10. 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 1 and on 2 (use two tailed test with (a = .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.