Question

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

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

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

2. Run a multiple regression using both number of payroll in thousands and the indicator variable manufacturing to predict workers compensation premiums.

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

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

c. Are both independent variables useful in predicting workers compensation premiums? Please explain why or why not? (2 points)

d. Interpret the relationship between each independent variable and the dependent variable in terms of the coefficients. (2 points)

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

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

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

5. Using the best model, predict the manufacturing company’s workers compensation premiums assuming payroll of $850,000 and that the company is a manufacturing company. (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

Answer 1

1

we enter the data in excel and then goto data > data analysis tab and select regression

the results are

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.987940576
R Square	0.976026582
Adjusted R Square	0.974827911
Standard Error	0.857386831
Observations	22
ANOVA
	df	SS	MS	F	Significance F
Regression	1	598.5705	598.5705	814.2573	1.11708E-17
Residual	20	14.70224	0.735112
Total	21	613.2727
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 99.0%	Upper 99.0%
Intercept	4.976298951	0.367747	13.53187	1.58E-11	4.209192801	5.743405	3.929935	6.022663
Payroll in thousands	0.008208885	0.000288	28.53519	1.12E-17	0.007608804	0.008809	0.00739	0.009027

useful

we see the r2 value is 0.9760 , this means that the model is able to explain 97.6% variation in the data , which is a very good model

Interpretation

we see the coefficient is 0.0082 for Payroll

this means that for every unit increase in the value of payroll the premium increases by 0.0082 units

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