**Midterm Exam**

**Midterm Exam**

计量经济学期中代考 Note: Create a Word file for the answers that should also include the relevant R output and code. Convert the file into pdf, using your first

** Note**:

*Create a Word file for the answers that should also include the*

*relevant*

*R output and code. Convert the file into pdf, using your first and last name in the filename, and upload it in the clearly marked subfolder on Canvas. You must turn in the exam on time; late submissions will be penalized.*### 1.Answer any two of the following three parts (*6 points*). 计量经济学期中代考

*6 points*a.Among other variables, the salaries for project managers are known to depend on the size of the firm. The larger the firm size, the higher the salaries. It is also known that the variability of salaries also depends on the firm size. Suppose we run a linear regression model (LRM) for the salaries where the firm size, along with other variables, are the explanatory variables. Describe which LRM assumption is violated, the consequences of ignoring this assumption, and a possible remedy.

b.When testing for * q*linear restrictions, the value of the test statistic is calculated as

*where*

*df*_{1}=

*and*

*q*

*df*_{2}= ; are the residual sum of squares of the restricted and the unrestricted model, respectively; is the number of explanatory variables in the unrestricted model. Clearly show how this test specializes to the standard

*test, , of joint significance where*

*F*

*df*_{1}=

*and*

*df*_{2}= .计量经济学期中代考

c.The marketing manager of an online apparel store decides to offer daily discounts, of various values, on the discount page of its website. She wants to analyze the influence of price discounts on customer spending. Consider a simple linear regression model This model suffers from a possible omitted variable bias because big spenders are generally rich people who are less likely to visit the discount page of the store’s website. The true model for this application is given by . Since the Income variable is not included in the regression, clearly discuss the direction of the bias for the estimator for of the estimated model.

### 2.Sales Representatives build relationships with buyers in a wide variety of businesses to sell goods and services. 计量经济学期中代考

The primary responsibility of sales representative is to get their products into the hands of customers. Consider the **Salary**data on 160 sales representatives of a technology firm. For each sales representative, the data include salary, age, sex (Female = 1 if female, 0 otherwise), the number of relevant certificates earned. Use the entire data to answer the following questions (you need not cross-validate). (

**)计量经济学期中代考**

*14 points*a.Compare a linear and a loglinear model for salary using age, sex, and certificates as the explanatory variables for both models. Which is the preferred model for predictions?

#### The loglinear model is preferred because of its higher value (0.3720 > 0.3450). (4 points)

b.Extend the selected model in part a to allow for a quadratic effect of age on salary or log of salary. Use two goodness-of-fit measures to show that the quadratic model is preferable to the selected model in part a? At what age is the salary maximized? (4 points)计量经济学期中代考

The quadratic model is higher adjusted (0.3215 > 0.3048) and lower standard error of the estimate (0.2344 < 0.2372)

c.Use the estimated quadratic model in part b to create a graph with simulated values of age, from 22 to 60, on the horizontal axis and salaries (not log salaries) for the male and female sales representatives on the vertical axis. Use four certificates for the simulations. (3 points)

d.It has been argued that compared to males, female representatives do not get compensated equally for earning an additional certificate. Extend the selected quadratic model in part b to capture this interaction. Conduct a test to determine if females get a lower compensation for earning an additional certificate than males. Use a 10% level of significance for the test. Provide the details. (3 points)

* p*-value = 0.1444/2 = 0.0722; reject At the 10% level of significance, we conclude that females get a lower compensation for earning an additional certificate than males.

### 3.The college experience is formative for most individuals and can affect the risk-taking behavior of CEOs.计量经济学期中代考

In this question, we will analyze pay-for-performance measure, delta. Delta captures the dollar change in the CEO’s wealth associated with a 1% change in the firm’s stock price.Specifically, we will explore if delta is influenced by CEOs earning their undergraduate degree from an elite school and/or by their undergraduate field of study. Use **Delta** data for the analysis. (

**)计量经济学期中代考**

*10 points*a.Use the entire sample to estimate a linear regression model using the natural log of delta as the dependent variable. The explanatory variables consist of the following:

- Natural log of industry-adjusted assets
- Industry Type (Finance/Technology/Manufacturing/Other)
- Elite or non-Elite School
- Field of Study (Business/STEM/Humanities)

Note: Delta (in $1,000) and Assets (in $ millions) need to be log-transformed. (2 points)

b.Use the AIC/SIC criteria to determine if the above model is superior to the one that does not include the quality of school (Elite/Non-elite) and the field of study (Business/STEM/Humanities). In addition, use a 5% level to verify this result by testing the joint significance of the Elite and Field variables. Provide the details. (5 points)计量经济学期中代考

We have conflicting results. Model 1 is superior according to AIC and Model 2 is superior according to SIC. The partial test suggests that the restrictions are not valid (p-value = 0.03526; reject Ho). Overall, I might pick Model 1.

c.Use the holdout method with RMSE to compare the predictability of the two models using the first 500 observations for training and the remaining 300 observations for validation. (Note: Since both models are based on the log-transformed delta, you may make the comparison in log-transformed delta.) (3 points)计量经济学期中代考

Model 1 is superior because of its lower RMSE in the validation set (1.311732 < 1.319441).

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