City officials trying to estimate heath utilization by city residents conducted a regression analysis of doctor's office visits (visits) based on the following predictors: resident's count of illnesses (illness), whether they suffer from chronic conditions like high blood pressure, asthma, or diabetes (chronic: yes/no), whether they have private insurance (insurance: yes/no), their gender, age, and annual income (in thousands of dollars). The model and results are shown below.

log(visits) ~ illness + I(illness * illness) + chronic + chronic * illness + gender + age + log(income) + insurance

Coefficients:

EstimateStd. Errort valuePr(>|t|)

(Intercept)0.0310.0231.3660.172

illness0.0990.0109.572< 2e-16 ***

I(illness * illness)- 0.0070.002-2.8470.004 **

chronic_yes0.0010.0160.0690.945

gender_male-0.0290.011-2.7220.007 **

age0.0020.0016.3801.92e-10 ***

log(income)0.0230.0092.5530.011 *

insurance_yes0.0100.0100.9470.344

insurance_yes:chronic_yes-0.0190.008-2.4750.013 *

---

Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 0.3546 on 5181 degrees of freedom

Multiple R-squared: 0.08008,Adjusted R-squared: 0.07866

F-statistic: 56.37 on 8 and 5181 DF,p-value: < 2.2e-16

1.Explain the marginal effect of income on doctor's office visits.

2.In the regression output, explain the nature of the overall effect of illness on doctor's office visits.

3.From the regression output, does private insurance have an effect on doctor's office visits? Why or why not?