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# Statistics Help! Need in 20 minutes 10.

Statistics Help! Need in 20 minutes
10. (TCO E) An insurance firm wishes to study the relationship between driving experience (X1, in years), number of driving violations in the past three years (X2), and current monthly auto insurance premium (Y). A sample of 12 insured drivers is selected at random. The data is given below (in MINITAB):

Y X1 X2 Predict X1 Predict X2
74 5 2 8 1
38 14 0
50 6 1
63 10 3
97 4 6
55 8 2
57 11 3
43 16 1
99 3 5
46 9 1
35 19 0
60 13 3

Regression Analysis: Y versus X1, X2

The regression equation is
Y = 55.1 - 1.37 X1 + 8.05 X2

Predictor Coef SE Coef T P
Constant 55.138 7.309 7.54 0.000
X1 -1.3736 0.4885 -2.81 0.020
X2 8.053 1.307 6.16 0.000

S = 6.07296 R-Sq = 93.1% R-Sq(adj) = 91.6%

Analysis of Variance

Source DF SS MS F P
Regression 2 4490.3 2245.2 60.88 0.000
Residual Error 9 331.9 36.9
Total 11 4822.3

Predicted Values for New Observations

New Obs Fit SE Fit 95% CI 95% PI
1 52.20 2.91 (45.62, 58.79) (36.97, 67.44)

Values of Predictors for New Observations

New Obs X1 X2
1 8.00 1.00

Correlations: Y, X1, X2

Y X1
X1 -0.800
0.002

X2 0.933 -0.660
0.000 0.020

Cell Contents: Pearson correlation
P-Value

a. Analyze the above output to determine the multiple regression equation.
b. Find and interpret the multiple index of determination (R-Sq).
c. Perform the t-tests on βˆ1 and on βˆ2 (use two tailed test with (= .05). Interpret your results.
d. Predict the monthly premium for an individual having 8 years of driving experience and 1 driving violation during the past 3 years. Use both a point estimate and the appropriate interval estimate.

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