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regression results

6. Assume Y is household income and HE is household expenditures on health care. Use the information from the regression output to answer the following:

a. Use the regression results to write out the linear equation. Are the parameter estimates statistically significant? What does this imply? How would you interpret the parameter estimates? What does the coefficient of determination (R2) imply?
b. Using the regression output and the appropriate data, forecast health care expenditures for households (id) 16, 17, and 18.
c. Suppose our newly elected President determines that $5000 of annual household spending on health care is necessary to maintain the health of family members in the typical household. What is the â??income thresholdâ? at which it is expected that households would not be meeting this target?
d. Given the actual data used in the regression analysis, and assuming there are 10 additional households earning $0 income, how much would a subsidy total in order for each family to reach the targeted amount?

id Y HE
1 10000 4600
2 15000 5600
3 20000 7200
4 25000 6700
5 30000 7700
6 35000 6600
7 40000 6900
8 45000 7900
9 50000 8800
10 55000 9100
11 60000 9400
12 65000 10400
13 70000 10000
14 75000 11300
15 80000 12000
16 85000
17 90000
18 95000

Regression output
Dependent variable HE
Number of obs 15
R-squared 0.9231

Independent variable Parameter estimate Std. Err. t-stat P>t
Y 0.09 0.007 12.49 0.0000
Intercept 4204 361.840 11.62 0.0000

Solution Preview

The regression results are the following:

Dependent variable HE
Number of observations 15
R-squared 0.9231

Independent variable Parameter estimate Std. Err. t-stat P>t
Y 0.09 0.007 12.49 0.0000
Intercept 4204 361.840 11.62 0.0000

(a) The relationship between health expenditure and income can then be stated as

HE = Intercept + (Coefficient Estimate)*Y

Here, intercept is given as 4204, and estimated value of the coefficient is 0.09. Thus, the required relationship is

HE = 4204 + 0.09Y.

The estimates are statistically significant. The t-values obtained are very high and are all significant even at 1% level. The value R-squared is given to be 0.9231 suggesting that 92.31% of all variation in health expenditure is explained by ...

Solution Summary

The regression results are clearly depicted.

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