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Linear Regression Excel Task Essay Assignment
Problem Set 2 Download the spreadsheet entitled “Height weight data.xls” from the Datasets tab on Blackboard. This file contains the height, weight, age, gender, and eye color of students in my past three classes of econometrics. We use this to run our first regression: how does Y=weight depend on X=height. Perform the calculations listed below. Indicate clearly in the spreadsheet where you are answering each question. Then upload the spreadsheet on Blackboard as your submission. 1) For height and weight: at the bottom of each column calculate the mean (=AVERAGE), the variance (=VAR), and the standard deviation (=STDEV) for each variable.
2) For x=height, create a column which contains ( xxi – ), the deviations from the mean. What is the mean of this column? Explain.
3) Create another column that has these terms squared: ( xxi – ) 2. Show how you can use these data to calculate the variance, and get exactly the same answer as in question 1. Explain the formula you used.
4) Now let y=weight, and create a column with the values of ( yyi – ), and yet another column with the products, xx )( i – yy )( i – . Using the data in this column, calculate the sample covariance between height and weight. State which formula you used.
5) Use the Chart function on the main menu to draw an X-Y scatter plot with height on the x-axis and weight on the y-axis. Then right-click on a point and select Add Trendline. Choose the Linear trend line and under Options check “Display Equation on Chart.” That gives you the linear regression equation and draws the line of fitted values. Also check “Display R-squared on Chart”.
6) Using the means, variances and covariances calculated above, find the following: a) The slope coefficient: beta1hat – should be same as Excel’s equation for trend line b) The intercept: beta0hat – should be same as Excel’s equation for trend line c) A column of predicted values: yhats d) A column of residuals: uhats
7) Show that the fitted values have the same mean as the actual y-values, and that the residuals have mean zero.
8) Show that the variance of the fitted values plus the variance of the residuals adds up to the variance of y. Find R2.
9) Calculate the correlation coefficient between height and weight using the formula Corr(X,Y)=Cov(X,Y)/(SD(X)*SD(Y)) which is a version of equation C.15. Confirm you get the same thing using Excel’s =CORREL().
RUBRIC |
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Excellent Quality 95-100%
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Introduction
45-41 points The background and significance of the problem and a clear statement of the research purpose is provided. The search history is mentioned. |
Literature Support 91-84 points The background and significance of the problem and a clear statement of the research purpose is provided. The search history is mentioned. |
Methodology 58-53 points Content is well-organized with headings for each slide and bulleted lists to group related material as needed. Use of font, color, graphics, effects, etc. to enhance readability and presentation content is excellent. Length requirements of 10 slides/pages or less is met. |
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Average Score 50-85% |
40-38 points More depth/detail for the background and significance is needed, or the research detail is not clear. No search history information is provided. |
83-76 points Review of relevant theoretical literature is evident, but there is little integration of studies into concepts related to problem. Review is partially focused and organized. Supporting and opposing research are included. Summary of information presented is included. Conclusion may not contain a biblical integration. |
52-49 points Content is somewhat organized, but no structure is apparent. The use of font, color, graphics, effects, etc. is occasionally detracting to the presentation content. Length requirements may not be met. |
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Poor Quality 0-45% |
37-1 points The background and/or significance are missing. No search history information is provided. |
75-1 points Review of relevant theoretical literature is evident, but there is no integration of studies into concepts related to problem. Review is partially focused and organized. Supporting and opposing research are not included in the summary of information presented. Conclusion does not contain a biblical integration. |
48-1 points There is no clear or logical organizational structure. No logical sequence is apparent. The use of font, color, graphics, effects etc. is often detracting to the presentation content. Length requirements may not be met |
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Linear Regression Excel Task Essay Assignment |
Linear Regression Excel Task Essay Assignment