Question

A random sample of eight drivers insured with a company and having similar auto insurance policies was selected. The following table lists their driving experiences (in years) and monthly auto insurance premiums.

Driving Experience (years)	Monthly Auto Insurance Premium $
5	64
2	87
12	50
9	71
15	44
6	56
25	42
16	60

a. Does the insurance premium depend on the driving experience or does the driving experience depend on the insurance premium? Do you expect a positive or a negative relationship between these two variables?

b. Compute SSxx, SSyy, and SSxy.

c. Find the least squares regression line by choosing appropriate dependent and independent variables based on your answer in part a.

d. Interpret the meaning of the values of a and b calculated in part c.
e. Plot the scatter diagram and the regression line.
f. Calculate r and r2 and explain what they mean.
g. Predict the monthly auto insurance premium for a driver with 10 years of driving experience. h. Compute the standard deviation of errors.

Answer 1

insurance premium depend on the driving experience

WE EXPECT NEGATIVE RELATIONSHIP

.........

b)

	ΣX	ΣY	Σ(x-x̅)²	Σ(y-ȳ)²	Σ(x-x̅)(y-ȳ)
total sum	90.00	474.00	383.50	1557.50	-593.50
mean	11.25	59.25	SSxx	SSyy	SSxy

...........

c)

Sample size,   n =   8      
here, x̅ = Σx / n=   11.250          
ȳ = Σy/n =   59.250          
SSxx =    Σ(x-x̅)² =    383.5000      
SSxy=   Σ(x-x̅)(y-ȳ) =   -593.5      
              
estimated slope , ß1 = SSxy/SSxx =   -593.5/383.5=   -1.5476      
intercept,ß0 = y̅-ß1* x̄ =   59.25- (-1.5476 )*11.25=   76.6604      
              
Regression line is, Ŷ=   76.660   + (   -1.548   )*x

....

d)

if experince is 0 , then prwmium will be 76.660

if we increase experience by 1 year, premium will decrease by 1.548

........

e)

.......

f)

correlation coefficient ,    r = SSxy/√(SSx.SSy) =   -0.768

negarive , moderate and linear relationship

R² =    (SSxy)²/(SSx.SSy) =    0.5897
Approximately    58.97%   of variation in observations of variable Y, is explained by variable x

........

g)

Predicted Y at X=   10   is          
Ŷ=   76.66037   +   -1.54759   *10=   61.184

h)

SSE=   (SSxx * SSyy - SS²xy)/SSxx =    639.0065
std error ,Se =    √(SSE/(n-2)) =    10.3199

...........

Please let me know in case of any doubt.

Thanks in advance!

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