12.89 A study was conducted to assess the various factors considered in a health index. A random sample of 110 adults are selected and determined the following estimated model:

yn = 5.025 - 1.793x1 - 2.401x2 + 3.3759x3 + 2.953x4 10.6562 10.3942 10.7882 11.0212

- 0.986x5 - 1.004x6 - 0.973x7 10.1452 10.8032 10.3192 R2 = 0.869 where yn = health index x1 = age x2 = average working hours per day x3 = average sleeping hours per night x4 = average exercise hours per week x5 = body mass index (kg/m2)

x6 = daily average blood pressure (mm Hg)

x7 = daily average cholesterol level (mg/dL)

The numbers in parentheses under the coefficients are the estimated coefficient standard errors.

a. Interpret the estimated regression coefficients.

b. Interpret the coefficient of determination.

c. Find a 90% confidence interval for the increase in health index resulting from a one-unit increase in the body mass index, with all other variables unchanged.

d. Test, against a two-sided alternative at the 5%

level, the null hypothesis that, all else remaining equal, the average sleeping hours per night does not influence health index.

e. Test, against a two-sided alternative at the 5%

level, the null hypothesis that, all else remaining equal, the daily average blood pressure does not influence health index.

f. Test the null hypothesis that, taken together, these seven independent variables do not influence health index.