A sample of 15 computers reveals the following data in years of service (X1, YEARS), whether the computer is a MAC or not (X2, 1=Mac computer, 0=not a Mac computer), and the total number of breakdowns (Y, BREAKDOWNS).
The results are found below.
YEARS MAC BREAKDOWNS
1 1 0 1 0 1 2 1 0
2 0 2 2 1 1 2 0 3
3 1 1 3 0 4 4 1 2
4 0 5 4 0 6 5 1 3
5 0 7 6 0 8
Correlations: YEARS, MAC, BREAKDOWNS YEARS MAC MAC -0.168 0.549 BREAKDOWNS 0.810 -0.664 0.000 0.007
Cell Contents: Pearson correlation P-Value
Regression Analysis: BREAKDOWNS versus YEARS, MAC The regression equation is BREAKDOWNS = 0.462 + 1.19 YEARS – 2.68 MAC. Predictor Coef SE Coef T P Constant 0.4625 0.4456 1.04 0.320 YEARS 1.1946 0.1169 10.22 0.000 MAC -2.6805 0.3470 -7.72 0.000
S = 0.649016 R-Sq = 94.2% R-Sq(adj) = 93.3%
Analysis of Variance Source DF SS MS F P Regression 2 82.679 41.339 98.14 0.000 Residual Error 12 5.055 0.421 Total 14 87.733 Predicted Values for New Observations New Obs Fit SE Fit 95% CI 95% PI 1 3.755 0.367 (2.956, 4.554) (2.131, 5.379)
Values of Predictors for New Observations New Obs YEARS MAC 1 5.00 1.00
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 multiple regression t-tests on βˆ1, βˆ2(use two tailed test with (a = .10). Interpret your results.
d. Predict the total number of breakdowns for a single computer that is a 5-year-old MAC. Use both a point estimate and the appropriate interval estimate. (Points : 31)
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