Question

A hospital would like to develop a regression model to predict the total hospital bill for a patient based on the age of the patient (x1), his or her length of stay (x2), and the number of days in the hospital's intensive care unit(ICU) (x3). Data for these variables can be found below. Complete parts a through e below.

a) Construct a regression model using all three independent variables. (Round to the nearest whole number as needed.)

b) Interpret the meaning of the regression coefficients.

c) Predict the average hospital bill for a 69-year-old person hospitalized for ten days with no days spent in the ICU. (Round to the nearest dollar as needed.)

d) Construct a 95% confidence interval for the average hospital bill for the patient described in part c. (Round to the nearest dollar as needed.)

e) Construct a95% prediction interval for the average hospital bill for the patient described in part c, that is, a 69-year-old person hospitalized for ten days with no days spent in the ICU. (Round to the nearest dollar as needed.)

Below is the excel table given.

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55 X fox D E F G с Days 21 A B 1 Costs_($) Age 1430 3 1969 4 2730 ICU 1 0 N 36 1 0 2 1 5 2832 34 27 35 3 0 6 1 0 7 3164 3620 3938 25 2 0 8 28 2 0 ୨ 4281 44 3 0 1 1 10 11 28 37 1 0 12 29 4 2 1 0 13 34 14 47 4 0 4718 4879 5129 5832 6260 6573 6719 6997 7653 9892 15 5 1 2 16 17 18 27 29 23 26 0 0 4 1 0 19 2 0 62 311 20 5 2 8970 8031 21 51 1 0 22 8046 45 4 0 23 8197 31 4 ol

Answer 1

ANSWER:

For the given data

The Excel output is:

A1017 f D E F I - MS 35,49,45,597.9865 6,76,94,998.4744 F 5.24 А B с 1017 1018 Regression Analysis 1019 1020 R2 0.255 1021 Adjusted R 0.206 1022 R 0.505 1023 Std. Error 8227.697 1024 n 50 1025 k 3 1026 Dep. Var. Costs 1027 1028 ANOVA table 1029 Source SS df 1030 Regression 1,06,48,36,793.9596 3 1031 Residual 3,11,39,69,929.8204 46 1032 Total 4,17,88,06,723.7800 49 1033 1034 1035 Regression output 1036 variables coefficients std. error 1037 Intercept 6,043.0087 1038 7.9605 17.2334 1039 Days 1,146.8118 455.7147 1040 ICU 672.5956 1,632.0741 1041 1042 Predicted values for: Costs 1043 1044 Age Days ICU 1045 69 10 1046 p-value .0034 confidence interval 95% lower 95% upper t (df=46) p-value Age 0.462 2.517 .6463 -26.7284 42.6494 .0154 229.5058 2,064.1178 .6822 -2,612.5993 3,957.7904 0.412 Predicted 18,060.401 95% Confidence Interval lower upper 11,635.829 24,484.973 95% Prediction Interval lower upper Leverage 296.442 35,824.360 0.150 0

a)

y = 6043 + 8*x1 + 1147*x2 + 673*x3

b)

For every additional age of a patient, the bill will increase by 8.

For every additional length of stay of a patient, the bill will increase by 1147.

For every additional length of stay in ICU of a patient, the bill will increase by 673.

c)

y = 18060

d)

The 95% confidence interval is between $11636 and $24485.

e)

The 95% prediction interval is between $296 and $35824.

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