Suppose that we have found the following data from a survey of 25 individuals randomly sampled from the Texas border region. The variables are i) the number of doctor visits (y) in the last one year, ii) insurance status with three categories (no insurance, having private insurance, having Medicaid), iii) age iv) highest education (below high school, high school, more than high school). Save the data file in your computer.

"y" "age" "education" "insurance"

"1" 2 57 "High School" "No insurance"

"2" 0 56 "High School" "Medicaid"

"3" 0 55 "High School" "Private insurance"

"4" 3 60 "Below High School" "Private insurance"

"5" 2 59 "Below High School" "No insurance"

"6" 4 57 "Below High School" "No insurance"

"7" 3 59 "Below High School" "No insurance"

"8" 5 61 "Above High School" "No insurance"

"9" 0 64 "Above High School" "Private insurance"

"10" 2 57 "High School" "No insurance"

"11" 3 57 "Above High School" "Private insurance"

"12" 1 53 "High School" "No insurance"

"13" 1 57 "High School" "Medicaid"

"14" 0 59 "Below High School" "Medicaid"

"15" 2 53 "Above High School" "No insurance"

"16" 4 60 "High School" "Medicaid"

"17" 0 57 "High School" "Private insurance"

"18" 1 56 "Above High School" "No insurance"

"19" 2 51 "High School" "Private insurance"

"20" 0 64 "Above High School" "Private insurance"

"21" 3 62 "High School" "No insurance"

"22" 1 60 "Below High School" "Private insurance"

"23" 2 56 "High School" "Medicaid"

"24" 0 56 "Below High School" "No insurance"

"25" 4 59 "High School" "No insurance"

"26" 3 64 "Below High School" "Medicaid"

"27" 1 56 "Below High School" "Medicaid"

"28" 0 51 "High School" "Private insurance"

"29" 0 57 "High School" "Private insurance"

"30" 2 61 "Above High School" "Medicaid"

"31" 0 55 "Below High School" "Private insurance"

"32" 0 53 "Below High School" "Medicaid"

"33" 0 63 "Above High School" "Medicaid"

"34" 2 65 "High School" "Medicaid"

"35" 3 54 "Below High School" "No insurance"

"36" 4 65 "Below High School" "Private insurance"

"37" 1 65 "High School" "Private insurance"

"38" 1 55 "Above High School" "Medicaid"

"39" 3 58 "Below High School" "Medicaid"

"40" 2 50 "High School" "No insurance"

"41" 2 54 "High School" "Medicaid"

"42" 6 62 "Above High School" "No insurance"

"43" 3 58 "High School" "No insurance"

"44" 1 57 "Below High School" "Private insurance"

"45" 3 61 "Above High School" "Medicaid"

"46" 1 52 "Above High School" "Medicaid"

"47" 2 60 "High School" "Private insurance"

"48" 2 53 "Above High School" "Medicaid"

"49" 0 60 "Above High School" "Private insurance"

"50" 1 56 "Below High School" "Medicaid"

Suppose that we want to model y, the number of doctor visits, in terms of the above mentioned explanatory variables. In your model do not include any interaction term between the explanatory variables.

(a) Fit a Poisson model to the data with age, education and insurance status as explanatory variables. Write the prediction equation in terms of the estimated coefficients and then predict the number of doctor visits for person of age 55 years, with high school education and Medicaid insurance.

(b) Again fit a Poisson model to the data but with age and insurance status as the explanatory variables. Compare the two model fittings (a) and (b), and then test the effect of education status on the response variable for the underlying population.