PROBLEM 1. (Weight 50 Points). The data below represents the need for labor in 16 U.S. Navy hospitals, where: y = monthly labor hours required

X1 = monthly x-ray exposures

X2 = monthly occupied bed days

X3 = average length of patient stay ( in days)

Monthly Labor Hrs X-Ray exposures Occupied Bed Days Length of Stay

566.2 2463 472.92 4.45

696.82 2048 1339.75 6.92

1033.15 3940 620.25 4.28

1603.62 6505 568.33 3.90

1611.37 5723 1497.6 5.50

1613.27 11520 1365.83 4.60

1854.17 5779 1687.00 5.62

2160.55 5969 1639.92 5.15

2305.58 8461 2872.33 6.18

3503.93 20106 3655.08 6.15

3571.89 13313 2912.00 5.88

3741.40 10771 3921.00 4.88

4026.52 15543 3865.67 5.50

11732.17 34703 12446.33 10.78

15414.94 39204 14098.40 7.05

18854.45 86533 15524.00 6.35

a. Find and interpret b0, b1, b2 and b3.

b. Forecast Labor hours, for XRay = 56,194, BedDays = 14,077.88 and LengthStay = 6.89.

c. Report R-Sq and Adj R-SQ. Explain there differences and explain their meaning in the context of this problem.

d. Calculate the F-value. Verify this value on your printout.

e. Test the entire Model for significance. Let alpha equal .05.

f. Test the entire Model for significance. Let alpha equal .01.

Problem 2. (Weight 15 points) Using the data from #1 above:

1. Find the t statistics for testing \({{H}_{0}}:{{B}_{j}}=0\) vs. \({{H}_{a}}:{{B}_{j}}\ne 0\), and report their values. Show how these t values were calculated.

2. Using these t values test each independent variable separately; i.e. test

Ho: B1 = 0 vs. Ha: B1 not equal to 0 AND Ho: B2 = 0 vs Ha: B2 not equal to 0 AND

Ho: B3 = 0 vs. Ha: B3 not equal to 0. Let alpha =.05.

3. Find the p-values for the two different test you completed in 2.2. Using

these p-values determine the significance of the independent variables for

alphas = .1.,.05, .01 and .001. What can you conclude about the

significance of the independent variables?

PROBLEM 3 (Weight 35 pts). A certain type of cable was advertised as having a breaking strength of 1000 pounds. A test of 64 pieces of this cable was conducted and the mean breaking strength of this sample was 960 pounds with a sample standard deviation of 45 pounds. Conduct a two-tail hypotheses test at alpha = .05 to determine if this sample data provides sufficient evidence to indicate that the cable is as strong as advertised.

PROBLEM 4 (Weight 15 pts). Conduct a 95% confidence interval on the sample data in Problem 4 above.

PROBLEM 5 (Weight 10 Points). Define Alpha (for a hypothesis test) [Alpha (for a hypothesis test)].

PROBLEM 6 (Weight 15 points).

a) Define multicollinearity.

b) Explain the R² method of telling if multicollinearity is a problem for this regression. How can

one easily determine if multicollinearity is a problem using Minitab. This is a rule of thumb.

c) How do you correct for multicollinearity?

PROBLEM 7 (Weight 10 Points).

a) When is autocorrelation potentially a problem?

b) How do you check for it?

c) How do you correct for it?

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