Exploring the Relationship Between Exercise Hours and Happiness Levels

Apr 6, 2024, 6:53 AM

How does exercise hours relate to happiness?

Summary of Findings: Relationship Between Exercise Hours and Happiness

A scatter plot was created to visualize the relationship between the number of hours spent exercising per week and the level of happiness.
The plot includes a trendline (using ordinary least squares regression) to help identify any potential relationship.
Observation: There appears to be a positive correlation between the number of hours spent exercising and happiness levels. This suggests that as the number of exercise hours increases, happiness levels tend to increase as well.
Note: Some data points were missing happiness values and were excluded from the analysis to ensure accuracy.

Continue the analysis

To deepen our analysis, we'll perform a correlation analysis between the number of hours spent exercising per week and happiness levels. This will provide a numerical value indicating the strength and direction of the relationship between these two variables.

Extended Analysis: Correlation Between Exercise Hours and Happiness

A correlation analysis was conducted to quantitatively assess the relationship between exercise hours and happiness.
Correlation Coefficient: 0.9787
Interpretation: The high correlation coefficient indicates a strong positive relationship between the number of hours spent exercising per week and happiness levels. This supports the observation from the scatter plot analysis, suggesting that increased exercise hours are associated with higher happiness levels.

Research Question:

Does the number of hours spent exercising per week have a significant effect on the level of happiness?

To address this research question, we'll perform a linear regression analysis. This will help us understand not just the relationship but also the significance of the effect of exercise hours on happiness levels.

Linear Regression Analysis: Effect of Exercise Hours on Happiness

R-squared: 0.958
- This value indicates that approximately 95.8% of the variability in happiness levels can be explained by the number of hours spent exercising per week.
F-statistic: 204.9
- The F-statistic and its associated p-value (Prob (F-statistic)) suggest that the model is statistically significant.
Coefficient for Hours exercising per week: Positive
- This indicates that there is a significant positive effect of exercise hours on happiness levels. As the number of hours spent exercising increases, happiness levels tend to increase as well.
Conclusion: The analysis supports the hypothesis that the number of hours spent exercising per week has a significant effect on the level of happiness.

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Visualization Summary: Exercise Hours vs. Happiness with Regression Analysis

A scatter plot with actual data points and a regression line was created to visually represent the relationship between exercise hours and happiness.
Actual Data Points: Displayed as markers, these represent the observed values of happiness for different hours of exercise per week.
Regression Line: Represents the predicted happiness levels based on the linear regression model. This line clearly shows a positive trend, indicating that as the number of hours spent exercising increases, happiness levels tend to increase as well.
Conclusion: The visualization supports the findings from the regression analysis, confirming a significant positive effect of exercise hours on happiness levels.

Null Hypothesis (H0):

There is no significant relationship between the number of hours spent exercising per week and the level of happiness among individuals.

So formally:

H0: μ1 = μ2

Where:

μ1 is the mean happiness level for individuals spending x hours exercising per week.
μ2 is the mean happiness level for individuals in the population regardless of the number of hours spent exercising per week.

To test the null hypothesis stated, we would typically conduct a hypothesis testing analysis, such as a t-test if comparing two groups, or ANOVA if comparing more than two groups, considering the exercise hours as a categorical variable (e.g., low, medium, high exercise hours). This would allow us to statistically evaluate if the mean happiness levels differ significantly based on the number of hours spent exercising per week.

However, since our dataset does not categorize exercise hours or provide a comparison group (individuals not exercising or exercising differently), we cannot directly apply this hypothesis testing approach without additional data or assumptions.

For a more tailored analysis or advice on how to proceed, more specific details or data would be required.

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