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

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
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...

1. For a pair of sample x- and y-values, what is the difference
between the observed value of y and the predicted value of y? a) An
outlier b) The explanatory variable c) A residual d) The response
variable
2. Which of the following statements is false:
a) The correlation coefficient is unitless. b) A correlation
coefficient of 0.62 suggests a stronger correlation than a
correlation coefficient of -0.82. c) The correlation coefficient,
r, is always between -1 and 1....

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