1. Run a simple regression using payroll inthousands to predict workers compensation premiums in thousandswith a 99% confidence interval.

a. Please explain to the risk manager howuseful this model is. (1 point)

b. Interpret the relationship between theindependent variable and the dependent variable in terms of thecoefficients. (1 point)

2. Run a multiple regression using both numberof payroll in thousands and the indicator variable manufacturing topredict workers compensation premiums.

a. Please explain how useful this model is tothe risk manager. (1 point)

b.Write out the estimated regression equationin terms of Y =a+b₁X₁+b₂X₂ (1point)

c. Are both independent variables useful inpredicting workers compensation premiums? Please explain why or whynot? (2 points)

d. Interpret the relationship between eachindependent variable and the dependent variable in terms of thecoefficients. (2 points)

e. Explain specifically how confident you arewith regard to each of the coefficients of the model (using 95%confident interval). (2 points)

3. Run a multiple regression using all threeindependent variables: payroll, manufacturing, and metropolitan.Are all three variables useful in predicting workers compensationpremiums? Please explain why or why not. (1.5 points)

4. Compare all three models - which one is thebest? Please explain why. (1 point)

5. Using the best model, predict themanufacturing company’s workers compensation premiums assumingpayroll of $850,000 and that the company is a manufacturingcompany. (1.5 points)

Data:

Company	WC premium in thousands	Payroll in thousands	Manufacturing	Metropolitan
A	7	380	0	0
B	7.3	410	0	0
C	7.8	443	0	1
D	8.2	480	0	0
E	8.5	520	0	1
F	9.2	566	0	0
G	9.9	616	1	0
H	10.6	672	0	0
I	11.4	733	1	1
J	12.2	802	0	1
K	12.9	878	1	0
L	13.5	963	0	1
M	14.5	1057	1	1
N	15.6	1161	1	0
O	16.8	1277	1	1
P	17.3	1405	1	0
Q	18.2	1548	1	0
R	19.8	1706	1	1
S	20.5	1882	1	1
T	21.5	2077	1	0
U	23	2293	1	1
V	24.1	2534	1	1