Question

Question 4 (25pts) 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 in Q4data.xlsx. 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 a 95% 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.)

please show all the work. if you use excel please show the screenshots. Thank you !

Answer 1

(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.

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

The data is:

Costs	Age	Days	ICU
1430	21	1	0
19691	36	1	0
2730	34	2	1
2832	27	3	0
3164	35	1	0
3620	25	2	0
3938	28	2	0
4281	44	3	0
4718	28	1	1
48791	37	1	0
5129	29	4	1
5832	34	2	0
6260	47	4	0
6573	27	5	1
6719	29	2	0
6997	23	4	0
7653	26	1	0
9892	62	2	0
8970	31	5	2
8031	511	1	0
8046	45	4	0
8197	31	4	0
8502	20	5	1
9268	22	2	0
9503	43	8	0
10556	38	7	1
9694	37	4	0
10026	69	6	0
10654	24	1	0
10779	73	4	0
12132	35	3	0
12528	44	8	0
12485	28	8	1
12730	72	5	0
12938	34	7	0
13297	85	5	0
13603	66	10	2
13753	35	7	0
18507	52	12	3
17096	54	7	0
18290	42	12	2
18885	83	5	0
17301	48	8	3
20598	45	4	0
14621	39	10	0
28339	55	8	2
28823	65	15	3
22584	52	8	0
32477	48	15	4
34656	68	9	1