 6942 | 676 | 71289 |
39 | 25 | 267 | 6675 | 625 | 71289 |
R=.06 | ∑x=1164 | ∑y=11338 | ∑xy=338870 | ∑x^2=34082 | ∑y^2=3208088 |
Model | B | Std Error | Standardized Coefficients Beta | t | Sig | |
1 Constant | 275.146 | 17.817 | 15.443 | .000 | ||
Age | .522 | .589 | .144 | .885 | .382 |
-The R-value of the linear model represents a correlation of 0.144. This is a low correlation. R square represents the variation of the DV, batting averages. This is a weak correlation of 0.6%.
- Select at least three variables that you believe have a linear relationship.
- Specify which variable is dependent and which are independent.
- Independent variable: MLB baseball player’s ages
- Dependent variable: Batting averages in 2016
- 3rd variable: Player # used to chronologically order players to help eliminate outliers
- Collect the data for these variables and describe your data collection technique and why it was appropriate as well as why the sample size was best.
- -Data was collected through a website that listed the top 2016 MLB baseball players by age and batting average. There were 39 players total which reflected the total top batters in 2016 aside from the total MLB baseball player population.
- Submit the data collected by submitting the SPSS data file with your submission.
- Frequency Table:
- Find the Correlation coefficient for each of the possible pairings of dependent and independent variables and describe the relationship in terms of strength and direction.
- -The constant is the batting average (y). The sig for the DV is 0, and the ID, age is 382 which is Pearson’ correlation coefficient (r). A sig with a small value between 0 and 1, the greater chance the correlation sign similar would be observed.
- Coefficients
- Unstandardized Coefficients
- Find a linear model of the relationship between the three (or more) variables of interest.
Model SummaryModelRR square Adjusted r square Std Error of the estimate 1.873^2.762.749874.779 |
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-A linear correlation is best represented with a regression line (straight). Based upon the data collected, the relationship between ages of MLB players and batting averages is positive, although weak. There is no statistical significance of a strong correlation in the questioned relationship.
- Explain the validity of the model.
Reference
Witte, R. S., & Witte, J. S. (2015). Statistics (10th ed.). Hoboken, NJ: Wiley.
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