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?

Answer 1

Ce prerotum -4o depend on serrum P s a expewence s an independent crivi rg variable E e penaent mcde Considered a hig r 3tis ana he nai to pay empcunte emfum autO epentence' negave elationship bl +heje. Paioncorelai ther rds,bon ve able Ceefh' cenP and Eope cted be neqative 6 dre

XValues YValues 64 87 50 71 90 80 56 42 60 25 16 70 M: 11.25 60 M: 59.25 50 40 ד 21 28 x-Independent Regression Line(-1.55x 76.66) Estimate Calculation Summary Sum of X 90 Sum of Y 474 Mean X= 1 1 .25 Mean Y 59.25 Sum of squares (SS) 383.5 Sum of products (SP)593.5 Regression Equation-y-bx-a b SPISSx593.5/383.5-1.54759 a My - bMx 59.25 (1.55 11.25) 76.66037 =-1.54759x+ 76.66037 (X- M)2 X- Mx (xMYMy) 39.0625 85.5625 0.5625 5 , 0625 14.0625 27.5625 189.0625 22.5625 6.25 -9.25 0.75 -2.25 3.75 -5.25 13.75 4.75 4.75 27.75 -9.25 11.75 -15.25 3.25 -17.25 0.75 -29.6875 -256.6875 -6.9375 -26.4375 -57.1875 17.0625 -237.1875 3.5625 SS: 383.5 SP: -593.5

ressron ine - (interc e 6 . 6 c 6 -59 , 2 5-(-1.SSX 11. 25)ニ My-bHx 3 833
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