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

(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)
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Customer: replied 3 years ago.

After the quesion is answered. Thank you

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Customer: replied 3 years ago.
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Thanks.
Customer: replied 3 years ago.
Thanks
You are welcome.
Here they are ...

(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.