Linear Regression Excel Task Essay Assignment
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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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