Question

1. Find the mean hours of exercise per week by the participant.  
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.

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

Answer 1

Problem statement: Based on the observed data points try to answer a set of questions.

Given: Hours of exercise per week and life satisfaction observed of twenty individuals.

Solution:

(a):Mean hours of exercise per week for all participants is given by : summit = 8.85 Hours.

(b): Variance and standard deviation of exercise hours is given by : Variance== 13.39

standard deviation= square root(Variance)= 3.66

(c): Correlation : This provides the strength of linear relationship along with the direction (positive or negative) between weekly exercise and life satisfaction.

Correlation= Covariance ( Weekly exercise and life satisfaction)/(standard deviation(weekly exercise)*standard deviation(life satisfaction)= -0.10346. With this correlation value , we can conclude that there is no linear relationship weekly exercise hours and life satisfaction.

(d) A simple linear regression model is built using life satisfaction as target variable and weekly exercise as predictor variable.

regression equation

life satisfaction= 1*(weekly exercise)+₀

We observe that the P-value of the regression model is 0.664, implying that weekly exercise is not a good predictor variable to compute life satisfaction.

The R² obtained for the model is  0.01. This implies 1% variation in the life satisfaction is attributed to weekly exercise hours.

(e) : Model equation

life satisfaction= -0.07* (weekly exercise in hours)+ 5.67

Since the p-value for weekly exercise is>0.05, the variable weekly exercise is not adding any information to the regression model.