Question

Run a regression analysis and find a best model to predict White Speck count from cotton fiber properties given to you. Make sure to show all your steps on how you came up with the best model. Word or text file.

Harvdate date of cotton	Cotton fiber Length	Cotton fiber Strength	Short fiber content	Cotton fineness	Immature fiber content	Cotton trash count	Cotton dust count	Cotton nep count	y=White Specks
1	1.06	31.8	21.8	196	6.36	75	404	253	17.8
1	1.06	31.0	21.0	197	6.05	76	292	247	11.6
1	1.07	30.3	24.0	193	6.98	102	390	291	11.0
1	1.06	30.6	20.9	196	6.58	49	188	297	10.2
1	1.04	31.0	25.7	195	7.24	67	298	262	10.6
1	1.05	30.5	25.0	196	7.05	37	181	262	10.8
3	1.05	30.7	20.6	198	6.02	63	259	247	11.0
3	1.04	30.3	20.5	199	5.93	29	131	220	7.6
3	1.05	29.5	21.0	197	6.46	43	194	306	9.6
3	1.05	29.3	19.8	198	6.17	31	187	258	6.0
3	1.04	30.5	21.6	199	6.62	59	278	310	14.0
3	1.05	30.2	21.9	197	6.87	32	172	272	13.4
4	1.03	30.7	23.5	198	6.47	88	339	275	14.8
4	1.04	30.0	20.5	194	5.92	69	264	236	16.4
4	1.03	29.5	24.9	195	6.99	104	382	347	17.4
4	1.03	29.3	21.7	196	7.11	72	270	297	16.4
4	1.02	29.6	22.7	196	6.64	115	348	270	17.2
4	1.01	30.6	20.7	197	6.29	64	270	239	17.4
4	1.04	30.8	24.4	193	6.44	118	412	300	25.2
4	1.05	30.6	24.4	197	6.77	94	346	298	18.8
4	1.04	30.0	24.1	196	6.60	90	323	282	21.8
4	1.05	29.4	21.3	195	6.44	83	255	261	18.0
4	1.01	29.6	22.2	196	5.95	120	409	227	11.4
4	1.02	29.9	22.6	196	6.60	88	311	268	18.6
5	1.04	30.3	24.8	196	7.35	91	266	295	19.8
5	1.05	29.1	23.4	196	7.08	72	274	291	13.4
5	1.03	29.3	27.0	197	7.49	139	514	330	18.2
5	1.04	28.7	23.1	196	7.37	71	271	310	17.0
5	1.01	29.0	23.1	196	6.81	79	326	284	13.2
5	1.00	29.2	24.4	197	7.10	60	272	270	19.4
5	1.06	30.1	23.9	196	7.01	142	464	310	19.0
5	1.06	29.7	22.1	197	6.61	92	296	268	20.4
5	1.04	29.8	22.6	194	6.56	113	347	246	31.6
5	1.05	29.6	21.7	193	6.40	120	391	290	18.8
5	1.06	29.8	21.7	195	6.75	140	432	285	17.2
5	1.06	30.2	20.1	197	6.83	100	351	256	22.0
6	1.04	28.1	22.8	197	6.46	65	218	327	25.2
6	1.03	28.8	23.6	199	6.43	63	217	247	26.6
6	1.03	28.8	24.4	198	6.86	80	294	294	28.4
6	1.03	28.8	22.7	197	7.26	61	257	313	16.2
6	1.03	28.8	23.8	197	6.56	81	293	313	17.4
6	1.01	29.0	21.6	196	6.49	67	262	256	16.6
6	1.03	29.4	23.0	198	6.35	80	294	267	22.8
6	1.03	29.4	23.7	197	6.49	60	215	267	10.0
6	1.05	29.3	21.1	195	6.26	70	241	255	11.6
6	1.03	29.1	24.9	197	6.89	70	237	266	13.4
6	1.05	28.8	22.6	199	7.09	100	318	321	18.2
6	1.04	28.7	24.0	197	6.90	76	261	319	17.2
7	1.04	30.0	25.2	195	7.02	85	431	277	21.4
7	1.03	28.7	23.1	193	6.44	66	280	322	18.6
7	1.04	28.8	23.0	194	7.18	78	376	298	18.6
7	1.04	28.5	21.0	196	6.67	56	230	298	16.0
7	1.01	28.4	22.3	195	6.36	69	280	262	12.0
7	1.03	28.7	22.1	194	6.66	64	257	296	11.6
7	1.04	29.9	22.4	195	6.83	103	361	276	17.0
7	1.03	29.9	21.6	194	6.34	64	196	237	18.4
7	1.04	28.3	21.3	192	6.14	84	251	260	17.6
7	1.04	28.7	21.2	193	5.87	81	280	297	22.2
7	1.04	29.2	22.6	193	6.25	88	290	291	20.4
7	1.04	28.4	19.9	194	6.30	68	212	286	24.8

Answer 1

The regression output is:

	R²	0.358
	Adjusted R²	0.242
	R	0.598
	Std. Error	4.455
	n	60
	k	9
	Dep. Var.	y=White Specks
ANOVA table
Source	SS	df	MS	F	p-value
Regression	552.7251	9	61.4139	3.09	.0050
Residual	992.5443	50	19.8509
Total	1,545.2693	59
Regression output					confidence interval
variables	coefficients	std. error	t (df=50)	p-value	95% lower	95% upper	VIF
Intercept	-70.6480
Harvdate date of cotton	1.5150	0.5459	2.775	.0077	0.4186	2.6114	2.846
Cotton fiber Length	12.3279	49.7865	0.248	.8054	-87.6711	112.3270	1.619
Cotton fiber Strength	1.2766	1.3843	0.922	.3609	-1.5038	4.0570	3.713
Short fiber content	0.4694	0.5532	0.849	.4001	-0.6417	1.5805	2.269
Cotton fineness	0.0948	0.3752	0.253	.8015	-0.6588	0.8485	1.224
Immature fiber content	-0.9472	2.1974	-0.431	.6683	-5.3609	3.4664	2.241
Cotton trash count	0.1006	0.0530	1.900	.0632	-0.0057	0.2070	5.325
Cotton dust count	-0.0156	0.0184	-0.845	.4021	-0.0526	0.0215	6.071
Cotton nep count	0.0124	0.0301	0.411	.6828	-0.0481	0.0728	2.066

Since VIF of all independent variables is less than 10, we keep all the variables in the regression.

Now, let's do the backward elimination and remove the variable which is highly insignificant(high p-value).

We will remove Cotton fiber Length because it has the highest p-value = 0.8054.

Running the regression again, we get:

	R²	0.357
	Adjusted R²	0.256
	R	0.597
	Std. Error	4.414
	n	60
	k	8
	Dep. Var.	y=White Specks
ANOVA table
Source	SS	df	MS	F	p-value
Regression	551.5079	8	68.9385	3.54	.0025
Residual	993.7614	51	19.4855
Total	1,545.2693	59
Regression output					confidence interval
variables	coefficients	std. error	t (df=51)	p-value	95% lower	95% upper	VIF
Intercept	-57.9993
Harvdate date of cotton	1.4954	0.5351	2.795	.0073	0.4212	2.5697	2.786
Cotton fiber Strength	1.3786	1.3094	1.053	.2974	-1.2501	4.0072	3.384
Short fiber content	0.4193	0.5101	0.822	.4149	-0.6047	1.4434	1.965
Cotton fineness	0.0803	0.3672	0.219	.8278	-0.6569	0.8174	1.194
Immature fiber content	-0.8658	2.1526	-0.402	.6892	-5.1874	3.4557	2.191
Cotton trash count	0.1035	0.0512	2.021	.0486	0.0007	0.2063	5.073
Cotton dust count	-0.0165	0.0179	-0.921	.3613	-0.0524	0.0195	5.830
Cotton nep count	0.0149	0.0280	0.533	.5966	-0.0413	0.0711	1.824

Now, let's do the backward elimination and remove the variable which is highly insignificant(high p-value).

We will remove Cotton fineness because it has the highest p-value = 0.8278.

Running the regression again, we get:

	R²	0.356
	Adjusted R²	0.270
	R	0.597
	Std. Error	4.374
	n	60
	k	7
	Dep. Var.	y=White Specks
ANOVA table
Source	SS	df	MS	F	p-value
Regression	550.5762	7	78.6537	4.11	.0012
Residual	994.6931	52	19.1287
Total	1,545.2693	59
Regression output					confidence interval
variables	coefficients	std. error	t (df=52)	p-value	95% lower	95% upper	VIF
Intercept	-42.7089
Harvdate date of cotton	1.4823	0.5268	2.814	.0069	0.4251	2.5395	2.751
Cotton fiber Strength	1.3847	1.2970	1.068	.2906	-1.2179	3.9874	3.383
Short fiber content	0.4239	0.5050	0.839	.4051	-0.5895	1.4372	1.962
Immature fiber content	-0.7970	2.1099	-0.378	.7072	-5.0308	3.4368	2.144
Cotton trash count	0.1025	0.0506	2.028	.0477	0.0011	0.2040	5.035
Cotton dust count	-0.0168	0.0177	-0.947	.3478	-0.0523	0.0187	5.802
Cotton nep count	0.0146	0.0277	0.528	.6000	-0.0410	0.0702	1.820

Now, let's do the backward elimination and remove the variable which is highly insignificant(high p-value).

We will remove Immature fiber content because it has the highest p-value = 0.7072.

Running the regression again, we get:

Now, let's do the backward elimination and remove the variable which is highly insignificant(high p-value).

We will remove the Cotton nep count because it has the highest p-value = 0.6754.

Running the regression again, we get:

Now, let's do the backward elimination and remove the variable which is highly insignificant(high p-value).

We will remove the Cotton dust count because it has the highest p-value = 0.3527.

Running the regression again, we get:

​​​​​​​

Now, let's do the backward elimination and remove the variable which is highly insignificant(high p-value).

We will remove the Short fiber content​​​​​​​ because it has the highest p-value = 0.4831.

Running the regression again, we get:

​​​​​​​

Now, let's do the backward elimination and remove the variable which is highly insignificant(high p-value).

We will remove the Cotton fiber Strength​​​​​​​ because it has the highest p-value = 0.4368.

Running the regression again, we get:

The final model is:

​​​​​​​
Please give me a thumbs-up if this helps you out. Thank you!