Question

You are interested in the effects of time spent viewing television and Body Mass Index on cardiovascular fitness (CVF) in children. You have a sample of 60 middle school students. Each student reports on their average daily T.V. viewing (in hours). You also have a Body Mass Index (BMI) score for each of these individuals. As a measure of CVF, your dependent variable is their score on the PACER run (Progressive Aerobic Cardiovascular Endurance Run), a well-accepted measure of cardiovascular fitness in children. A higher PACER score (more completed laps) indicates better cardiovascular fitness (CVF). The results from your sample are below. Enter these data into SPSS and answer the following questions:

TV Time     BMI           PACER

1.00    19.00   30.00

1.00    18.00   30.00

1.00    20.00   29.00

1.00    19.00   28.00

1.00    20.00   26.00

1.00    19.00   25.00

1.00    18.00   25.00

1.00    20.00   22.00

1.00    21.00   23.00

1.00    25.00   18.00

1.00    23.00   21.00

1.00    22.00   20.00

1.00    27.00   15.00

1.00    26.00   17.00

1.00    21.00   22.00

2.00    18.00   25.00

2.00    19.00   24.00

2.00    25.00   18.00

2.00    27.00   14.00

2.00    28.00   14.00

2.00    26.00   15.00

2.00    24.00   18.00

2.00    25.00   16.00

2.00    20.00   21.00

2.00    22.00   20.00

2.00    18.00   25.00

2.00    19.00   26.00

2.00    18.00   24.00

2.00    22.00   20.00

2.00    21.00   22.00

3.00    28.00   12.00

3.00    29.00   11.00

3.00    30.00   10.00

3.00    28.00   11.00

3.00    26.00   12.00

3.00    25.00   13.00

3.00    22.00   20.00

3.00    18.00   25.00

3.00    19.00   21.00

3.00    19.00   26.00

3.00    20.00   25.00

3.00    27.00   9.00

3.00    26.00   11.00

3.00    21.00   21.00

3.00    20.00   22.00

4.00    31.00   9.00

4.00    20.00   23.00

4.00    20.00   22.00

4.00    23.00   21.00

4.00    22.00   20.00

4.00    24.00   18.00

4.00    31.00   12.00

4.00    30.00   11.00

4.00    29.00   14.00

4.00    28.00   15.00

4.00    27.00   17.00

4.00    29.00   13.00

4.00    31.00   10.00

4.00    22.00   21.00

4.00    24.00   18.00

1.    Are there problems with collinearity/multicolinearity? How do you know? Present evidence of all three criteria discussed in lecture.

There are no problems with collinearity. We know that because

1. The two predictor variables are correlated <.8

2. The VIF <10

3. tolerance >.1

Give SPSS screenshots of output and give the SPSS codes and paths how to get the answers

Answer 1

Solution:

Multicollineraity Dignostics: Regression

Model Summaryb
Model	R	R Square	Adjusted R Square	Std. Error of the Estimate	Change Statistics					Durbin-Watson
					R Square Change	F Change	df1	df2	Sig. F Change
1	.933a	.870	.866	2.091	.870	191.434	2	57	.000	.847
a. Predictors: (Constant), BMI, TVTime
b. Dependent Variable: PACER

ANOVAb
Model		Sum of Squares	df	Mean Square	F	Sig.
1	Regression	1674.158	2	837.079	191.434	.000a
	Residual	249.242	57	4.373
	Total	1923.400	59
a. Predictors: (Constant), BMI, TVTime
b. Dependent Variable: PACER

Coefficientsa
Model		Unstandardized Coefficients		Standardized Coefficients	t	Sig.	95% Confidence Interval for B		Collinearity Statistics
		B	Std. Error	Beta			Lower Bound	Upper Bound	Tolerance	VIF
1	(Constant)	49.471	1.596		31.002	.000	46.276	52.667
	TVTime	-.443	.271	-.088	-1.636	.107	-.986	.099	.793	1.261
	BMI	-1.255	.076	-.890	-16.620	.000	-1.406	-1.104	.793	1.261
Dependent Variable: PACER

Collinearity Diagnosticsa
Model	Dimension	Eigenvalue	Condition Index	Variance Proportions
				(Constant)	TVTime	BMI
1	1	2.887	1.000	.00	.01	.00
	2	.100	5.369	.07	.88	.02
	3	.013	14.809	.93	.11	.98
a. Dependent Variable: PACER

Residuals Statisticsa
	Minimum	Maximum	Mean	Std. Deviation	N
Predicted Value	8.79	26.44	19.10	5.327	60
Residual	-5.256	5.072	.000	2.055	60
Std. Predicted Value	-1.935	1.377	.000	1.000	60
Std. Residual	-2.513	2.426	.000	.983	60
a. Dependent Variable: PACER

RESULTS: 1. From the table of ‘Coefficients^a_’ we observed that VIF < 10 and tolerance >0.1 there for ther is no presence of multicollinearity in data.

               2. Also the correlation between predictor variable is 0.4548 < 0.8 which provide the information that there is no presence of multiollinearity.

               3. PATH: input the data on spss spread sheet / import