Linear Regression
Examine pairs of variables, using the method of linear regression, to determine if there is any correlation between the variables. Afterwards, you will postulate whether this correlation reveals a causal relationship (and why).
Click here to open the Excel spreadsheet containing the data for this assignment.
This spreadsheet contains the data from a study that attempted to see if there is a correlation between the hours that students studied and the grade that they earned on a test. The correlation test you are about to run will help you to determine if there is, in fact, a correlation between study time and test score. If you find a strong correlation, then you will postulate whether you feel this indicates a causal relationship.
In the Excel spreadsheet, perform the following operations:
1. Save the spreadsheet to your computer.
2. 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''''ll 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 boxes next to Display Equation on chart and 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''''ll also see the linear regression equation and r2 value displayed next to the line.
To see an example spreadsheet containing a completed analysis click here.
Now that you've completed your analysis and determined the linear regression formula and r2, it is now time to report on the results of your study and examine your findings.
In a Microsoft Word document, respond to the following:
1. Report the sample you selected and the question that was explored in the study.
2. Report 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 (simply the square root of r2)?
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. Are there other variables that you think should have been examined that would have improved this study or helped to pinpoint what factors are causal?
Explain the implication of any linear relation, including its three components (scatterplot, r2 value and linear equation) found between hours spent studying, and the exam score earned.