Brain Weight 3.385 0.48 1.35 465 36.33 27.66 14.83 1.04 4.19 0.425 0.101 0.92 1 0.005 0.06 3.5 2 1.7 2547 0.023 187.1 521 0.785 10 3.3 0.2 1.41 529 207 85 0.75 62 6654 3.5 6.8 35 4.05 0.12 0.023 0.01 1.4 250 2.5 55.5 100 52.16 10.55 0.55 60 3.6 4.288 0.28 0.075 0.122 0.048 192 3 160 0.9 1.62 0.104 4.235 Body Weight 44.5 15.5 8.1 423 119.5 115 98.2 5.5 58 6.4 4 5.7 6.6 0.14 1 10.8 12.3 6.3 4603 0.3 419 655 3.5 115 25.6 5 17.5 680 406 325 12.3 1320 5712 3.9 179 56 17 1 0.4 0.25 12.5 490 12.1 175 157 440 179.5 2.4 81 21 39.2 1.9 1.2 3 0.33 180 25 169 2.6 11.4 2.5 50.4 Question: Is there a correlation between brain weight and body weight across mammalian species? References: Spaeth, H. (1991). Mathematical algorithms for linear regression. New York, NY: Academic Press. Weisberg, S. (1980). Applied linear regression. New York, NY: John Wiley & Sons. Water Temperature 25 Length of Fish 620 25 25 25 25 25 25 25 25 25 25 27 27 27 27 27 27 27 27 27 27 27 29 29 29 29 29 29 29 29 29 29 29 31 31 31 31 31 31 31 31 31 31 31 1315 2120 2600 3110 3535 3935 4465 4530 4570 4600 625 1215 2110 2805 3255 4015 4315 4495 4535 4600 4600 590 1305 2140 2890 3920 3920 4515 4520 4525 4565 4566 590 1205 1915 2140 2710 3020 3030 3040 3180 3257 3214 Question: Is there a correlation between water temperature and the length that fish grow to? Age 39 47 45 47 65 46 67 42 67 56 64 56 59 34 42 48 45 17 20 19 36 50 39 21 44 53 63 29 25 69 Systolic Blood Pressure 144 220 138 145 162 142 170 124 158 154 162 150 140 110 128 130 135 114 116 124 136 142 120 120 160 158 144 130 125 175 Question: Is there a correlation between age and systolic blood pressure? Chirps/Second 20 16 19.8 18.4 17.1 15.5 14.7 15.7 15.4 16.3 15 17.2 16 17 14.4 Temperature (F) 88.6 71.6 93.3 84.3 80.6 75.2 69.7 71.6 69.4 83.3 79.6 82.6 80.6 83.5 76.3 Question: Is there a correlation between the number of times a cricket chirps per second and air temperature? 100 90 f(x) = 3.4103229995x + 22.8489823081 R = 0.6922946529 80 70 60 Column B Linear (Column B) 50 40 30 20 10 0 14 15 16 17 18 19 20 21 Assignment 2: Testing for Correlation by Linear Regression The goal of many studies is to determine if there is a relationship between factors. In other words, does one factor influence the outcome of another factor? If there is a relationship between the factors, then there is a correlation. Through this module's lectures and readings, you will know that finding a correlation does not necessarily mean that you have found a causal relationship. This would need to be determined by another layer of investigation. Indeed, many times correlation does not always lead to the determination of causation, but it can help to identify if there is not a causal relationship between the variables in the study. One way to determine correlation is to see if there is a linear relationship between the factors. A linear relationship can be tested by graphing a scatter plot of the data in the study and seeing if a best-fit line can be drawn to represent this data. This method of analysis is called linear regression. The formulas for linear regression are cumbersome, but luckily, most spreadsheets have built-in functions for performing these tedious calculations. In this assignment, you will use a spreadsheet to examine pairs of variables, using the method of linear regressions, to determine if there is any correlation between the variables. Afterwards, postulate whether this correlation reveals a causal relationshipwhy or why not? Directions: Click here to open the Excel spreadsheet containing the data for this assignment. Notice that there are several tabs on the spreadsheet, each containing a different set of data from different studies. On each of these sample tabs, you will also find the question that was explored in that study. Select the data set that you find interesting, and perform the analysis below. You are only required to perform this analysis on one set of data. There is a tab labeled Example where you can see how your analysis should look when done. In the Excel spreadsheet, perform the following operations: 1. Save the spreadsheet on your computer. 2. Select the study data you want to use. With your mouse, highlight all of the data on the spreadsheet in columns A and B. 3. In the tabs at the top of the page, click Insert. 4. In the Insert ribbon, in the Charts section, click Scatter. Be sure to select the option where it will just plot dots, it will be called Scatter with only Markers. If you do this right, then you will see a chart on the page. 5. Now, on the chart, right-click on one of the data points (dots). Just pick a dot somewhere near the middle of the distribution. 6. Select Add Trendline from the drop-down menu that appears when you right-click on a dot. 7. A new menu will appear. Select Linear, select Automatic, and click the box next to Display R-squared value on chart. 8. Click Close. 9. Now, you should see a line drawn through the dots. It will roughly cut through the middle of the dot distribution. 10. You will also see the R2 value displayed next to the line. In a Word document, respond to the following: 1. What was the sample you selected and the question that was explored in the study? 2. What was the R2 linear correlation coefficient and the linear regression equation produced in the Excel spreadsheet? 3. What would be the value of Pearson's R? 4. Would Pearson's R be positive or negative? What does this imply about the relationship between the factors in this study? 5. What is the implication of any correlation found between the variables in the study you picked? 6. Does this correlation imply a causal relationship? Explain. 7. Were there other variables that you think should have been examined? How would have those variables improved the correlation results of this study or helped to pinpoint where the factors were causal? For this assignment, submit a summary of your responses to the questions above in a 1-2-page Word document. Apply APA standards to citation of sources. Name your Word document as follows: LastnameFirstInitial_M3_A2.doc. Submit it to the M3: Assignment 2 Dropbox by Wednesday, July 8, 2015. Grading Criteria and Rubric Assignment 2 Grading Criteria Identified the selected sample and question that was explored in the study. Identified the R2 linear correlation coefficient and the linear regression equation produced in the Excel spreadsheet. Determined the value of Pearson's R. Determined if Pearson's R is positive or negative, and what it implied about the relationship between the factors in the study. Determined the implication of a correlation between the variables in the study. Explained whether the correlation was an implied causal relationship. Determined if other variables should have been examined. Explained how those variables would have improved the correlation results of the study or helped to pinpoint where the factors were causal. Wrote in a clear, concise, and organized manner; demonstrated ethical scholarship in accurate representation Maximum Points 12 12 12 12 12 20 20 and attribution of sources; displayed accurate spelling, grammar, and punctuation. Total: 100