Question

A random sample of eight auto drivers insured with a company and having similar auto insurance policies
was selected. The following table lists their driving experience (in years) and the monthly auto insurance
premium (in dollars).
Driving Experience(years) 5 2 12 9 15 6 25 16
Monthly Premium(dollars) 64 87 50 71 44 56 42 60
Answer the following questions.
(a) Does the insurance premium depend on driving experience or does the driving experience depend on
insurance premium? Do you expect a positive or a negative relationship between these two variables?
Part of the Minitab Computer output is the following.
The regression equation is
premium = 76.7 - 1.55 years
Predictor Coef Stdev t-ratio p
Constant 76.660 6.961 11.01 0.000
years -1.5476 0.5270 -2.94 0.026
s = 10.32 R-sq = 59.0%
(b) Plot the scatter diagram and the regression line.
(c) What does the intercept, β0, mean in the context of this problem?
(d) Construct a 95% confidence interval for the intercept, β0.
(e) What does the slope, β1, mean in the context of the problem? What is the implication for the relationship
of the premium and the years of driving experience when β1 = 0?
(f) Test H0 : β1 = 0, versus H1 : β1 6= 0 at 1% siginificance level based on
i) T-test statistic
ii) on P-value.
(g) What is the estimate for σ, the standard deviation of the error?
(h) What is the value of the correlation coefficient, r? Is the linear relationship between the price and the
age strong?
(i) From s and Stdev in your minitab output, calculate Sxx.
(j) Predict the average monthly auto insurance premium for drivers with 10 years of driving experience and
provide the 95% confidence interval.
(k) Predict the monthly auto insurance premium for a driver with 10 years of driving experience and provide
the 95% prediction interval.

Answer 1