A sample of 15 computers reveals the following data in years

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 1, 2 (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.

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

Solution

Here dependent variable is BREAKDOWNS.

and the dependent variables are YEARS and MAC.

Analyze the above output to determine the multiple regression equation.

The regression equation is
BREAKDOWNS = 0.462 + 1.19 YEARS - 2.68 MAC.

b. Find and interpret the multiple index of determination (R-Sq).

In the output is,

R² = 94.2%

It expresses the it is the percentage of the response variable variation that is explained by a multiple linear model.

Perform the multiple regression t-tests on 1, 2 (use two tailed test with (a = .10). Interpret your results.

The test of hypothesis is,

H0 : 1=2=0 Vs H1 : at least one slope is not 0.

alpha = 0.10

From the output t-test statstic for YEARS and MAC are 10.22 and -7.72 respectively.

P-value for YEARS and MAC are 0.000

P-value < 0.10(alpha)

Reject H0 at 0.1 level of significance.

Atleast one slope is not 0.

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.

YEAR = 5, MAC = 1, BREAKDOWN = ?

BREAKDOWNS = 0.462 + 1.19 YEARS - 2.68 MAC.

= 0.462 + 1.19*5 - 2.68*1 = 3.732 approximately 4.

BREAKDOWNS = 4.