Linear regression for charges vs days in the hospital

Question

Discuss the below:

Q1. Do charges incurred by a patient depend on the type of insurance the patient has? If so, how? This is a hypothesis test where we could examine the average charges for patients with "managed care" vs. average charges for patients with "commercial" insurance.

Q2. Do charges incurred by patients depend on which doctor treats them? If so, how? We could create a confidence interval for each doctor, then see if the true population mean for each could be the same. If not, which doctor is most expensive?

Q3.What is an appropriate linear regression for Charges vs. Days in the hospital? Are Charges related to Days, Physician, and/or Payor? If so, how?

VARIABLE MEANING

DAYS is the number of days the patient spent in the hospital.

CHRGS is the total expenses charged to that patient

PHYS is a code identifying the physician

PAYOR indicated the type of insurance the patient carried:

1 for managed care and 0 for commercial insurance.

DAYS	CHRGS	PHYS	PAYOR
2	1701	10	0
2	3500	4	1
2	3165	10	0
1	1953	14	1
2	2607	2	1
2	2944	12	1
4	5063	2	1
2	2396	13	1
4	4903	2	1
2	2280	7	1
2	2939	7	1
3	3585	4	1
2	3073	13	1
2	2880	14	1
2	2358	10	0
3	3418	2	1
3	3604	2	0
3	3480	6	1
2	3306	10	0
3	3047	4	1
2	2157	11	1
2	2439	4	1
3	2647	11	1
2	1874	6	1
1	2139	10	1
2	2424	14	1
2	2450	12	1
2	2198	14	0
2	3355	10	1
2	2609	4	0
2	2324	2	1
2	2207	12	1
2	2649	11	0
3	3375	10	1
2	3906	6	1
3	4049	14	1
2	2564	13	1
2	2745	11	1
3	1254	6	1
2	2953	2	1
2	2334	7	1
2	2809	7	1
2	929	13	1
3	3464	14	1
2	3173	10	0
2	3034	14	1
2	3716	12	1
2	2137	6	1
3	3430	6	1
3	3041	6	1
2	2247	12	1
3	4357	12	1
2	3050	12	1
2	2779	12	1
2	2357	4	1
2	2620	7	1
3	3369	13	1
2	3090	7	1
4	6340	11	1
2	2900	10	1
3	3709	2	1
3	3503	4	1
2	2991	12	1
2	2941	14	1
2	2668	14	1
2	2138	2	1
2	2227	12	0
2	2838	10	0
2	2681	2	0
3	3945	7	1
2	2026	4	0
3	3160	10	1
2	3270	12	0
3	4146	6	1
2	3757	11	1
2	2435	7	1
2	2343	10	1
3	3932	2	1
2	2285	10	1
2	3001	14	1
2	1864	7	0
3	4711	12	1
3	3283	2	0
2	2592	7	1
1	2081	12	1
1	1791	14	1
2	3729	2	1
2	2117	10	1
3	4510	11	1
2	2017	7	1
2	3118	14	1
3	3392	2	1
2	1854	4	1
14	14898	2	1
3	3819	2	1
3	2644	4	1
3	2331	13	0
3	3492	11	1
2	2666	7	0
3	4248	2	1
3	2500	4	1
2	3112	10	1
3	2955	7	1
2	2761	14	1
2	1905	2	1
3	3394	10	1
2	3663	10	1
3	3059	6	1
2	2528	10	1
2	2823	2	1
6	6710	11	1
2	2543	13	1
3	2785	2	0
2	2589	12	0
2	3183	11	1
1	1806	10	1
2	3115	10	0
2	3204	7	1
2	2921	2	0
3	4933	2	0
2	4722	13	1
3	5633	13	1
2	2780	10	0
2	2798	4	1
3	2066	7	1
3	2494	11	1
3	2724	10	0
2	2352	11	0
1	1793	7	1
2	2629	4	1
2	3094	14	0
2	2804	2	0
2	2801	13	0
2	2638	7	1
2	2263	10	0
2	2449	11	0
2	2473	11	0
3	2864	6	1
2	2534	11	1
2	2550	10	1
2	3768	12	1
2	3194	10	0
1	2153	12	0
1	1840	7	0
2	2522	12	1
1	2145	12	1
2	2403	6	1
3	3287	2	1
2	2979	6	1
2	3182	7	0
2	2954	10	0
2	2158	11	0
2	3455	12	0
2	2367	14	1
3	2798	10	1
2	2408	11	1
2	2468	11	1
3	3081	12	1
2	2218	7	1
3	2133	11	0
4	5499	13	1
2	2251	12	1
2	2310	11	0
1	2220	11	0
2	2176	10	0
1	2048	2	1
2	2566	11	1
2	2450	11	0
2	2582	11	1
2	2612	7	0
2	2683	6	1
2	2827	14	0
2	3202	10	1
3	3779	10	1
2	2833	12	1
2	3458	10	0
1	2789	7	1
2	1590	7	1
3	3868	7	1
2	3077	12	1
2	3109	10	0
3	2697	4	0
2	3182	13	1
2	3034	6	1
1	2179	14	1
1	2178	7	1
3	4185	11	1
2	1567	10	1
2	2347	14	1
1	2268	10	1
3	3617	2	0
2	2858	10	1
2	2542	10	1
2	2665	7	1
2	2436	6	1
2	2392	12	1
2	2739	7	0
3	2181	12	0
2	2308	4	0
2	3800	13	0
2	2242	12	1
2	2314	7	1
1	1960	6	0
3	4183	11	1
1	1663	4	1
1	2070	7	0
3	2753	6	1
3	2209	6	0
3	3218	10	1
2	2419	13	0
3	3289	11	0
2	2222	4	1
1	2741	4	0
3	3454	10	1
2	3848	10	1
2	2292	7	0
2	2594	7	1
2	2378	6	1
1	902	7	0
3	2935	7	1
2	3230	6	1
2	2219	2	0
3	2687	12	1
2	1848	14	1
3	2891	4	0
2	2698	12	0
2	3032	7	0
1	2886	10	1
1	3381	2	0
2	2752	10	0
1	3675	13	1
2	2840	13	1
2	3105	13	0
2	2288	11	1
2	3128	14	0
2	2289	7	0
2	2602	10	0
2	2604	14	1
2	1023	12	0
1	1899	10	0
2	2334	10	1
2	2310	2	1
3	3636	6	1
2	4206	7	0
2	2414	12	1
2	2206	13	1
3	2907	2	1
2	3017	14	1
2	3050	14	1
2	1973	7	1
2	2692	10	1
3	2564	11	0
2	3693	10	1
2	2741	13	1
2	2888	2	1
2	3279	6	0
3	2873	7	1
2	2582	10	1
2	2640	2	0
1	2068	14	1
2	2123	10	0
3	3480	14	1
3	4475	6	0
2	2312	14	1
2	2898	4	1
3	3708	10	0
1	2078	10	0
2	2570	11	1
3	3639	14	1
2	4674	12	0
2	2534	14	0
2	2797	7	0
2	3139	12	0
3	3826	2	0
2	2067	10	0
2	2840	2	1
2	2465	12	1
1	1947	12	0
1	2167	7	0
2	2840	10	0
2	2711	6	1
2	3137	2	0
1	2955	2	0
2	2563	10	1
1	1924	4	1
1	2062	6	0
2	2663	13	0
1	2184	2	0
2	3064	10	1