# A sample of 15 computers reveals the following data in years of service (X1, YEARS), whether the computer …

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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