Question: (20 points)
See Exercise 12.114 on page 525 of your textbook.
The data file HEI Cost Data Variable Subset 2 contains considerable information on randomly selected individuals who participated in an extended interview and medical examination. The variables are described in the data dictionary in the Chapter 10 appendix. 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 dependent variable is HEI2005 and the independent variables include the ratio of waist measure to obese waist measure (waistper), age (age), the body mass index (BMI), number of hours in front of computer or TV screen (screen_hours), and level of activities with 1=sedentary, 2=active, 3=very active, (activity_level).

1. Use D escriptive statistics in Data Analysis to get the printout of the descriptive statistics of six variables.
2. Use Correlation in Data Analysis to get the printout of the correlation matrix with six variables.
3. Based on the printout from part b , identify three pairs of two variables with the highest absolute values of correlation among all pairs.
4. Use HEI2005 as the dependent variable to get six regression results. For the first five regressions, use HEI2005 as the dependent variable and each one of the rest five variables as the independent variable to get five simple linear regression results. In the sixth regression, use HEI2005 as the dependent variable and all the rest five variables as the independent variables. Get the printouts of six regressions. Organize your six regression results as in the following table.

   		(2)	(3)	(4)	(5)	(6)
   Intercept	52.17 (0.99)	xxxx (xxxx)	xxxx (xxxx)	xxxx (xxxx)	xxxx (xxxx)	Xxxx (xxxx)
   Waistper	0.919 (0.937)					Xxxx (xxxx)
   Age		xxxx (xxxx)				Xxxx (xxxx)
   BMI			xxxx (xxxx)			Xxxx (xxxx)
   Screen_hours				xxxx (xxxx)		Xxxx (xxxx)
   Activity_level					xxxx (xxxx)	Xxxx (xxxx)
   R-Squared	0.0001	0.xxx	0.xxx	0.xxx	0.xxx	0.xxx

   
   The first column shows the regression results with HEI2005 as the dependent variable and Waistper as the independent variable. It includes the estimated coefficient of intercept and its standard error in the parenthesis below, the estimated coefficient of Waistper and its standard error in the parenthesis below, and the R -squared. The second column shows the results with HEI2005 as the dependent variable and Age as the independent variable.And so on. The results for column (1) are giving. You need to complete the rest part of the table. An example of this table is on page 329 of the course packet.
   You will use the regression printouts and this table to answer the following questions.
5. For the regression results in column (3) with BMI as the independent variable, what sign do you expect for the coefficient of BMI ? Explain why it is positive or negative. Conduct a test based on your hypothesis. Use the 5% significance level and the rejection region approach to conduct the test.
6. For the regression results in column (4) with Screen_hours as the independent variable, what sign do you expect for the coefficient of Screen_hours ? Explain why it is positive or negative. Conduct a test based on your hypothesis. Use the 5% significance level and the p -value approach to conduct the test.
7. Compare five simple linear regression results from columns (1) to (5), which simple regression model is the best? Explain why.
8. Compare the R-squares in columns (1) – (5) in the table and the correlation matrix in part b . Explain the relationship between R-squared and correlation.
9. Divide BMI by 1000 and define this new variable as BMI2 . Get the regression printout for the regression with HEI2005 as the dependent variable and BMI2 as the independent variable. Compare the estimated coefficients, t -statistics, p -values, and R -squared from this regression with those corresponding numbers from the regression results in column (3).
10. Divide HEI2005 by 100 and define this new variable as HEI20052 . Get the regression printout for the regression with HEI20052 as the dependent variable and BMI as the independent variable. Compare the estimated coefficients, t -statistics, p -values, and R -squared from this regression with those corresponding numbers from the regression results in column (3).
11. Without running a regression, if you keep HEI2005 the same and multiply Screen_hours by 100, how your estimated coefficients, t -statistics, p -values, and R-squared for this regression are related to those corresponding numbers from the results in column (4).
12. Write the regression model and the estimated equation for the regression in column (6).
13. For the regression in column (6), explain the meaning of the estimated coefficient of Screen_hours .
14. For the regression in column (6), explain the meaning of the estimated coefficient of Activity_level .
15. For the regression in column (6), construct a 95% confidence interval for the coefficient of Screen_hours .
16. For the regression in column (6), what sign do you expect for the coefficient of Screen_hours ? Explain why it is positive or negative. Conduct a test on the coefficient of Screen_hours based on your hypothesis. Use the 5% significance level and the p -value approach to conduct the test.
17. For the regression in column (6), what sign do you expect for the coefficient of Activity_level ? Explain why it is positive or negative. Conduct a test on the coefficient of Activity_level based on your hypothesis. Use the 5% significance level and the p -value approach to conduct the test.
18. For the regression in column (6), find the values of and . Explain the meaning of the .
19. For the regression in column (6), construct the ANOVA table.
20. Use the F statistic in the ANOVA table in part s to conduct the F test with the 5% significance level.

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