***Must be calculated in SPSS*** A researcher is interested to learn if there is
ID: 3300925 • Letter: #
Question
***Must be calculated in 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
a. Find the mean hours of exercise per week by the participants.
b. Find the variance of the hours of exercise per week by the participants.
c. Determine if there is a linear relationship between the hours of exercise per week and the life satisfaction by using the correlation coefficient.
d. Describe 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.
e. Develop a model of the linear relationship using the regression line formula.
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
Explanation / Answer
(***Must be calculated in SPSS***)
a. Find the mean hours of exercise per week by the participants.
Answer:
The mean hours of exercise per week by the participants is given as 8.85.
Required SPSS output 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
b. Find the variance of the hours of exercise per week by the participants.
Answer:
From the above output, we have given standard deviation for hours of exercise as 3.66024.
So, required variance = 3.66024^2 = 13.39736
c. Determine if there is a linear relationship between the hours of exercise per week and the life satisfaction by using the correlation coefficient.
Answer:
The SPSS output for correlation coefficient is given as below:
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
From above output, the correlation coefficient between the hours of exercise and life satisfaction is given as -0.103, which means there is a low or weak negative linear relationship or association exists between the given two variables such as hours of exercise and life satisfaction.
d. Describe 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.
Answer:
The amount of variation in the life satisfaction ranking is explained by the coefficient of determination or the value of R square. Coefficient of determination is given as below:
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
The value of coefficient of determination or R square is given as 0.011, which means only 1.1% of the variation in the dependent variable life satisfaction ranking is explained by the independent variable hours of exercise.
e. Develop a model of the linear relationship using the regression line formula.
Answer:
SPSS output for the required regression model is given as below:
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
As the p-value for this regression model is 0.664, it is not statistically significant model.
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
Regression line is given as below:
Life satisfaction = 5.671 – 0.070*Hours of exercise
Descriptive Statistics
Mean
Std. Deviation
N
Life Satisfaction
5.0500
2.48098
20
Hours of exercise
8.8500
3.66024
20
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