Question

In what follows use any of the following tests/procedures: Regression, multiple regression, confidence intervals, one sided T-test or two sided T-test. All the procedures should be done with 5% P-value or 95% confidence interval.Some answers are approximated, choose the most appropriate answer. Open Cars04 data. SETUP: Is it reasonable to claim that cars with higher city MPG have also higher Highway MPG? Given the data your job is to help answer this question.

I. What test/procedure did you perform? (6.66 points)

a. One sided T-test

b. Two sided T-test

c. Regression

d. Confidence interval

II. Statistical interpretation? (6.66 points)

a. Since P-value is small we are confident that the slope is not zero.

b. Since P-value is small we are confident that the averages are different.

c. Since P-value is too large the test is inconclusive.

d. None of these.

III. Conclusion? (6.66 points)

a. Yes, we confirm that this was a reasonable claim.

b. No, we cannot confirm that this was a reasonable claim.

Vehicle Name	Hybrid	SuggestedRetailPrice	DealerCost	EngineSize	Cylinders	Horsepower	CityMPG	HighwayMPG	Weight	WheelBase	Length	Width
Chevrolet Aveo 4dr	0	11690	10965	1.6	4	103	28	34	2370	98	167	66
Chevrolet Aveo LS 4dr hatch	0	12585	11802	1.6	4	103	28	34	2348	98	153	66
Chevrolet Cavalier 2dr	0	14610	13697	2.2	4	140	26	37	2617	104	183	69
Chevrolet Cavalier 4dr	0	14810	13884	2.2	4	140	26	37	2676	104	183	68
Chevrolet Cavalier LS 2dr	0	16385	15357	2.2	4	140	26	37	2617	104	183	69
Dodge Neon SE 4dr	0	13670	12849	2	4	132	29	36	2581	105	174	67
Dodge Neon SXT 4dr	0	15040	14086	2	4	132	29	36	2626	105	174	67
Ford Focus ZX3 2dr hatch	0	13270	12482	2	4	130	26	33	2612	103	168	67
Ford Focus LX 4dr	0	13730	12906	2	4	110	27	36	2606	103	168	67
Ford Focus SE 4dr	0	15460	14496	2	4	130	26	33	2606	103	168	67
Ford Focus ZX5 5dr	0	15580	14607	2	4	130	26	33	2691	103	168	67
Honda Civic DX 2dr	0	13270	12175	1.7	4	115	32	38	2432	103	175	67
Honda Civic HX 2dr	0	14170	12996	1.7	4	117	36	44	2500	103	175	67
Honda Civic LX 4dr	0	15850	14531	1.7	4	115	32	38	2513	103	175	68
Hyundai Accent 2dr hatch	0	10539	10107	1.6	4	103	29	33	2255	96	167	66
Hyundai Accent GL 4dr	0	11839	11116	1.6	4	103	29	33	2290	96	167	66
Hyundai Accent GT 2dr hatch	0	11939	11209	1.6	4	103	29	33	2339	96	167	66
Hyundai Elantra GLS 4dr	0	13839	12781	2	4	138	26	34	2635	103	178	68
Hyundai Elantra GT 4dr	0	15389	14207	2	4	138	26	34	2635	103	178	68
Hyundai Elantra GT 4dr hatch	0	15389	14207	2	4	138	26	34	2698	103	178	68
Kia Optima LX 4dr	0	16040	14910	2.4	4	138	23	30	3281	106	186	72
Kia Rio 4dr manual	0	10280	9875	1.6	4	104	26	33	2403	95	167	66
Kia Rio 4dr auto	0	11155	10705	1.6	4	104	25	32	2458	95	167	66
Kia Spectra 4dr	0	12360	11630	1.8	4	124	24	32	2661	101	178	68
Kia Spectra GS 4dr hatch	0	13580	12830	1.8	4	124	24	32	2686	101	178	68
Kia Spectra GSX 4dr hatch	0	14630	13790	1.8	4	124	24	32	2697	101	178	68
Mini Cooper	0	16999	15437	1.6	4	115	28	37	2524	97	143	67
Nissan Sentra 1.8 4dr	0	12740	12205	1.8	4	126	28	35	2513	100	178	67
Nissan Sentra 1.8 S 4dr	0	14740	13747	1.8	4	126	28	35	2581	100	178	67
Pontiac Sunfire 1SA 2dr	0	15495	14375	2.2	4	140	24	33	2771	104	182	68
Saturn Ion1 4dr	0	10995	10319	2.2	4	140	26	35	2692	103	185	67
Saturn lon2 4dr	0	14300	13393	2.2	4	140	26	35	2692	103	185	67
Saturn lon3 4dr	0	15825	14811	2.2	4	140	26	35	2692	103	185	67
Saturn lon2 quad coupe 2dr	0	14850	13904	2.2	4	140	26	35	2751	103	185	68
Saturn lon3 quad coupe 2dr	0	16350	15299	2.2	4	140	26	35	2751	103	185	68
Scion xA 4dr hatch	0	12965	12340	1.5	4	108	32	38	2340	93	154	67
Suzuki Aeno S 4dr	0	12884	12719	2.3	4	155	25	31	2676	98	171	68
Suzuki Aerio LX 4dr	0	14500	14317	2.3	4	155	25	31	2676	98	171	68
Suzuki Forenza S 4dr	0	12269	12116	2	4	119	24	31	2701	102	177	68
Suzuki Forenza EX 4dr	0	15568	15378	2	4	119	22	30	2756	102	177	68
Toyota Corolla CE 4dr	0	14085	13065	1.8	4	130	32	40	2502	102	178	67
Toyota Corolla S 4dr	0	15030	13650	1.8	4	130	32	40	2524	102	178	67
Toyota Corolla LE 4dr	0	15295	13889	1.8	4	130	32	40	2524	102	178	67
Toyota Echo 2dr manual	0	10760	10144	1.5	4	108	35	43	2035	93	163	65
Toyota Echo 2dr auto	0	11560	10896	1.5	4	108	33	39	2085	93	163	65
Toyota Echo 4dr	0	11290	10642	1.5	4	108	35	43	2055	93	163	65
Buick Century Custom 4dr	0	22180	20351	3.1	6	175	20	30	3353	109	195	73
Chevrolet Impala 4dr	0	21900	20095	3.4	6	180	21	32	3465	111	200	73
Chevrolet Malibu 4dr	0	18995	17434	2.2	4	145	24	34	3174	106	188	70
Chevrolet Malibu LS 4dr	0	20370	18639	3.5	6	200	22	30	3297	106	188	70
Chevrolet Monte Carlo LS 2dr	0	21825	20026	3.4	6	180	21	32	3340	111	198	73
Chrysler PT Cruiser 4dr	0	17985	16919	2.4	4	150	22	29	3101	103	169	67
Chrysler PT Cruiser Limited 4dr	0	22000	20573	2.4	4	150	22	29	3105	103	169	67
Chrysler Sebring 4dr	0	19090	17805	2.4	4	150	22	30	3173	108	191	71
Chrysler Sebring Touring 4dr	0	21840	20284	2.7	6	200	21	28	3222	108	191	71
Dodge Intrepid SE 4dr	0	22035	20502	2.7	6	200	21	29	3469	113	204	75
Dodge Stratus SXT 4dr	0	18820	17512	2.4	4	150	21	28	3182	108	191	71
Dodge Stratus SE 4dr	0	20220	18821	2.4	4	150	21	28	3175	108	191	71
Ford Focus SVT 2dr	0	19135	17878	2	4	170	21	28	2750	103	168	67
Ford Taurus LX 4dr	0	20320	18881	3	6	155	20	27	3306	109	198	73
Ford Taurus SES Duratec 4dr	0	22735	20857	3	6	201	19	26	3313	109	198	73
Honda Accord LX 2dr	0	19860	17924	2.4	4	160	26	34	2994	105	188	71
Honda Accord EX 2dr	0	22260	20080	2.4	4	160	26	34	3047	105	188	71
Honda Civic EX 4dr	0	17750	16265	1.7	4	127	32	37	2601	103	175	68
Honda Civic Si 2dr hatch	0	19490	17849	2	4	160	26	30	2782	101	166	67
Honda Civic Hybrid 4dr manual (gas/electric)	1	20140	18451	1.4	4	93	46	51	2732	103	175	68
Honda Insight 2dr (gas/electric)	1	19110	17911	2	3	73	60	66	1850	95	155	67
Hyundai Sonata GLS 4dr	0	19339	17574	2.7	6	170	19	27	3217	106	187	72
Hyundai Sonata LX 4dr	0	20339	18380	2.7	6	170	19	27	3217	106	187	72
Kia Optima LX V6 4dr	0	18435	16850	2.7	6	170	20	27	3279	106	186	72
Mazda6 i 4dr	0	19270	17817	2.3	4	160	24	32	3042	105	187	70
Mercury Sable GS 4dr	0	21595	19848	3	6	155	20	27	3308	109	200	73
Mini Cooper S	0	19999	18137	1.6	4	163	25	34	2678	97	144	67
Nissan Altima S 4dr	0	19240	18030	2.5	4	175	21	26	3039	110	192	70
Nissan Sentra SE-R 4dr	0	17640	16444	2.5	4	165	23	28	2761	100	178	67
Oldsmobile Alero GX 2dr	0	18825	17642	2.2	4	140	24	32	2946	107	187	70
Pontiac Grand Am GT 2dr	0	22450	20595	3.4	6	175	20	29	3118	107	186	70
Pontiac Grand Prix GT1 4dr	0	22395	20545	3.8	6	200	20	30	3477	111	198	74
Pontiac Sunfire 1SC 2dr	0	17735	16369	2.2	4	140	24	33	2771	104	182	68
Saturn L300-2 4dr	0	21410	19801	3	6	182	20	28	3197	107	190	69
Subaru Impreza 2.5 RS 4dr	0	19945	18399	2.5	4	165	22	28	2965	99	174	69
Subaru Legacy L 4dr	0	20445	18713	2.5	4	165	21	28	3285	104	184	69
Suzuki Verona LX 4dr	0	17262	17053	2.5	6	155	20	27	3380	106	188	72
Toyota Camry LE 4dr	0	19560	17558	2.4	4	157	24	33	3086	107	189	71
Toyota Camry LE V6 4dr	0	22775	20325	3	6	210	21	29	3296	107	189	71
Toyota Camry Solara SE 2dr	0	19635	17722	2.4	4	157	24	33	3175	107	193	72
Toyota Camry Solara SE V6 2dr	0	21965	19819	3.3	6	225	20	29	3417	107	193	72
Toyota Prius 4dr (gas/electric)	1	20510	18926	1.5	4	110	59	51	2890	106	175	68
Volkswagen Golf GLS 4dr	0	18715	17478	2	4	115	24	31	2897	99	165	68
Volkswagen GTI 1.8T 2dr hatch	0	19825	18109	1.8	4	180	24	31	2934	99	168	68
Volkswagen Jetta GLS TDI 4dr	0	21055	19638	1.9	4	100	38	46	3003	99	172	68
Volkswagen New Beetle GLS 1.8T 2dr	0	21055	19638	1.8	4	150	24	31	2820	99	161	68
Acura RSX Type S 2dr	0	23820	21761	2	4	200	24	31	2778	101	172	68
Acura TSX 4dr	0	26990	24647	2.4	4	200	22	29	3230	105	183	69
Audi A4 1.8T 4dr	0	25940	23508	1.8	4	170	22	31	3252	104	179	70
BMW 325i 4dr	0	28495	26155	2.5	6	184	20	29	3219	107	176	69
Buick LeSabre Custom 4dr	0	26470	24282	3.8	6	205	20	29	3567	112	200	74
Buick Regal LS 4dr	0	24895	22835	3.8	6	200	20	30	3461	109	196	73
Buick Regal GS 4dr	0	28345	26047	3.8	6	240	18	28	3536	109	196	73
Chevrolet Impala LS 4dr	0	25000	22931	3.8	6	200	20	30	3476	111	200	73
Chevrolet Impala SS 4dr	0	27995	25672	3.8	6	240	18	28	3606	111	200	73
Chevrolet Malibu LT 4dr	0	23495	21551	3.5	6	200	23	32	3315	106	188	70
Chevrolet Monte Carlo SS 2dr	0	24225	22222	3.8	6	200	18	28	3434	111	198	73
Chrysler 300M 4dr	0	29865	27797	3.5	6	250	18	27	3581	113	198	74
Chrysler Concorde LX 4dr	0	24130	22452	2.7	6	200	21	29	3479	113	208	74
Chrysler Concorde LXi 4dr	0	26860	24909	3.5	6	232	19	27	3548	113	208	74
Chrvsler PT Cruiser GT 4dr	0	25955	24172	2.4	4	220	21	27	3217	103	169	67
Chrysler Sebring convertible 2dr	0	25215	23451	2.4	4	150	22	30	3357	106	194	64
Dodge Intrepid ES 4dr	0	24885	23058	3.5	6	232	18	27	3487	113	204	75
Ford Crown Victoria 4dr	0	24345	22856	4.6	8	224	17	25	4057	115	212	78
Ford Crown Victoria LX 4dr	0	27370	25105	4.6	8	224	17	25	4057	115	212	78
Honda Accord LX V6 4dr	0	23760	21428	3	6	240	21	30	3349	108	190	72
Honda Accord EX V6 2dr	0	26960	24304	3	6	240	21	30	3294	105	188	71
Hyundai XG350 4dr	0	24589	22055	3.5	6	194	17	26	3651	108	192	72
Hyundai XG350 L 4dr	0	26189	23486	3.5	6	194	17	26	3651	108	192	72
Infiniti G35 4dr	0	28495	26157	3.5	6	260	18	26	3336	112	187	69
Infiniti G35 Sport Coupe 2dr	0	29795	27536	3.5	6	280	18	26	3416	112	182	72
Jaguar X-Type 2.5 4dr	0	29995	27355	2.5	6	192	18	26	3428	107	184	70
Mercedes-Benz C230 Sport 2dr	0	26060	24249	1.8	4	189	22	30	3250	107	178	68
Mercedes-Benz C320 Sport 2dr	0	28370	26435	3.2	6	215	19	26	3430	107	178	68
Mercury Grand Marquis GS 4dr	0	24695	23217	4.6	8	224	17	25	4052	115	212	78
Mercury Grand Marquis LS Premium 4dr	0	29595	27148	4.6	8	224	17	25	4052	115	212	78
Mercury Sable LS Premium 4dr	0	23895	21918	3	6	201	19	26	3315	109	200	73
Mitsubishi Diamante LS 4dr	0	29282	27250	3.5	6	205	18	25	3549	107	194	70
Mitsubishi Galant GTS 4dr	0	25700	23883	3.8	6	230	18	26	3649	108	191	72
Nissan Altima SE 4dr	0	23290	21580	3.5	6	245	21	26	3197	110	192	70
Nissan Maxima SE 4dr	0	27490	25182	3.5	6	265	20	28	3473	111	194	72
Nissan Maxima SL 4dr	0	29440	26966	3.5	6	265	20	28	3476	111	194	72
Oldsmobile Alero GLS 2dr	0	23675	21485	3.4	6	170	20	29	3085	107	187	70
Pontiac Grand Prix GT2 4dr	0	24295	22284	3.8	6	200	20	30	3484	111	198	74
Subaru Legacy GT 4dr	0	25645	23336	2.5	4	165	21	28	3395	104	184	69
Subaru Outback Limited Sedan 4dr	0	27145	24687	2.5	4	165	20	27	3495	104	184	69
Subaru Outback H6 4dr	0	29345	26660	3	6	212	19	26	3610	104	184	69
Toyota Avalon XL 4dr	0	26560	23693	3	6	210	21	29	3417	107	192	72
Toyota Camry XLE V6 4dr	0	25920	23125	3	6	210	21	29	3362	107	189	71
Toyota Camry Solara SLE V6 2dr	0	26510	23908	3.3	6	225	20	29	3439	107	193	72
Volkswagen Jetta GLI VR6 4dr	0	23785	21686	2.8	6	200	21	30	3179	99	172	68
Volkswagen New Beetle GLS convertible 2dr	0	23215	21689	2	4	115	24	30	3082	99	161	68
Volkswagen Passat GLS 4dr	0	23955	21898	1.8	4	170	22	31	3241	106	185	69
Volvo S40 4dr	0	25135	23701	1.9	4	170	22	29	2767	101	178	68
Acura TL 4dr	0	33195	30299	3.2	6	270	20	28	3575	108	186	72
Audi A41.8T convertible 2dr	0	35940	32506	1.8	4	170	23	30	3638	105	180	70
Audi A4 3.0 4dr	0	31840	28846	3	6	220	20	28	3462	104	179	70
Audi A4 3.0 Quattro 4dr manual	0	33430	30366	3	6	220	17	26	3583	104	179	70
Audi A4 3.0 Quattro 4dr auto	0	34480	31388	3	6	220	18	25	3627	104	179	70
Audi A6 3.0 4dr	0	36640	33129	3	6	220	20	27	3561	109	192	71
Audi A6 3.0 Quattro 4dr	0	39640	35992	3	6	220	18	25	3880	109	192	71
BMW 325Ci 2dr	0	30795	28245	2.5	6	184	20	29	3197	107	177	69
BMW 325Ci convertible 2dr	0	37995	34800	2.5	6	184	19	27	3560	107	177	69
BMW 325xi 4dr	0	30245	27745	2.5	6	184	19	27	3461	107	176	69
BMW 330i 4dr	0	35495	32525	3	6	225	20	30	3285	107	176	69
BMW 330Ci 2dr	0	36995	33890	3	6	225	20	30	3285	107	176	69
BMW 330xi 4dr	0	37245	34115	3	6	225	20	29	3483	107	176	69
BMW 525i 4dr	0	39995	36620	2.5	6	184	19	28	3428	114	191	73
Buick LeSabre Limited 4dr	0	32245	29566	3.8	6	205	20	29	3591	112	200	74
Buick Park Avenue 4dr	0	35545	32244	3.8	6	205	20	29	3778	114	207	75
Cadillac CTS VVT 4dr	0	30835	28575	3.6	6	255	18	25	3694	113	190	71
Chrysler 300M Special Edition 4dr	0	33295	30884	3.5	6	255	18	27	3650	113	198	74
Chrysler Sebring Limited convertible 2dr	0	30950	28613	2.7	6	200	21	28	3448	106	194	69
Ford Crown Victoria LX Sport 4dr	0	30315	27756	4.6	8	239	17	25	4057	115	212	78
Infiniti G35 4dr	0	32445	29783	3.5	6	260	18	26	3677	112	187	69
Infiniti I35 4dr	0	31145	28320	3.5	6	255	19	26	3306	108	194	70
Jaguar X-Type 3.0 4dr	0	33995	30995	3	6	227	18	25	3516	107	184	70
Lexus ES 330 4dr	0	32350	28755	3.3	6	225	20	29	3460	107	191	71
Lexus IS 300 4dr manual	0	31045	27404	3	6	215	18	25	3255	105	177	68
Lexus IS 300 4dr auto	0	32415	28611	3	6	215	18	24	3285	105	177	68
Lincoln LS V6 Luxury 4dr	0	32495	29969	3	6	232	20	26	3681	115	194	73
Lincoln LS V6 Premium 4dr	0	36895	33929	3	6	232	20	26	3681	115	194	73
Mercedes-Benz C240 4dr	0	32280	30071	2.6	6	168	20	25	3360	107	178	68
Mercedes-Benz C240 4dr	0	33480	31187	2.6	6	168	19	25	3360	107	178	68
Mercedes-Benz C320 Sport 4dr	0	35920	33456	3.2	6	215	19	26	3430	107	178	68
Mercedes-Benz C320 4dr	0	37630	35046	3.2	6	215	20	26	3450	107	178	68
Mercury Grand Marquis LS Ultimate 4dr	0	30895	28318	4.6	8	224	17	25	4052	115	212	78
Mercury Marauder 4dr	0	34495	31558	4.6	8	302	17	23	4195	115	212	78
Saab 9-3 Arc Sport 4dr	0	30860	29269	2	4	210	20	28	3175	105	183	69
Saab 9-3 Aero 4dr	0	33360	31562	2	4	210	20	28	3175	105	183	69
Saab 9-5 Arc 4dr	0	35105	33011	2.3	4	220	21	29	3470	106	190	71
Saab 9-5 Aero 4dr	0	39465	37721	2.3	4	250	21	29	3470	106	190	71
Subaru Outback H-6 VDC 4dr	0	31545	28603	3	6	212	19	26	3630	104	184	69
Toyota Avalon XLS 4dr	0	30920	27271	3	6	210	21	29	3439	107	192	72
Volkswagen Passat GLX V6 4MOTION 4dr	0	33180	30583	2.8	6	190	19	26	3721	106	185	69
Volkswagen Passat W8 4MOTION 4dr	0	39235	36052	4	8	270	18	25	3953	106	185	69
Volvo S60 2.5 4dr	0	31745	29916	2.5	5	208	20	27	3903	107	180	71
Volvo S60 T5 4dr	0	34845	32902	2.3	5	247	20	28	3766	107	180	71
Volvo S60 R 4dr	0	37560	35382	2.5	5	300	18	25	3571	107	181	71
Volvo S80 2.9 4dr	0	37730	35542	2.9	6	208	20	28	3576	110	190	72
Volvo S80 2.5T 4dr	0	37885	35688	2.5	5	194	20	27	3691	110	190	72
Acura 3.5 RL 4dr	0	43755	39014	3.5	6	225	18	24	3880	115	197	72
Acura 3.5 RL w/Navigation 4dr	0	46100	41100	3.5	6	225	18	24	3893	115	197	72
Audi A4 3.0 convertible 2dr	0	42490	38325	3	6	220	20	27	3814	105	180	70
Audi A4 3.0 Quattro convertible 2dr	0	44240	40075	3	6	220	18	25	4013	105	180	70
Audi A6 2.7 Turbo Quattro 4dr	0	42840	38840	2.7	6	250	18	25	3836	109	192	71
Audi A6 4.2 Quattro 4dr	0	49690	44936	4.2	8	300	17	24	4024	109	193	71
Audi A8 L Quattro 4dr	0	69190	64740	4.2	8	330	17	24	4399	121	204	75
Audi S4 Quattro 4dr	0	48040	43556	4.2	8	340	14	20	3825	104	179	70
BMW 330Ci convertible 2dr	0	44295	40530	3	6	225	19	28	3616	107	177	69
BMW 530i 4dr	0	44995	41170	3	6	225	20	30	3472	114	191	73
BMW 545iA 4dr	0	54995	50270	4.4	8	325	18	26	3814	114	191	73
BMW 745i 4dr	0	69195	63190	4.4	8	325	18	26	4376	118	198	75
BMW 745Li 4dr	0	73195	66830	4.4	8	325	18	26	4464	123	204	75
Buick Park Avenue Ultra 4dr	0	40720	36927	3.8	6	240	18	28	3909	114	207	75
Cadillac Deville 4dr	0	45445	41650	4.6	8	275	18	26	3984	115	207	74
Cadillac Deville DTS 4dr	0	50595	46362	4.6	8	300	18	26	4044	115	207	74
Cadillac Seville SLS 4dr	0	47955	43841	4.6	8	275	18	26	3992	112	201	75
Infiniti M45 4dr	0	42845	38792	4.5	8	340	17	23	3851	110	197	70
Infiniti Q45 Luxury 4dr	0	52545	47575	4.5	8	340	17	23	3977	113	200	73
Jaguar S-Type 3.0 4dr	0	43895	40004	3	6	235	18	26	3777	115	192	72
Jaguar S-Type 4.2 4dr	0	49995	45556	4.2	8	294	18	28	3874	115	192	72
Jaguar S-Type R 4dr	0	63120	57499	4.2	8	390	17	24	4046	115	192	72
Jaguar Vanden Plas 4dr	0	68995	62846	4.2	8	294	18	28	3803	119	200	73
Jaguar XJ8 4dr	0	59995	54656	4.2	8	294	18	28	3803	119	200	73
Jaguar XJR 4dr	0	74995	68306	4.2	8	390	17	24	3948	119	200	73
Lexus GS 300 4dr	0	41010	36196	3	6	220	18	25	3649	110	189	71
Lexus GS 430 4dr	0	48450	42232	4.3	8	300	18	23	3715	110	189	71
Lexus LS 430 4dr	0	55750	48583	4.3	8	290	18	25	3990	115	197	72
Lincoln LS V8 Sport 4dr	0	40095	36809	3.9	8	280	17	24	3768	115	194	73
Lincoln LS V8 Ultimate 4dr	0	43495	39869	3.9	8	280	17	24	3768	115	194	73
Lincoln Town Car Signature 4dr	0	41815	38418	4.6	8	239	17	25	4369	118	215	78
Lincoln Town Car Ultimate 4dr	0	44925	41217	4.6	8	239	17	25	4369	118	215	78
Lincoln Town Car Ultimate L 4dr	0	50470	46208	4.6	8	239	17	25	4474	124	221	78
Mercedes-Benz C32 AMG 4dr	0	52120	48522	3.2	6	349	16	21	3540	107	178	68
Mercedes-Benz CL500 2dr	0	94820	88324	5	8	302	16	24	4085	114	196	73
Mercedes-Benz CL600 2dr	0	128420	119600	5.5	12	493	13	19	4473	114	196	73
Mercedes-Benz CLK320 coupe 2dr (convertible)	0	45707	41966	3.2	6	215	20	26	3770	107	183	69
Mercedes-Benz CLK500 coupe 2dr (convertible)	0	52800	49104	5	8	302	17	22	3585	107	183	69
Mercedes-Benz E320 4dr	0	48170	44849	3.2	6	221	19	27	3635	112	190	71
Mercedes-Benz E500 4dr	0	57270	53382	5	8	302	16	20	3815	112	190	71
Mercedes-Benz S430 4dr	0	74320	69168	4.3	8	275	18	26	4160	122	203	73
Mercedes-Benz S500 4dr	0	86970	80939	5	8	302	16	24	4390	122	203	73
Saab 9-3 Arc convertible 2dr	0	40670	38520	2	4	210	21	29	3480	105	182	69
Saab 9-3 Aero convertible 2dr	0	43175	40883	2	4	210	21	30	3700	105	182	69
Volvo C70 LPT convertible 2dr	0	40565	38203	2.4	5	197	21	28	3450	105	186	72
Volvo C70 HPT convertible 2dr	0	42565	40083	2.3	5	242	20	26	3450	105	186	72
Volvo S80 T6 4dr	0	45210	42573	2.9	6	268	19	26	3653	110	190	72

Answer 1

c. Regression

a. Since P-value is small we are confident that the slope is not zero.

a. Yes, we confirm that this was a reasonable claim.

Sum x	Sum y	Sum x^2	Sum y^2	Sum xy	N
5101.0000	6879.0000	118853.0000	208949.0000	46532.0000	48.0000

Corr coef, r =
{n*sum(XY)-sum(X)*sum(Y)}/{ sqrt(n*sum(x^2)-[sum(x)]^2) * sqrt(n*sum(y^2)-[sum(y)]^2) }
{48*46532-5101*6879}/{ sqrt(48*118853-[5101]^2) * sqrt(48*208949-[6879]^2) }
0.7838

Ho: correlation Coefficient is not significant. v/s H1: correlation Coefficient is significant

R= 0.7838
n= 48.0000

t = r*sqrt((n-2)/(1-r^2))
0.7838*SQRT((48-2)/(1-0.7838^2))
8.560

p-value
2*(1-P(T<|t|)
2*(1-P(T<abs(8.56018696646156))
T.DIST.2T(abs(8.56018696646156),48-2)
0.0000

With (t=8.56, p<5%), I reject the null hypothesis at 5% level of significance and conclude that correlation Coefficient is significant.

X	Y	X^2	Y^2	Xy
28	34	784	1156	952
28	34	784	1156	952
26	37	676	1369	962
26	37	676	1369	962
26	37	676	1369	962
29	36	841	1296	1044
29	36	841	1296	1044
26	33	676	1089	858
27	36	729	1296	972
26	33	676	1089	858
26	33	676	1089	858
32	38	1024	1444	1216
36	44	1296	1936	1584
32	38	1024	1444	1216
29	33	841	1089	957
29	33	841	1089	957
29	33	841	1089	957
26	34	676	1156	884
26	34	676	1156	884
26	34	676	1156	884
23	30	529	900	690
26	33	676	1089	858
25	32	625	1024	800
24	32	576	1024	768
24	32	576	1024	768
24	32	576	1024	768
28	37	784	1369	1036
28	35	784	1225	980
28	35	784	1225	980
24	33	576	1089	792
26	35	676	1225	910
26	35	676	1225	910
26	35	676	1225	910
26	35	676	1225	910
26	35	676	1225	910
32	38	1024	1444	1216
25	31	625	961	775
25	31	625	961	775
24	31	576	961	744
22	30	484	900	660
32	40	1024	1600	1280
32	40	1024	1600	1280
32	40	1024	1600	1280
35	43	1225	1849	1505
33	39	1089	1521	1287
35	43	1225	1849	1505
20	30	400	900	600
21	32	441	1024	672
24	34	576	1156	816
22	30	484	900	660
21	32	441	1024	672
22	29	484	841	638
22	29	484	841	638
22	30	484	900	660
21	28	441	784	588
21	29	441	841	609
21	28	441	784	588
21	28	441	784	588
21	28	441	784	588
20	27	400	729	540
19	26	361	676	494
26	34	676	1156	884
26	34	676	1156	884
32	37	1024	1369	1184
26	30	676	900	780
46	51	2116	2601	2346
60	66	3600	4356	3960
19	27	361	729	513
19	27	361	729	513
20	27	400	729	540
24	32	576	1024	768
20	27	400	729	540
25	34	625	1156	850
21	26	441	676	546
23	28	529	784	644
24	32	576	1024	768
20	29	400	841	580
20	30	400	900	600
24	33	576	1089	792
20	28	400	784	560
22	28	484	784	616
21	28	441	784	588
20	27	400	729	540
24	33	576	1089	792
21	29	441	841	609
24	33	576	1089	792
20	29	400	841	580
59	51	3481	2601	3009
24	31	576	961	744
24	31	576	961	744
38	46	1444	2116	1748
24	31	576	961	744
24	31	576	961	744
22	29	484	841	638
22	31	484	961	682
20	29	400	841	580
20	29	400	841	580
20	30	400	900	600
18	28	324	784	504
20	30	400	900	600
18	28	324	784	504
23	32	529	1024	736
18	28	324	784	504
18	27	324	729	486
21	29	441	841	609
19	27	361	729	513
21	27	441	729	567
22	30	484	900	660
18	27	324	729	486
17	25	289	625	425
17	25	289	625	425
21	30	441	900	630
21	30	441	900	630
17	26	289	676	442
17	26	289	676	442
18	26	324	676	468
18	26	324	676	468
18	26	324	676	468
22	30	484	900	660
19	26	361	676	494
17	25	289	625	425
17	25	289	625	425
19	26	361	676	494
18	25	324	625	450
18	26	324	676	468
21	26	441	676	546
20	28	400	784	560
20	28	400	784	560
20	29	400	841	580
20	30	400	900	600
21	28	441	784	588
20	27	400	729	540
19	26	361	676	494
21	29	441	841	609
21	29	441	841	609
20	29	400	841	580
21	30	441	900	630
24	30	576	900	720
22	31	484	961	682
22	29	484	841	638
20	28	400	784	560
23	30	529	900	690
20	28	400	784	560
17	26	289	676	442
18	25	324	625	450
20	27	400	729	540
18	25	324	625	450
20	29	400	841	580
19	27	361	729	513
19	27	361	729	513
20	30	400	900	600
20	30	400	900	600
20	29	400	841	580
19	28	361	784	532
20	29	400	841	580
20	29	400	841	580
18	25	324	625	450
18	27	324	729	486
21	28	441	784	588
17	25	289	625	425
18	26	324	676	468
19	26	361	676	494
18	25	324	625	450
20	29	400	841	580
18	25	324	625	450
18	24	324	576	432
20	26	400	676	520
20	26	400	676	520
20	25	400	625	500
19	25	361	625	475
19	26	361	676	494
20	26	400	676	520
17	25	289	625	425
17	23	289	529	391
20	28	400	784	560
20	28	400	784	560
21	29	441	841	609
21	29	441	841	609
19	26	361	676	494
21	29	441	841	609
19	26	361	676	494
18	25	324	625	450
20	27	400	729	540
20	28	400	784	560
18	25	324	625	450
20	28	400	784	560
20	27	400	729	540
18	24	324	576	432
18	24	324	576	432
20	27	400	729	540
18	25	324	625	450
18	25	324	625	450
17	24	289	576	408
17	24	289	576	408
14	20	196	400	280
19	28	361	784	532
20	30	400	900	600
18	26	324	676	468
18	26	324	676	468
18	26	324	676	468
18	28	324	784	504
18	26	324	676	468
18	26	324	676	468
18	26	324	676	468
17	23	289	529	391
17	23	289	529	391
18	26	324	676	468
18	28	324	784	504
17	24	289	576	408
18	28	324	784	504
18	28	324	784	504
17	24	289	576	408
18	25	324	625	450
18	23	324	529	414
18	25	324	625	450
17	24	289	576	408
17	24	289	576	408
17	25	289	625	425
17	25	289	625	425
17	25	289	625	425
16	21	256	441	336
16	24	256	576	384
13	19	169	361	247
20	26	400	676	520
17	22	289	484	374
19	27	361	729	513
16	20	256	400	320
18	26	324	676	468
16	24	256	576	384
21	29	441	841	609
21	30	441	900	630
21	28	441	784	588
20	26	400	676	520
19	26	361	676	494