Analysis of data

We checked for normality of for  Weekly Leisure Activity Score (refer to figure 1) and Well-being (refer to figure 2) through the skewness of data. Looking at the data for Weekly Leisure Activity Score and well-being, we found that the skewness value lies within 2 standard deviations from the standard error of skewness. Hence, both of the variables are normally distributed.

Figure 1: Skewness of Weekly Leisure Activity Score data

Figure 2: Skewness of Well-being data

To double confirm the normality, we ran the Q-Q plots for both variables and found that most of the points close to or on the line (refer to figure 3 and 4).

Figure 3: Q-Q plot for Weekly Leisure Activity Score data

Figure 4: Q-Q plot for Well-being data

The scatter plot for Weekly Leisure Activity Score vs Well-being is ran and a weak positive relationship was found between the two variables (refer to figure 5).

Figure 5: Scatter plot for weekly Leisure Activity Score vs Well-being

Since our research question is a correlation question, and both our variables are continuous data, Pearson’s R was chosen to be the statistical test.

Running the Pearson's R, we found that the Pearson's R value is 0.113 (refer to figure 6). As the value is < 0.2, there is a very weak relationship. Looking at the R² value of 0.013, the data points are not well-fitted to the regression line. Together with scatter plot, there is a very weak positive relationship between the frequency of exercise and emotional well-being.

Looking at the P-value (refer to figure 6), the P-value is 0.524. Since P-value > 0.05, we will not reject H0 and conclude that there is no relationship between frequency of exercise and emotional well-being.  

Figure 6: Pearson's R value & P-value