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(TCO E) A sample of 15 computers reveals the following data

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(TCO E) 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)

(a) It is BREAKDOWNS = 0.462 + 1.19 YEARS - 2.68 MAC

(b) R^2 = 94.2%. This means the predictor variables YEARS and MAC in the model are together able to account for about 94.2% of the variation in the BREAKDOWNS

(c) From the output, we see that the p- values for both β1 and β2 are < 0.10. This means both YEARS and MAC are significant predictors of BREAKDOWNS

(d) The predicted number of breakdowns for a 5-year old Mac is 3.755. The prediction interval is [2.131, 5.379]. This means the predicted number of breakdowns for a 5-year old Mac will lie between 2.131 and 5.379, 95% of the time.

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