Question

The following data from a large health insurance company was gathered randomly from 4 of their clients: the claims (in million $) that was used to predict their profit (in million $). Use the data below to answer the following questions:

State	Claims	Surplus
State 1	273	100
State 2	142	25
State 3	259	57
State 4	894	141
	Mean= 392	Mean 80.75
	Std. Deviation= 3400	Std. Deviation= 51

a) Find the correlation coefficient for the dataset.
b) Find the linear regression equation for the dataset.
c) Interpret the slope of the linear regression.
d) Predict the surplus amount if the claims amount is 678.
e) Find the residual if the surplus amount is 150.
f) How much variance is accounted for by the independent variable?

Answer 1

Calculation:

State	Claims (x)	Surplus (y)
State 1	273	100
State 2	142	25
State 3	259	57
State 4	894	141
	Mean= 392	Mean 80.75
	Std. Deviation= 340	Std. Deviation= 51
a) Correlation Coefficent	0.874	using formula =CORREL(Array1,Array2) in Excel
b) Regression equation of
1)	y on x:
		or, y=80.75+0.874*51/340(x-392)
		or, y=29.359+0.131x
	c) Slope	0.131
2)	x on y :
		or, x=392+0.874*340/51(y-80.75)
		or, x=5.827y - 78.503
	c) Slope	5.827
d) x = 678 unit	y = 118.177	If claims amount is 678 unit, predicted surplus amount is 118.177 million $