Question

nasal length	nasal width
609	241
629	222
620	233
564	207
645	247
493	189
606	226
660	240
630	215
672	231
778	263
616	220
727	271
810	284
778	279
823	272
755	268
710	278
701	238
803	255
855	308
838	281
830	288
864	306
635	236
565	204
562	216
580	225
596	220
597	219
636	201
559	213
615	228
740	234
677	237
675	217
629	211
692	238
710	221
730	281
763	292
686	251
717	231
737	275
816	275

In the kangaroo noses tab in the data file, We have data on the nasal length and width of grey kangaroos in mm. Use this data to complete the following exercises.

a) Run a regression and report your findings with nasal length as the dependent variable and nasal width as the independent variable, i.e. length = b0 + b1 × width

b) Interpret the estimate for b1.

c) Test the hypothesis that the ?1 coefficient is equal to 1.

d) Construct a 95% confidence interval for the b0 coefficient.

Answer 1

	nasal length	nasal width	(X-Mx)^2	(Y-My)^2	(X-Mx)(Y-My)	Y'	(Y-Y')^2
	609	241	6146.56	9.957531	247.3956	221.6067	376.0983
	629	222	3410.56	490.8686	1293.884	227.359	28.71881
	620	233	4542.76	124.4464	751.8844	224.7705	67.72497
	564	207	15227.56	1380.535	4584.996	208.6642	2.769526
	645	247	1797.76	8.090864	-120.604	231.9608	226.1778
	493	189	37791.36	3042.135	10722.24	188.2437	0.571973
	606	226	6625.96	329.6242	1477.862	220.7439	27.62649
	660	240	750.76	17.26864	113.8622	236.275	13.8758
	630	215	3294.76	850.0464	1673.529	227.6466	159.9366
	672	231	237.16	173.0686	202.5956	239.7263	76.14875
	778	263	8208.36	355.1131	1707.307	270.2132	52.03078
	616	220	5097.96	583.4909	1724.707	223.62	13.10464
	727	271	1568.16	720.6242	1063.04	255.545	238.8569
	810	284	15030.76	1587.58	4884.929	279.4168	21.00543
	778	279	8208.36	1214.135	3156.907	270.2132	77.20722
	823	272	18387.36	775.3131	3775.707	283.1558	124.4517
	755	268	4569.76	568.5575	1611.884	263.5982	19.37627
	710	278	510.76	1145.446	764.8844	250.6556	747.7165
	701	238	184.96	37.89086	-83.7156	248.0671	101.3462
	803	255	13363.36	117.602	1253.618	277.4035	501.9188
	855	308	28089.76	4076.113	10700.33	292.3594	244.6287
	838	281	22680.36	1357.513	5548.773	287.47	41.86062
	830	288	20334.76	1922.335	6252.218	285.1691	8.014112
	864	306	31187.56	3824.735	10921.73	294.9479	122.1489
	635	236	2745.76	66.51309	427.3511	229.0847	47.82182
	565	204	14981.76	1612.469	4915.04	208.9518	24.52034
	562	216	15725.16	792.7353	3530.707	208.089	62.58448
	580	225	11534.76	366.9353	2057.307	213.266	137.6871
	596	220	8353.96	583.4909	2207.818	217.8678	4.54634
	597	219	8172.16	632.802	2274.062	218.1554	0.713353
	636	201	2641.96	1862.402	2218.196	229.3723	804.9863
	559	213	16486.56	970.6686	4000.373	207.2261	33.3376
	615	228	5241.76	261.002	1169.662	223.3324	21.7863
	740	234	2766.76	103.1353	-534.182	259.284	639.2789
	677	237	108.16	51.20198	74.41778	241.1644	17.34212
	675	217	153.76	737.4242	336.7289	240.5892	556.4486
	629	211	3410.56	1099.291	1936.284	227.359	267.6167
	692	238	21.16	37.89086	-28.3156	245.4786	55.92905
	710	221	510.76	536.1798	-523.316	250.6556	879.4543
	730	281	1814.76	1357.513	1569.573	256.4078	604.7742
	763	292	5715.36	2289.091	3617.04	265.8991	681.2596
	686	251	1.96	46.84642	-9.58222	243.7529	52.52048
	717	231	876.16	173.0686	-389.404	252.6689	469.5404
	737	275	2460.16	951.3798	1529.884	258.4211	274.859
	816	275	16537.96	951.3798	3966.596	281.1425	37.73038
Mean	687.4	244.1556
Sum	30933	10987	377508.8	40195.91	108576.2	10987	8968.053

a) Y'=b0+b1*Width

b) To interpret, for every additonal unit of input output value increases by 0.287612 units.

c)

To test hypothesis:

and

Df= n-2= 43

The test statistic:

P-value= 0.000

The test statistic is significant and rejects H0 at coefficient value equal to 1. THere is insufficient evidence to support the claim that the coeffciient value is equal to 1.

d) 95% Confidence interval for b0:

t critical: