Question

Test a model that tries to explain differences in BMI based on parents' average BMI, a person's age, number of weekly hours of exercise, and the number of times a person eats outside.

Which independent variable (IV) does not explain variability in a person's BMI? Explain.

Observation	BMI	Average parents' BMI	Age	Weekly Exercise	Number of times eating outside
1	24	28	34	4	3
2	26	33	23	3	4
3	30	30	56	0	3
4	32	28	45	1	4
5	27	25	65	2	2
6	34	38	34	0	6
7	19	22	54	6	0
8	22	28	65	6	0
9	25	30	35	4	3
10	34	37	24	0	6
11	30	35	19	0	6
12	27	30	24	1	5
13	29	25	23	0	5
14	34	30	32	0	6
15	19	24	54	5	0
16	25	24	36	4	3
17	28	25	52	3	3
18	19	25	65	4	0
19	25	30	34	2	3
20	30	28	54	1	5
21	31	29	65	1	5
22	16	15	35	7	0
23	19	20	23	6	0
24	26	25	56	3	2
25	34	28	45	0	6
26	33	39	65	0	4
27	29	37	34	1	4
28	32	35	32	0	6
29	22	27	54	5	0
30	27	30	36	3	2
31	24	22	52	4	1

Answer 1

Solution:

Here our Dependent variable(Y) = BMI

And Independent Variables :

X1=Average parents BMI

X2=Age

X3=Weekly Exercise

X4=Number of times eating outside.

Here , we will perform Multiple Regression in SPSS.

Our Entered data :

Case Summariesa
	Observation	Y	X1	X2	X3	X4
	1	24	28	34	4	3
	2	26	33	23	3	4
	3	30	30	56	0	3
	4	32	28	45	1	4
	5	27	25	65	2	2
	6	34	38	34	0	6
	7	19	22	54	6	0
	8	22	28	65	6	0
	9	25	30	35	4	3
	10	34	37	24	0	6
	11	30	35	19	0	6
	12	27	30	24	1	5
	13	29	25	23	0	5
	14	34	30	32	0	6
	15	19	24	54	5	0
	16	25	24	36	4	3
	17	28	25	52	3	3
	18	19	25	65	4	0
	19	25	30	34	2	3
	20	30	28	54	1	5
	21	31	29	65	1	5
	22	16	15	35	7	0
	23	19	20	23	6	0
	24	26	25	56	3	2
	25	34	28	45	0	6
	26	33	39	65	0	4
	27	29	37	34	1	4
	28	32	35	32	0	6
	29	22	27	54	5	0
	30	27	30	36	3	2
	31	24	22	52	4	1

To perform Multiple regression in SPSS

Steps : Analyse ---Regression---Linear---Dependent(Y)---Independent(X1,X2,X3,X4)---method(stepwise)---Ok ---Statistics(tick estimates,model fit,descriptive)--- Save(tick unstandarised predicted and unstandardised residual)---Ok

Descriptive Statistics
	Mean	Std. Deviation	N
Y	26.84	5.139	31
X1	28.45	5.501	31
X2	42.74	14.944	31
X3	2.45	2.234	31
X4	3.13	2.187	31

Model Summaryd
Model	R	R Square	Adjusted R Square	Std. Error of the Estimate	Change Statistics
					R Square Change	F Change	df1	df2	Sig. F Change
1	.931a	.868	.863	1.902	.868	190.048	1	29	.000
2	.944b	.890	.882	1.762	.023	5.791	1	28	.023
3	.956c	.914	.904	1.589	.024	7.408	1	27	.011

ANOVAa
Model		Sum of Squares	df	Mean Square	F	Sig.
1	Regression	687.314	1	687.314	190.048	.000b
	Residual	104.880	29	3.617
	Total	792.194	30
2	Regression	705.289	2	352.645	113.620	.000c
	Residual	86.904	28	3.104
	Total	792.194	30
3	Regression	723.999	3	241.333	95.550	.000d
	Residual	68.195	27	2.526
	Total	792.194	30

from the above anova table all the model 1,2,3 are  significant to explain change in dependent variable Y i.e. BMI.

Coefficientsa
Model		Unstandardized Coefficients		Standardized Coefficients	t	Sig.
		B	Std. Error	Beta
1	(Constant)	32.092	.512		62.711	.000
	X3	-2.143	.155	-.931	-13.786	.000
2	(Constant)	27.810	1.841		15.103	.000
	X3	-1.430	.329	-.622	-4.340	.000
	X4	.810	.336	.345	2.407	.023
3	(Constant)	21.902	2.733		8.013	.000
	X3	-.977	.341	-.425	-2.868	.008
	X4	1.425	.378	.606	3.765	.001
	X2	.067	.025	.195	2.722	.011

Our fitted Model :

Y= 21.902+0.067*X2-0.977*X3+1.425*X4

where,

X2=Age

X3=Weekly Exercise

X4=Number of times eating outside.

so , from the above regression analysis we have seen that only Independent variable X1=Average parents BMI

does not explain variability in Dependent variable.