Question

Please answer and explain a-d fully by using R as well. Thank you

R code below presents data concerning the need for hospital labor in n = 17 U.S. Navy Hospitals. Here, denotes average daily patient load, denotes monthly X-ray exposures,denotes monthly occupied bed days, denotes eligible population in the area (divided by . 1000), denotes average length of patients' stay in days, and y denotes monthly labor hours.

#R code

x1 <- c(15.57, 44.02, 20.42, 18.74, 49.2, 44.92, 55.48, 59.28, 94.39, 128.02, 96, 131.42, 127.21, 252.9, 409.2, 463.7, 510.22)

x2 <- c(2463, 2048, 3940, 6505, 5723, 11520, 5779, 5969, 8461, 20106, 13313, 10771, 15543, 36194, 34703, 39204, 86533)

x3 <- c(472.92, 1339.75, 620.25, 568.33, 1497.60, 1365.83, 1687.00, 1639.92, 2872.33, 3655.08, 2912.00, 3921.00, 3865.67, 7684.10, 12446.33, 14098.40, 15524.00)

x4 <- c(18, 9.5, 12.8, 36.7, 35.7, 24, 43.3, 46.7, 78.7, 180.5, 60.9, 103.7, 126.8, 157.7, 169.4, 331.4, 371.6)

x5 <- c(4.45, 6.92, 4.28, 3.9, 5.5, 4.6, 5.62, 5.15, 6.18, 6.15, 5.88, 4.88, 5.5, 7, 10.78, 7.05, 6.35)

y <- c(566.52, 696.82, 1033.15, 1603.62, 1611.37, 1613.27, 1854.17, 2160.55, 2305.58, 3503.93, 3571.89, 3741.40, 4026.52, 10343.81, 11732.17, 15414.94, 18854.45)

A good model describing the hospital labor needs data in is:

Note that this model includes only one of the three highly collinear independent variables

a. Build the model and show t statistics, prob-values, and variance inflation factors associated with the independent variables in this model.

b. Compare the above variance inflation factors with the variance inflation factors given in the model containing all five independent variables . Which model has less multicollinearity?

c. The variance inflation factor for (monthly occupied bed days) is . What does measures in the model?

d. Explain why, logically, (and thus ) VIF is larger for the five-independent-variable model than for the three-independent-variable model.

Answer 1

Answer:-

#R code

x1 <- c(15.57, 44.02, 20.42, 18.74, 49.2, 44.92, 55.48, 59.28, 94.39, 128.02, 96, 131.42, 127.21, 252.9, 409.2, 463.7, 510.22)

x2 <- c(2463, 2048, 3940, 6505, 5723, 11520, 5779, 5969, 8461, 20106, 13313, 10771, 15543, 36194, 34703, 39204, 86533)

x3 <- c(472.92, 1339.75, 620.25, 568.33, 1497.60, 1365.83, 1687.00, 1639.92, 2872.33, 3655.08, 2912.00, 3921.00, 3865.67, 7684.10, 12446.33, 14098.40, 15524.00)

x4 <- c(18, 9.5, 12.8, 36.7, 35.7, 24, 43.3, 46.7, 78.7, 180.5, 60.9, 103.7, 126.8, 157.7, 169.4, 331.4, 371.6)

x5 <- c(4.45, 6.92, 4.28, 3.9, 5.5, 4.6, 5.62, 5.15, 6.18, 6.15, 5.88, 4.88, 5.5, 7, 10.78, 7.05, 6.35)

y <- c(566.52, 696.82, 1033.15, 1603.62, 1611.37, 1613.27, 1854.17, 2160.55, 2305.58, 3503.93, 3571.89, 3741.40, 4026.52, 10343.81, 11732.17, 15414.94, 18854.45)