Question

In: Statistics and Probability

Is there at least one independent variable with a non-Zero regression coefficient (is at least one...

Is there at least one independent variable with a non-Zero regression coefficient (is at least one independent variable predictive)?

Use the t statistics computed for each dependent variable.

Which independent variables are not shown to be significant predictors at the 95% level?

Compute a multiple regression using only independent variables that are statistically significant predictors of Self Esteem.

What is the new multiple regression equation?

What is the multiple standard error using only statistically significant independent variables?

What is the newly computed Coefficient of Multiple Determination?

City	County	State	Gender	Age	Months Unemployed	Wage at last job	Social support	Financial Hardship	SE	GSE	JSSE
Boise	Ada	ID	1	58	26.23	13	38	53	43	34	24
Parma	Canyon	ID	0	17	3.02	15	47	22	33	36	23
Vale	Malhuer	Or	0	18	3.25	8	40	44	38	36	27
Reno	Washoe	NV	0	19	2.36	12	21	37	38	35	18
Ontario	Malhuer	OR	1	20	2.33	9	50	21	46	45	12
Reno	Washoe	NV	1	20	0.71	11	41	57	40	44	30
Reno	Washoe	NV	1	20	2.92	16	50	46	47	45	30
Reno	Washoe	CA	0	23	0.71	9	50	50	50	45	29
Caldwell	Canyon	ID	0	24	0.62	22	50	40	50	45	30
Ontario	Malhuer	OR	0	25	7.29	9	40	46	44	44	27
Reno	Washoe	NV	0	25	6.83	18	40	52	38	32	28
Boise	Ada	ID	0	26	2.62	9	45	29	45	37	25
Reno	Washoe	NV	0	26	3.58	8	38	44	40	36	24
Ontario	Malhuer	OR	0	27	50.06	10	49	50	39	35	30
Reno	Wahoe	VN	0	27	4.73	11	39	55	43	40	27
Kuna	Ada	Id	1	27	26.75	16	21	59	25	26	16
Reno	Washoe	NV	1	29	59.30	10	46	47	32	32	21
Nampa	Canyon	ID	1	29	3.11	12	20	70	27	24	17
Nyssa	Malhuer	Or	1	30	3.28	8	27	42	45	42	29
Ontario	Malhuer	Or	0	30	2.46	23	34	45	29	33	22
Reno	Washoe	NV	1	30	4.79	20	41	45	41	16	19
Ontario	Malhuer	OR	1	31	17.32	8	39	41	35	35	19
Reno	Washoe	NV	0	31	28.86	14	36	48	35	27	17
Reno	Washoe	NV	0	31	8.31	26	50	44	48	45	29
boise	united states	id	0	31	7.82	12	27	59	33	45	30
Ontario	Malhuer	Or	0	32	13.44	24	40	38	40	34	21
Sparks	Washoe	NV	1	33	5.19	8	48	32	42	39	23
Reno	Washoe	NV	0	33	23.27	16	25	49	37	33	24
Nyssa	Malhuer	OR	1	34	0.32	14	46	50	31	26	26
Ontario	Malhuer	Or	1	35	2.85	14	31	47	36	33	20
Reno	Washoe	NV	1	36	11.56	14	30	50	30	37	17
boise	ada	id	0	36	12.98	13	46	42	36	30	20
Reno	Washoe	NV	0	37	3.74	11	50	63	50	40	30
Reno	Washoe	NV	1	37	3.08	15	50	68	13	13	30
Meridian	Ada	ID	0	38	12.65	15	47	34	48	36	25
Reno	Washoe	NV	0	38	17.91	12	32	51	31	26	19
Ontario	Malhuer	OR	0	39	2.13	9	32	53	35	29	25
Reno	Wahoe	NV	1	39	4.56	24	41	41	41	33	22
Sparks	Washoe	NV	1	41	2.26	9	50	66	50	38	23
Reno	Washoe	NV	0	41	6.27	8	33	46	38	34	13
Boise	Ada	ID	1	41	9.30	9	37	51	41	27	20
Parma	Canyon	ID	1	43	0.75	30	47	31	40	40	28
Sparks	Washoe	NV	1	44	3.81	15	39	35	31	24	25
nampa	canyon	id	1	44	11.60	9	49	51	44	43	25
Vale	Malhuer	Or	1	45	1.96	9	42	43	38	36	27
Reno	Washoe	NV	1	45	22.38	10	49	32	41	41	24
Meridian	Ada	ID	1	45	20.34	8	27	49	38	34	25
Reno	Washoe	NV	1	46	1.93	15	50	59	33	31	26
Ontario	Malhuer	Or	0	46	1.83	10	48	37	40	39	28
Reno	Washoe	NV	0	46	5.81	10	34	56	31	31	26
Ontario	Malhuer	OR	0	47	0.55	8	38	49	38	36	21
Nampa	Canyon	ID	1	47	46.25	12	38	60	20	20	19
Sparks	Washoe	NV	0	48	11.70	32	46	50	44	41	30
Ontario	Malhuer	Or	0	48	1.93	9	24	56	33	27	22
Reno	Washoe	NV	0	48	45.99	14	34	60	35	40	27
Reno	Washoe	NV	1	48	30.30	10	26	46	34	27	20
Reno	Washoe	NV	0	48	3.64	9	35	42	29	32	25
Reno	Washoe	NV	1	48	3.35	12	38	60	37	34	30
Boise	Ada	ID	1	48	5.81	11	35	66	22	33	21
Sparks	Washoe	NV	0	49	10.25	9	45	34	45	40	24
Ontario	Malhuer	OR	0	50	9.79	16	30	42	38	32	24
Sparks	Washoe	NV	1	50	11.86	9	46	62	30	41	28
Sparks	Washoe	NV	1	50	13.31	13	47	63	29	36	30
Vale	Malhuer	Or	1	50	2.59	17	45	46	49	45	30
Ontario	Malhuer	OR	0	51	9.36	9	39	44	42	42	20
Ontario	Malhuer	Or	0	52	4.27	15	50	62	37	27	21
Reno	Washoe	NV	1	52	7.75	20	50	51	47	39	30
Reno	Washoe	NV	1	52	28.86	14	32	42	34	33	25
Ontario	Malhuer	Or	0	53	0.78	17	41	38	41	36	27
Reno	Washoe	NV	0	53	23.27	11	32	55	26	27	18
Ontario	Malhuer	Or	0	53	1.96	9	18	56	29	28	20
Ontario	Malhuer	Or	1	53	20.61	9	35	57	27	28	22
Reno	Washoe	NV	0	53	2.79	8	38	51	38	36	22
Garden City	ADA	ID	1	53	11.47	10	27	52	44	31	25
Vale	Malhuer	OR	0	54	0.71	10	34	63	26	30	16
Sparks	Washoe	NV	1	54	10.25	9	23	70	36	36	21
Reno	Washoe	NV	1	54	3.54	9	12	60	38	34	28
Reno	Washoe	NV	0	54	2.65	13	10	42	40	33	18
Nyssa	Malhuer	Or	1	54	1.44	10	46	38	44	29	23
Reno	Washoe	NV	0	54	10.25	14	30	46	26	23	26
Sparks	Washoe	NV	0	55	0.95	10	35	40	40	34	25
Reno	Washoe	NV	1	55	12.95	19	30	45	38	38	28
Sparks	Washoe	NV	1	55	10.64	15	49	45	46	35	24
Ontario	Malhuer	Or	0	55	1.67	11	38	50	39	35	20
Boise	Ada	Id	1	55	8.87	18	36	55	29	32	21
Nampa	Canyon	ID	0	55	14.33	21	42	51	40	35	23
Vale	Malhuer	Or	0	56	2.75	8	32	50	42	34	30
Reno	Washoe	NV	0	56	12.25	17	48	59	48	43	28
Reno	Washoe	NV	1	56	21.92	16	37	58	44	38	25
Reno	Washoe	NV	1	56	22.71	21	45	60	41	39	26
Sun Valley	Washoe	NV	1	56	11.17	15	30	62	30	28	19
Boise	Ada	ID	1	56	6.96	19	43	47	32	36	27
Sparks	Washoe	NV	0	57	1.50	12	43	26	36	35	25
Reno	Washoe	NV	1	57	1.80	9	46	40	32	29	30
Reno	Washoe	NV	1	57	15.28	14	29	46	30	24	29
Ontario	Malhuer	Or	0	57	1.44	9	33	44	37	33	22
Nampa	Canyon	ID	0	57	139.91	8	38	49	38	35	25
Reno	Washoe	NV	0	57	3.64	10	36	49	43	37	29
Reno	Washoe	NV	1	57	65.35	17	30	32	38	33	14
Ontario	Mauhuer	Or	1	58	6.30	13	31	42	26	30	30
Reno	Washoe	NV	1	58	30.30	13	49	31	48	41	30
Caldwell, Id	Canyon	ID	1	59	7.88	15	43	44	50	41	29
Parma	Canyon	ID	0	60	1.80	9	47	56	23	22	18
Sparks	Washoe	NV	0	60	0.75	11	39	45	40	36	26
Reno	Washoe	NV	1	60	40.30	14	40	34	40	34	23
Sparks	Washoe	NV	0	61	4.27	26	44	58	40	42	28
Reno	Washoe	NV	0	61	4.92	18	30	39	30	28	30
Boise	ADA	Id	1	61	9.85	17	40	64	33	34	23
Reno	Washoe	NV	1	64	55.85	13	24	56	32	34	29
Sparks	Washoe	NV	0	64	1.27	8	37	50	45	37	30
Reno	Washoe	NV	1	64	23.89	14	44	60	44	41	27
Nampa	Canyon	ID	1	64	24.22	16	40	35	42	36	25
Reno	Washoe	NV	1	67	24.39	10	48	38	39	38	26
Ontario	Malhuer	Or	0	68	1.31	11	44	51	40	42	30
Reno	Washoe	NV	0	75	1.73	10	49	38	50	37	26
Sparks	Washoe	NV	0	87	1.04	12	48	33	45	36	19
Ontario	Malhuer	Or	0	121	17.61	14	40	45	40	32	20

Expert Solution

A smaller p value indicates that a variable is significant. In the above table, we can see that there are 2 independent variables that have p-value less than 0.05 and are thus significant.

So, there are two variables with Non Zero Regression Coefficient, viz. Financial Hardship and GSE.

All the other dependent variables, viz. Gender, Age, Months Unemployed, Wage at Last Job, Social Support and JSSE, are insignificant predictors at the 95% level as reflected in the above table.

Using only the significant predictors:

Thus, the new regression equation is;:

Y = 18.906 - .155*(Financial Hardship) + .76*(GSE)

The following table gives information about the multiple standard error and the coefficient of determination.

The multiple standard error when using only the two significant variables is 4.9907.

The coefficient of determination is a measure of how good fit is the model for the data and is given by R square. Here, the value is 0.535 indicating a moderate fit.

orchestra answered 2 years ago

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