Question 1:

This question is similar to Exercise 12.114 on page 525 of your textbook.

The data file 611h6_HEl contains 200 selected individuals who participated in an extended interview and medical examination. The variables are described in the data descriptions in the Chapter 10 appendix, page 394 . Consider regression models that relate a person's physical characteristics and quality of diet consumed as measured by the Healthy Eating Index (HEI2005). The higher value of HEI2005 indicates a higher quality of diet. The independent variables are

Waistper = the ratio of waist measure to obese waist measure

BMI = the body mass index

Age = age

Screen_hours = number of hours in front of computer or TV screen

Activity_level = level of activities with 1=sedentary, 2=active, 3=very active.

1. Get two regression printouts for the model with HEl2005 as the dependent variable. In the first model, use all five variables as the independent variables. In the second model, use only AGE, Activity_level as the independent variables. Use these two regression results to test if you can remove Waistper, BMI, and Screen_hours with the \(5 \%\) significance level.
2. Consider the regression with HEl2005 as the dependent variable and AGE, Activity_level, and Doc_bp as the independent variables. Doc_bp is a dummy variable with a value of 1 for the person with a doctor's diagnosis of high blood pressure and a value of 0 without high blood pressure. Get the regression printout.
3. Write the regression model and the estimated equation for the regression in part b.
4. Explain the meaning of the estimated coefficient of Doc_hp in partb.
5. Based on the results from part b, write the estimated equation for the individuals who were diagnosed with high blood pressure and the estimated equation for the individuals who were not diagnosed with high blood pressure.
6. Based on the results from part b, test the hypothesis that the individuals who were diagnosed with high blood pressure had a lower HEl2005. Use the p-value approach to conduct the test with the \(5 \%\) significance level.
7. For the regression model in part b, calculate the predicted value of HEl 2005 for an individual who were diagnosed with high blood pressure, and with an age of 50 and activity level of 3.
8. Use PhStat to get the prediction printout for the prediction in part g. Find a \(95 \%\) confidence interval for the mean predication for part g.
9. Get the regression printout with HEl 2005 as the dependent variable. The independent variables are Age, Activity_level, Doc_hp, Age*Doc_hp.
10. Based on the results from part i write the estimated equation for the individuals who were diagnosed with high blood pressure and the estimated equation for the individuals who were not diagnosed with high blood pressure.
11. Explain the meaning of the coefficient for Age*Doc_hp in part i

1. Based on the results from part i, test if the marginal impact of age is higher for the individuals with high blood pressure with the \(5 \%\) significance level.

m. Get three regression printouts for the linear, quadratic, and cubic models for Age. In each model, include Activity_level in the regression. Among the three regressions, determine which regression model would be most suitable. Explain.

n. Get the regression printout with the logarithm of HEl 2005 as the dependent variable, Activity_level (without the logarithm transformation), and the logarithm of AGE as the independent variables.

o. Write the regression model and the estimated equation for part n.

p. Explain the meaning of the estimated coefficient for the logarithm of Age in part n.

q. Use "Correlation" in the Data Analysis Tools to get the correlation matrix for all six variables, including HEI2005 and five independent variables in part a. Use the correlation matrix to check the multicollinearity problem for the unrestricted model in part a.

r. The restricted model in part a includes two independent variables: AGE and Activity_level. Test the heteroscedasticity problem for this restricted model with the \(5 \%\) significance level.

s. Explain the regression problems if you find heteroscedasticity in part r.

Question 2:

Consider the following data from Economics Data - FRED from the Federal Reserve Bank of St. Louis at http://research.stlouisfed.org/fred2/.

DJA: Dow Jones Industrial Average

UMCSENT: University of Michigan: Consumer Sentiment Index

FEDFUNDS : Effective Federal Funds Rate

These data are downloaded and stored in 611h6_DJIA. The growth and the difference of these variables are denoted as

GDJIA: growth of DJIA

GUMCSENT: growth of UMCSENT

DFEDFUNDS: changes in FEFUNDS

Use the data in 611h6_DJIA to generate the above growth and changes. When you generate the growth, you need to multiply the percentage change by 1200 . For example, you use "=(B3-B2)/B2* 1200" to calculate the growth of DJIA in February, 1978. For the changes, you don't multiply the changes by 1200. For example, the change in the federal funds rate in February, 1978 is "=(D3-D2)". We use two independent variables to estimate the growth of Dow Jones Industrial Average.

1. Get the printout of the descriptive statistics of the growth and the changes for these three variables. Don't print the data.
2. Use GDJIA as the dependent variable and GUMCSENT and DFEDFUNDS as the independent variables. Get the regression printout.
3. Write the regression model and estimated equation for part \(b\).
4. Explain the meaning of the estimated coefficient for GUMCSENT in part \(b\).
5. Explain the meaning of the estimated coefficient for DFEDFUNDS in part \(b\).
6. What sign do you expect for the coefficient of GUMCSENT in part \(b\) ? Conduct a one-tailed test for your hypothesis with the \(5 \%\) significance level.
7. For the regression printout in part \(b\), which variables have significant coefficients? Use one tailed test with the \(5 \%\) significance level. Use only one sentence to explain why you pick each of these variables. DO NOT write the whole testing procedure for each coefficient.
8. Use PhStat to get the DW test for the model in part \(b\) and test the serial correlation problem with the \(5 \%\) significance level.
9. Use the growth of Dow Jones Industrial Average as the dependent variable and the growth of the Consumer Sentiment Index as the independent variable. Get the regression printouts for the following three models: 1) the distributed lags model (DL), 2) autoregressive distributed lags model (ADL), and 3) vector autoregressive model (VAR). Use four lags for each model.
10. For each of the three regression printouts in part \(i\), identify significant coefficients with the two tailed test and the \(5 \%\) significance level. Use one sentence to explain how you pick these coefficients. DO NOT write the whole testing procedure for each coefficient.

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