In Example 3.11, we looked at quadratic and cubic polynomial models for the price of diamonds (TotalPrice)

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Question:

In Example 3.11, we looked at quadratic and cubic polynomial models for the price of diamonds (TotalPrice) based on the size (Carat). Another variable in the Diamonds datafile gives the Depth of the cut for each stone (as a percentage of the diameter). Run each of the models listed below, keeping track of the values for R2, adjusted R2, and which terms (according to the individual t-tests) are important in each model:

a. A quadratic model using Depth

b. A two-predictor model using Carat and Depth

c. A three-predictor model that adds interaction for Carat and Depth

d. A complete second-order model using Carat and Depth Among these four models as well as the quadratic and cubic models shown in Example 3.11, which would you recommend using for TotalPrice of diamonds? Explain your choice.Example 3.11

Carat	Color	Clarity	Depth	PricePerCt	TotalPrice
1.08	E	VS1	68.6	6693.3	7228.8
0.31	F	VVS1	61.9	3159	979.3
0.31	H	VS1	62.1	1755	544.1
0.32	F	VVS1	60.8	3159	1010.9
0.33	D	IF	60.8	4758.8	1570.4
0.33	G	VVS1	61.5	2895.8	955.6
0.35	F	VS1	62.5	2457	860
0.35	F	VS1	62.3	2457	860
0.37	F	VVS1	61.4	3402	1258.7
0.38	D	IF	60	5062.5	1923.8
0.38	E	VVS2	61.5	3496.5	1328.7
0.38	F	IF	61.8	4252.5	1616
0.39	D	VVS1	61.7	4158	1621.6
0.39	D	VS1	61.7	2983.5	1163.6
0.39	F	IF	61.3	3969	1547.9
0.39	F	VVS1	61.1	3422.3	1334.7
0.4	D	VVS2	59.7	3422.3	1368.9
0.4	D	VVS2	59.6	3422.3	1368.9
0.4	E	VS1	62.2	2937.6	1175
0.4	F	VVS2	60.8	2983.5	1193.4
0.4	F	VVS2	61.7	3121.2	1248.5
0.4	G	VVS1	61.7	3213	1285.2
0.41	E	IF	61.5	4039.2	1656.1
0.41	E	VVS1	60.2	3597.8	1475.1
0.41	F	VS1	61.7	2713.5	1112.5
0.41	F	VS2	61.5	2351.7	964.2
0.41	G	IF	61.1	3685.5	1511.1
0.42	D	VVS2	62.8	3422.3	1437.4
0.42	E	VVS1	59.7	3874.5	1627.3
0.43	G	VVS1	61.8	3307.5	1422.2
0.43	G	SI1	61.2	1984.5	853.3
0.44	G	VS2	62.5	2332.8	1026.4
0.46	D	VVS2	59.7	4036.5	1856.8
0.46	E	VS1	61.8	3591	1651.9
0.46	E	VS1	62	3334.5	1533.9
0.46	E	VS1	62.4	3334.5	1533.9
0.46	E	VS1	61.8	3334.5	1533.9
0.46	F	SI1	62	2268	1043.3
0.47	D	IF	62.4	6048	2842.6
0.47	D	VS1	62.5	3780	1776.6
0.47	F	VS2	61.1	2740.5	1288
0.48	E	VVS2	60.3	3969	1905.1
0.51	D	VVS2	60.1	5197.5	2650.7
0.51	D	VS1	61.4	4314.6	2200.5
0.51	E	VS1	60.4	4131	2106.8
0.52	E	VVS2	61.5	4681.8	2434.5
0.53	E	VS1	62	4131	2189.4
0.53	F	VVS2	61.4	4536	2404.1
0.54	D	VVS2	61.7	5197.5	2806.7
0.54	E	VVS2	61	4681.8	2528.2
0.54	F	VS1	61.7	4252.5	2296.4
0.55	E	VS1	61.5	4556.3	2505.9
0.55	E	VS2	61	3798.9	2089.4
0.55	F	VVS2	62.2	4860	2673
0.55	G	VVS1	61.2	4036.5	2220.1
0.57	D	VS1	61.2	4758.8	2712.5
0.58	E	VS2	61.8	3969	2302
0.58	F	VS2	61.5	3437.1	1993.5
0.58	G	VS2	61.2	3213	1863.5
0.59	E	VS1	61.7	4556.3	2688.2
0.59	E	VS2	61.9	3969	2341.7
0.59	E	VS2	62	4082.4	2408.6
0.59	G	VVS2	61.9	3773.3	2226.2
0.6	D	IF	60.6	7695	4617
0.6	D	VS2	61.6	4063.5	2438.1
0.6	E	VS1	61	3948.8	2369.3
0.6	E	SI1	63	3307.5	1984.5
0.6	E	SI3	61.4	1782	1069.2
0.6	F	VS2	61.6	3693.6	2216.2
0.6	J	SI1	60.4	1890	1134
0.61	D	VS2	62	4063.5	2478.7
0.61	E	VS1	59.7	3948.8	2408.7
0.61	E	VS2	60	3969	2421.1
0.61	E	VS2	61.4	3969	2421.1
0.62	E	VS1	62.2	3948.8	2448.2
0.62	H	VVS2	62.2	3499.2	2169.5
0.63	E	VS1	60.4	4374	2755.6
0.63	F	VVS1	60.8	4819.5	3036.3
0.64	D	SI1	60.6	3496.5	2237.8
0.65	D	IF	62.2	8208	5335.2
0.66	E	VS1	60	4374	2886.8
0.66	E	VS2	62.5	3969	2619.5
0.67	E	VS1	61.6	4434.8	2971.3
0.67	E	VS2	59.5	4252.5	2849.2
0.7	D	VS2	60.7	5467.5	3827.3
0.7	E	VS1	62.7	4738.5	3317
0.7	E	VS2	60.9	4613	3229.1
0.7	E	VS2	63	4131	2891.7
0.7	G	VS1	59.3	4212	2948.4
0.71	D	VS1	62.3	4932.9	3502.4
0.71	D	VS1	62.9	4932.9	3502.4
0.71	D	VS1	61.7	5089.5	3613.6
0.71	D	VS1	63.4	4854.6	3446.8
0.71	E	VS1	62.5	4738.5	3364.3
0.71	E	VS1	59.6	4592.7	3260.8
0.71	F	VVS2	62.6	5197.5	3690.2
0.71	F	VS1	61.7	4819.5	3421.9
0.71	G	VS2	61.7	4556.3	3234.9
0.72	D	VS1	62.7	5089.5	3664.4
0.72	D	VS2	62	4592.7	3306.7
0.72	D	VS2	60.2	5832	4199
0.72	D	VS2	61	4665.6	3359.2
0.72	E	SI1	62.9	4251.2	3060.8
0.72	F	VVS2	61.4	5197.5	3742.2
0.72	F	VS1	62.5	4819.5	3470
0.72	F	SI1	60.1	3861	2779.9
0.72	F	SI1	62	3979.8	2865.5
0.73	E	SI1	61.8	4124.3	3010.7
0.73	F	VVS2	62.2	5346	3902.6
0.73	F	SI1	59.3	3979.8	2905.3
0.73	G	VS2	62.7	4434.8	3237.4
0.73	I	VS2	62	3499.2	2554.4
0.74	D	VS2	62.4	4884.3	3614.4
0.74	E	VVS2	61.5	5734.8	4243.8
0.74	F	VS2	62.3	5184	3836.2
0.74	G	VVS1	61.1	5346	3956
0.75	G	VS1	62	4665.6	3499.2
0.76	D	VVS2	62.1	6318	4801.7
0.76	D	SI2	58.2	3979.8	3024.7
0.76	G	VS1	59.8	4730.4	3595.1
0.76	J	VS2	61.6	2754	2093
0.77	D	VS2	61.7	5686.2	4378.4
0.77	G	VS2	61.7	4252.5	3274.4
0.78	G	VVS2	62.1	5054.4	3942.4
0.78	H	VS1	62.2	4353.8	3395.9
0.8	D	SI1	62.4	4630.5	3704.4
0.8	D	SI2	59.8	4276.8	3421.4
0.8	E	VS1	63.8	5248.1	4198.5
0.8	E	VS2	62.6	4957.2	3965.8
0.8	E	SI1	62.9	4568.4	3654.7
0.8	F	VS1	62.2	5163.8	4131
0.8	F	VS2	62.4	4860	3888
0.8	G	VS1	62.7	4989.6	3991.7
0.8	G	VS2	62	4860	3888
0.8	H	VS1	61.6	4644	3715.2
0.8	H	VS2	61.6	4151.3	3321
0.81	D	VS2	62	5540.4	4487.7
0.81	E	VS2	62.5	5163.8	4182.6
0.81	E	SI1	59.1	4568.4	3700.4
0.81	E	SI1	62	4758.8	3854.6
0.81	E	SI1	62.1	4568.4	3700.4
0.81	E	SI1	62.1	4441.5	3597.6
0.82	E	SI1	60.9	4568.4	3746.1
0.82	I	VS2	61.6	3645	2988.9
0.82	I	SI1	61.9	3442.5	2822.9
0.85	J	VS2	62.8	3037.5	2581.9
0.88	E	SI1	62.3	4758.8	4187.7
0.88	G	VS1	60.6	5054.4	4447.9
0.9	F	VS1	61.9	5859	5273.1
0.9	F	SI1	62.2	5494.5	4945.1
0.9	G	VS1	61.4	5973.8	5376.4
0.9	G	VS1	62.1	5973.8	5376.4
0.9	G	VS1	60.8	6212.7	5591.4
0.9	G	SI1	58.9	5054.4	4549
0.9	I	IF	62.3	5292	4762.8
0.9	I	VS2	62	4471.2	4024.1
0.91	D	VS2	61.4	6844.5	6228.5
0.91	D	SI1	62.6	6176.3	5620.4
0.91	E	SI1	61.7	5481	4987.7
0.91	F	SI1	60.9	5568.8	5067.6
0.91	G	VS1	62.7	5734.8	5218.7
0.91	H	VS2	61.2	5248.8	4776.4
0.92	G	VVS2	61.3	6581.3	6054.8
0.93	D	IF	60.6	12757.5	11864.5
0.93	D	VS1	61.5	8147.3	7576.9
0.94	F	VVS2	59.7	7087.5	6662.3
0.94	F	SI2	62.4	4895.1	4601.4
0.97	E	SI2	61.8	4957.2	4808.5
1.01	E	VS1	60.4	9147.6	9239.1
1.01	F	VS2	61.9	7484.4	7559.2
1.02	E	SI1	61.1	6415.2	6543.5
1.02	F	VS1	61.9	9072	9253.4
1.02	G	VS1	60.6	7897.5	8055.5
1.02	G	VS1	60.3	7686.9	7840.6
1.03	F	VS1	60.6	9298.8	9577.8
1.04	E	SI1	60.8	6860.7	7135.1
1.04	G	VS1	63	6949.8	7227.8
1.07	F	VVS1	61.7	12117.6	12965.8
1.07	F	VVS1	61.8	12117.6	12965.8
1.07	G	VS2	62.3	7095.6	7592.3
1.08	F	SI1	59.7	6378.8	6889.1
1.09	F	VS2	60.1	8108.1	8837.8
1.09	G	VS2	61.3	7581.6	8263.9
1.1	G	VS1	59.5	8424	9266.4
1.1	G	VS2	60.7	7095.6	7805.2
1.1	H	VS1	61.9	6581.3	7239.4
1.11	F	SI1	60.1	5953.5	6608.4
1.11	G	VS1	61.7	8213.4	9116.9
1.11	G	VS1	61.3	8424	9350.6
1.11	H	VS1	61.6	7020	7792.2
1.13	E	VS1	60.7	9147.6	10336.8
1.13	E	VS2	60.5	8424	9519.1
1.13	F	VS1	61.7	9298.8	10507.6
1.15	G	VS1	62.1	8424	9687.6
1.16	H	VVS2	60.7	7079.4	8212.1
1.19	I	VS2	59.9	5366.3	6385.8
1.2	F	VS1	62.6	9185.4	11022.5
1.2	G	VS1	61.3	8739.9	10487.9
1.2	G	VS2	61.5	7776	9331.2
1.2	H	VS2	62	6779.7	8135.6
1.21	F	VS1	61.6	9412.2	11388.8
1.21	F	VS1	60.3	9412.2	11388.8
1.21	G	VS1	62.8	8634.6	10447.9
1.21	G	VS1	60.7	8634.6	10447.9
1.21	I	VS2	61.9	5509.4	6666.3
1.22	F	VS1	61	9298.8	11344.5
1.23	F	VS1	60.4	9525.6	11716.5
1.23	G	VVS1	61	10084.5	12403.9
1.23	I	VS1	61.2	5821.2	7160.1
1.24	E	VS1	62	10335.6	12816.1
1.24	F	VS2	61.6	8627.9	10698.5
1.25	G	VS1	62.1	8845.2	11056.5
1.25	G	VS1	61.7	8845.2	11056.5
1.26	F	VVS2	62.5	10405.8	13111.3
1.26	F	VS1	60.8	9639	12145.1
1.27	E	VS2	61.2	8640	10972.8
1.3	G	SI1	61.5	6372	8283.6
1.31	F	VVS1	61.8	12393	16234.8
1.31	G	VS1	62.1	9055.8	11863.1
1.31	G	VS1	60.4	8950.5	11725.2
1.31	G	SI1	60.6	6372	8347.3
1.31	H	VS2	60.9	7114.5	9320
1.31	H	VS2	61.8	7365.6	9648.9
1.33	E	VVS1	60.8	14158.8	18831.2
1.34	H	VVS2	60.5	8010.9	10734.6
1.37	G	VS1	61.7	9161.1	12550.7
1.41	I	VVS1	61.8	7365.6	10385.5
1.42	H	VS1	61.2	7897.5	11214.5
1.5	F	SI3	62.1	4050	6075
1.5	G	VS1	61.5	10187.1	15280.7
1.5	G	VS2	62.2	9563.4	14345.1
1.5	I	VS1	61.6	7588.4	11382.5
1.51	G	VVS2	60.7	11793.6	17808.3
1.51	H	SI2	62.2	5764.5	8704.4
1.51	I	VS2	62.8	7068.6	10673.6
1.54	F	VVS1	62	15525	23908.5
1.54	F	VS2	62.7	10395	16008.3
1.54	G	VS1	61.7	10584	16299.4
1.56	E	SI1	59.6	8505	13267.8
1.56	G	VS2	61.8	9563.4	14918.9
1.57	E	VS2	61.1	11232	17634.2
1.6	D	VS2	62.5	12213.5	19541.5
1.65	F	SI2	60.5	5589	9221.9
1.69	D	SI1	59.7	9416.3	15913.5
1.7	H	VS1	62.8	9077.4	15431.6
1.72	F	VS2	60.2	11880	20433.6
1.72	G	VS2	61.4	10805.4	18585.3
1.8	H	VS1	62.2	9963	17933.4
1.81	H	VS2	60	9278.6	16794.2
2.1	F	VS1	60.2	17367.8	36472.3
2.1	G	SI2	61.3	9396	19731.6
2.11	D	SI1	60.5	11340	23927.4
2.14	G	VS1	62.1	16023.2	34289.5
2.2	G	VS1	62.3	16409.3	36100.4
2.25	H	SI1	62	10405.8	23413.1
2.3	H	VS2	62.8	12213.5	28090.9
2.44	I	SI1	60.3	8964	21872.2
0.73	E	SI2	64.4	3044.3	2222.3
0.78	E	VS2	71.4	4131	3222.2
0.86	E	VS2	69.4	4475.3	3848.7
0.86	F	VS2	71.3	4212	3622.3
1.69	D	SI1	63.4	7749	13095.8
0.93	D	IF	62.6	8410.5	7821.8
1.35	D	VS1	68	6669	9003.2
0.5	E	SI1	68.3	2511	1255.5
0.52	E	SI1	74.1	2511	1305.7
0.54	E	VVS2	71.6	3321	1793.3
0.59	E	VS2	72.7	2754	1624.9
0.7	G	VS2	74.4	3948.8	2764.1
0.71	H	VS1	71.2	3773.3	2679
0.72	E	VS1	73.2	4650.8	3348.5
0.72	E	VS2	74.7	4268.7	3073.5
0.72	F	VS1	75.2	4475.3	3222.2
0.73	E	VS1	68.6	4650.8	3395.1
0.73	F	VS1	72.9	4131	3015.6
0.74	G	VS1	70.1	4082.4	3021
0.75	G	VS2	73.3	3948.8	2961.6
0.76	G	VVS1	73.8	4212	3201.1
0.77	F	VS2	68.7	4212	3243.2
0.77	H	VS1	73.8	3773.3	2905.4
0.8	F	VVS1	75.1	5197.5	4158
0.8	G	IF	73.3	4738.5	3790.8
0.8	G	VVS2	74.6	4387.5	3510
0.82	F	VVS1	79.2	4455	3653.1
0.83	E	VS1	69.9	4436.1	3682
0.9	E	VS1	71.8	5427	4884.3
0.98	E	VS1	74.9	5670	5556.6
1	D	VS2	71	6230.3	6230.3
1	F	VS1	72.4	5942.7	5942.7
1	F	VS1	71.5	6038.6	6038.6
1.01	F	VS1	75.5	6230.3	6292.6
1.01	H	VVS1	75	5018	5068.1
1.02	D	VVS1	77.8	8078.4	8240
1.02	G	VS1	76	5969.7	6089.1
1.04	F	VS1	72	6134.4	6379.8
1.05	D	VVS1	72.7	8553.6	8981.3
1.05	E	VS1	73.5	5994	6293.7
1.14	E	VS1	72.9	5994	6833.2
1.16	E	SI2	68.9	3442.5	3993.3
1.2	F	VS1	71.9	7188.8	8626.5
1.2	F	VS1	72.6	7188.8	8626.5
1.2	F	SI2	73.6	4860	5832
1.21	E	VS2	68.5	7265.7	8791.5
1.21	G	VS1	73.1	7055.1	8536.7
1.22	F	SI1	73	6264	7642.1
1.22	G	VVS2	73.6	7371	8992.6
1.22	G	VS2	69.9	6528.6	7964.9
1.22	H	VS1	74.5	5580.9	6808.7
1.23	G	VS2	71.4	6528.6	8030.2
1.24	F	VS1	73.7	7668	9508.3
1.24	G	VS1	72.6	7055.1	8748.3
1.24	G	VS1	70.9	7236	8972.6
1.24	G	VS2	74.6	6528.6	8095.5
1.25	D	SI1	69.2	6277.5	7846.9
1.25	E	VS1	72.9	7692.3	9615.4
1.25	H	VS1	70.9	5366.3	6707.8
1.25	H	VS2	75.8	5400	6750
1.26	D	VS2	76.1	7188.8	9057.8
1.3	F	SI1	75.1	6264	8143.2
1.3	G	IF	73.3	7695	10003.5
1.3	G	VS2	75	6696	8704.8
1.3	H	VVS1	71.7	5973.8	7765.9
1.32	F	VS1	74.3	7476.3	9868.7
1.37	H	IF	75	6719	9205
1.38	G	VVS1	73.8	7686.9	10607.9
1.42	D	VS1	72.9	8413.2	11946.7
1.52	D	VS2	75.5	8170.2	12418.7
1.52	G	VS2	75.7	7581.6	11524
1.7	G	VS2	73.3	7897.5	13425.8
1.71	F	VS2	76.4	8627.9	14753.6
1.71	G	VS2	70.3	8424	14405
1.77	E	VS2	73.1	9055.8	16028.8
1.79	F	VVS2	75.3	9963	17833.8
1.82	G	VS2	72	8213.4	14948.4
2.01	G	VS1	72.1	10189.8	20481.5
2.03	F	VS2	72.9	11340	23020.2
2.03	F	VS2	74.2	11037.6	22406.3
2.03	G	VS2	71.3	10428.8	21170.4
2.06	F	VVS1	70.5	14175	29200.5
2.33	G	VS2	74.2	10428.8	24299
2.53	G	IF	74.3	12757.5	32276.5
3.01	F	VVS1	71.5	17671.5	53191.2
3.01	G	VS1	72	14782.5	44495.3
3.17	F	VVS2	71.5	17313.8	54884.6
3.35	F	VVS2	75.2	16852.1	56454.4
1.52	F	SI2	63.4	4826.3	7335.9
0.8	H	VVS2	69.9	3645	2916
0.97	G	VVS1	70	5177.3	5021.9
1.25	G	VS2	71.9	5607.9	7009.9
1.52	F	VS1