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Homework Assignment 2 (Due: Monday, October 12)

计量经济学作业代写 With all 40 observations, estimate the linear model and the loglinear model that uses ln(y) as the dependent variable.

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. Please note that the homework will not be accepted after the due date.

1.Refer to the NPS data for this question. Use all observations for the analysis.  计量经济学作业代写

a. Estimate a linear regression model using NPS as the dependent variable.  The explanatory variables include the number of certificates along with the appropriate dummy variables for personality type.  Predict the NPS for a diplomat and an analyst with 3 certificates.

*Use Sentinels as reference:

The prediction of NPS for a diplomat with 3 certificates is 7.4396

The prediction of NPS for an analyst with 3 certificates is 4.7883

 b.Estimate a restricted model that assumes that analysts and sentinels exert the same influence on NPS and diplomats and explorers exert the same influence on NPS.

*Use Sentinels and Analysts as dummy variables (references)

c. Test if the restrictions imposed in part b are invalid at the 5% level.

P-value = 0.3507 > 0.05 , α = 0.05.

P-value > α, F-test, reject H0 (the null hypothesis) ,argument is valid

So the restrictions imposed in part b are valid.

P-value = 0.3507 > 0.05 , α = 0.05.

P-value > α, do not reject H0 ,argument is valid

So the restrictions imposed in part b are valid.

c. Use at least three measures to compare the two models estimated in parts a and b. Which is the preferred model?

*Unrestricted model

Call:

lm(formula = NPS ~ Certificates + analyst + diplomat + explorer,   data = npsdata)

*Restricted model

Call:

lm(formula = npsdata$NPS ~ I((npsdata$analyst) + (npsdata$sentinel)) +   npsdata$Certificates)

To compare the two models, we can choose the multiple R-squared, adjusted R-squared and the AIC value from the R output.

Unrestricted may be preferred because it has a slightly

lower standard error of the estimate (1.730 < 1.731) and

higher adjusted R-sq (0.4021 > 0.4015).

Restricted) is preferred because it has

lower AIC (3.0696 < 3.1164) and

SIC (3.2912 < 3.5002)

Overall, I prefer Restricted model  because AIC/SIC are considered better measures (penalize overfitting heavily).

   2.The accompanying data file contains 40 observations on the dependent variable y along with the explanatory variables x₁and x₂. (Data: Holdout)  计量经济学作业代写

A.With all 40 observations, estimate the linear model and the loglinear model that uses ln(y) as the dependent variable.  Use  values to identify the more appropriate predictive model.

Estimate Linear mode,  R-squared = 0.5449

Estimate Loglinear model, R-squared = 0.7107085

*Loglinear model is the more appropriate predictive model because the R-squared of the loglinear model is larger.

A.Use the holdout method to compare the predictability of the above two models using the first 30 observations for training and the remaining 10 observations for validation.

The RMSE (Root Mean Square Error) of the linear model is 192.70

The RMSE of the loglinear model is 77.01

*The preferable model is the Loglinear model because it has a smaller value of RMSE.

 Are the results for parts a and b consistent?

*For both parts the Loglinear model is the preferable model, so the results for part a and b are consistent.

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