## Math

Assignment 2: Linear Regression

In this assignment, you will use a spreadsheet to 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).

Clickhere 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 a student studies 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.

Below are instructions on how to perform this correlation test in Microsoft Excel.

In the Excel spreadsheet, perform the following operations:

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, clickInsert.
4.In the Insert ribbon, in the Charts section, clickScatter. Be sure to select the option where it will just plot dots, it will be calledScatter 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.SelectAddTrendline from the drop-down menu that appears when you right-click on a dot.
7.A new menu will appear. SelectLinear, selectAutomatic, and click the boxes next toDisplay Equation on chart andDisplay r-squared value on chart.
8.ClickClose.
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 r2value displayed next to the line.

To see an examplespreadsheet containing a completed analysis clickhere.

Now that you ve completed your analysis and determined the linear regression formula and r2, it 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 help to pinpoint what factors are causal?

For this assignment, you will submit a spreadsheet and a report. The spreadsheet will be the Microsoft Excel file containing yourscatterplot and analysis. Name your Microsoft Excel file as follows: LastnameFirstInitial_M3_A2.xls.

The report will be a Microsoft Word document in which you will address all of the questions in this assignment in the form of a narrative. Name your Microsoft Word document as follows: LastnameFirstInitial_M3_A2.docx.

Submit both files to theM3: Assignment 2Dropbox byTuesday, January 21, 2014.

Assignment 2 Grading Criteria

Maximum Points

Completescatterplot and attach as an Excel file (the fraction of variation in one variable should be accounted for by variation of the other).

56

Report the r2 correlation coefficient and linear regressionequation with slope and intercept included and stated whether the value of r is positive or negative.

96

Explain the implication of any linear relation, including its three components (scatterplot, r2value and linear equation) found between hours spent studying, and the exam score earned

 Hours of Study Exam score 7 63 4 60 3 48 2.5 51 16 80 5 65 1.7 53 13 83 12 80 6 73 9 65 18 82 4 85 8 67 9 69 11.5 72 12 74 14 75 17 78 21 91.5 20 94 25 97 22 93 24 89 19 90 26 88 27 95 18.5 84 25.5
 1 5 2 10 3 15 4 20 Start with your data
Posted on: January 10, 2019, by :