Enter the data in STATA, use STATA to develop the estimated regression equation that could be used to predict the percent

Instructions: 

1.   You should use STATA software for any calculations. You must paste your log/output onto your assignment (in a word document) to show your use of STATA; however, this output does not replace any of the steps outlined below.

2.  If you are performing a hypothesis test, make sure you state the hypotheses, the level of significance, the rejection region, the test statistic (and p-value, if requested), your decision (whether to reject or not to reject the null hypothesis), and a conclusion in managerial terms that answers the question posed. These steps must be completed in addition to any STATA output.

3.  The required STATA data files can be found in the corresponding folder of cuLearn 

4.  Please do not forget to write your name and student ID on the cover page of the assignment. 

Project 1: 

The Transactional Records Access Clearinghouse at Syracuse University reported data showing the odds of an Internal Revenue Service (IRS) audit. The following table shows the average adjusted gross income reported and the percent of the returns that were audited for 20 selected IRS districts.

(b)   At the 0.05 level of significance, determine whether the adjusted gross income and the percent audited are linearly related. 

(c)    Did the estimated regression equation provide a good fit? Explain. 

(d)   Use the estimated regression equation developed in part (a) to calculate a 95% confidence interval for the expected percent audited for districts with an average adjusted gross income of $35,000.

Project 2: 

How much does education affect wage rates? The data file cps4_small.dta contains 1000 observations on hourly wage rates, education, and other variables from the 2008 Current Population Survey (CPS).

(a)    Obtain the summary statistics and histograms for the variables WAGE and EDUC. Discuss the data characteristics, especially appropriate summary statistics (mean, median) and shape of the data. 

(b)   Estimate the linear regression 𝑊𝐴𝐺𝐸 = 𝛽1 + 𝛽2𝐸𝐷𝑈𝐶 + 𝜖 and discuss the results. Interpret the regression coefficients and comment on the quality of the fit. 

(c)    Calculate the least squares residuals and plot them against EDUC. Are any patterns evident? Comment on the assumptions (linearity, normality of errors, and constant variance of errors) of classical linear regression model. 

(d)   Estimate the quadratic regression 𝑊𝐴𝐺𝐸 = 𝛼1 + 𝛼2𝐸𝐷𝑈𝐶2 + 𝑒 and discuss the results. 

(e)    Plot the fitted linear model from part (b) and the fitted values from the quadratic model from part

(d) either in the same or separate graph with the data on WAGE and EDUC. Which model appears to fit the data better? Compare the sum of squared residuals (RSS) from the models in (b) and (d). Which model has a lower RSS?