Question

***SHOW SPSS**

A researcher is interested to learn if there is a linear relationship between the hours in a week spent exercising and a person’s life satisfaction. The researchers collected the following data from a random sample, which included the number of hours spent exercising in a week and a ranking of life satisfaction from 1 to 10 ( 1 being the lowest and 10 the highest).

Participant	Hours of Exercise	Life Satisfaction
1	3	1
2	14	2
3	14	4
4	14	4
5	3	10
6	5	5
7	10	3
8	11	4
9	8	8
10	7	4
11	6	9
12	11	5
13	6	4
14	11	10
15	8	4
16	15	7
17	8	4
18	8	5
19	10	4
20	5	4

1. Find the mean hours of exercise per week by the participants.
2. Find the variance and standard deviation of the hours of exercise per week by the participants.
3. Run a bivariate correlation to determine if there is a linear relationship between the hours of exercise per week and the life satisfaction. Report the results of the test statistic using correct APA formatting.
4. Run a linear regression on the data. Report the results, using correct APA formatting. Identify the amount of variation in the life satisfaction ranking that is due to the relationship between the hours of exercise per week and the life satisfaction (Hint: the R² value)
5. Report a model of the linear relationship between the two variables using the regression line formula.

1. 5 A researcher is interested in studying the effect that the amount of fat in the diet and amount of exercise has on the mental acuity of middle-aged women. The researcher used three different treatment levels for the diet and two levels for the exercise. The results of the acuity test for the subjects in the different treatment levels are shown below.

	Diet
Exercise	<30% fat	30% - 60% fat	>60% fat
<60 minutes	4	3	2
	4	1	2
	2	2	2
	4	2	2
	3	3	1
60 minutes	6	8	5
or more	5	8	7
	4	7	5
	4	8	5
	5	6	6

1. Perform a Two-way analysis of variance (ANOVA) and report the results using correct APA style; report whether significance was found for Factor A, Factor B, and/or an interaction between Factors A and B was found.
2. If the test statistic is significant, run a post hoc test to determine between what groups significance was found.
3. Report an effect size for all significant results.

Answer 1

Solution:

Here, we have to develop the regression model for the prediction of the dependent or response variable rating of life satisfaction based on the independent or explanatory variable hours of exercise in a week. The descriptive statistics and regression model by using SPSS is given as below:

Descriptive Statistics
	Mean	Std. Deviation	N
Life Satisfaction	5.0500	2.48098	20
Hours of Exercise	8.8500	3.66024	20

Correlations
		Life Satisfaction	Hours of Exercise
Pearson Correlation	Life Satisfaction	1.000	-.103
	Hours of Exercise	-.103	1.000
Sig. (1-tailed)	Life Satisfaction	.	.332
	Hours of Exercise	.332	.
N	Life Satisfaction	20	20
	Hours of Exercise	20	20

Variables Entered/Removedb
Model	Variables Entered	Variables Removed	Method
1	Hours of Exercisea	.	Enter
a. All requested variables entered.
b. Dependent Variable: Life Satisfaction

Model Summary
Model	R	R Square	Adjusted R Square	Std. Error of the Estimate
1	.103a	.011	-.044	2.53529
a. Predictors: (Constant), Hours of Exercise

ANOVAb
Model		Sum of Squares	df	Mean Square	F	Sig.
1	Regression	1.252	1	1.252	.195	.664a
	Residual	115.698	18	6.428
	Total	116.950	19
a. Predictors: (Constant), Hours of Exercise
b. Dependent Variable: Life Satisfaction

Coefficientsa
Model		Unstandardized Coefficients		Standardized Coefficients	t	Sig.
		B	Std. Error	Beta
1	(Constant)	5.671	1.516		3.740	.001
	Hours of Exercise	-.070	.159	-.103	-.441	.664
a. Dependent Variable: Life Satisfaction

Questions

Part a

Find the mean hours of exercise per week by the participants.

The required mean hours of exercise per week by the participants is given as 8.85 hours.

Part b

Find the variance and standard deviation of the hours of exercise per week by the participants.

The variance and standard deviation of the hours of exercise per week by the participants is given as below:

Standard deviation = 3.66024

Variance = 3.66024^2 = 13.397357

Part c

Run a bivariate correlation to determine if there is a linear relationship between the hours of exercise per week and the life satisfaction. Report the results of the test statistic using correct APA formatting.

The correlation coefficient between the two variables hours of exercise per week and the life satisfaction is given as -0.103. This means, there is a very low or weak negative linear relationship or association exists between the given two variables. The corresponding p-value from the above SPSS output is given as 0.332 which is greater than the level of significance or alpha value 0.05, so we do not reject the null hypothesis and conclude that this correlation coefficient is not statistically significant. This means, there is no statistically significant relationship exists between the hours of exercise per week and the life satisfaction.

Part d

Run a linear regression on the data. Report the results, using correct APA formatting. Identify the amount of variation in the life satisfaction ranking that is due to the relationship between the hours of exercise per week and the life satisfaction (Hint: the R² value)

From the given SPSS output, the value for the correlation coefficient is given as -0.103 which indicate a low or weak negative linear association between given two variables. The value of the R square or the coefficient of determination is given as 0.011, which means about 1.1% of the variation in the dependent variable or response variable life satisfaction ranking is explained by the regression or relationship between the hours of exercise per week and the life satisfaction.

The p-value for this overall regression model is given as 0.664 which is greater than the level of significance or alpha value 0.05, so we do not reject the null hypothesis. There is insufficient evidence to conclude that the given regression model is statistically significant. So, we cannot use this regression model for the prediction of the dependent variable life satisfaction based on independent variable hours of exercise. The slope of the regression equation is not statistically significant as the corresponding p-value is given as 0.664 which is greater than alpha value 0.05.

Part e

Report a model of the linear relationship between the two variables using the regression line formula.

From the given SPSS output, the regression equation is given as below:

Life satisfaction = 5.671 – 0.070*Hours of Exercise

ŷ = 5.671 – 0.070*x