Linear Regression Analysis Assumptions Include Homogeneity

linear Regression Analysis assumptions Include Homogeneity

Linear regression analysis assumes certain conditions to ensure valid results. These include the homogeneity of residuals, which means that the residuals (the differences between observed and predicted values) should have constant variance across all levels of the independent variable. Additionally, residuals should be normally distributed. In this study, the dependent variable is the number of hours worked last week, and the independent variable is respondent’s income, both measured on a ratio scale. The objective is to analyze the relationship between these two variables to determine if a linear association exists.

The hypothesis testing focuses on the significance of the regression model. The null hypothesis (H₀) states that the model is not significant and that there is no linear relationship between respondent’s income and hours worked. Conversely, the alternative hypothesis (H₁) posits that the model is significant and a linear relationship exists. Based on the F-test results (F=132.025, p-value

The estimated regression equation is: number_of_hours_worked_last_week = 7.431 + 2.726 * respondent’s_income. The intercept suggests that when respondent’s income is zero, the average number of hours worked last week is approximately 7.431 hours. The slope coefficient, 2.726, indicates that for each additional unit increase in respondent’s income, the number of hours worked last week increases by approximately 2.726 hours.

The correlation coefficient between the two variables is 0.357, which is significant at the 5% level of significance. This positive correlation suggests a modest but statistically significant positive linear relationship; as respondent’s income increases, the number of hours worked tends to increase slightly. The scatterplot, although not visually presented here, would typically depict this positive trend, with data points loosely clustered along an upward-sloping line.

The model’s R-squared value is 0.128, meaning approximately 12.8% of the variance in hours worked is explained by respondent’s income. While statistically significant, this indicates that income alone does not fully account for variations in hours worked, and other factors may influence this relationship.

Conclusion

The analyzed data provides evidence of a positive, albeit modest, linear relationship between respondent’s income and the number of hours worked last week. The significance of the regression model confirms that income is a predictor of hours worked, but the relatively low R-squared highlights the importance of considering additional variables. These findings are consistent with economic theories suggesting that higher income may incentivize increased work hours, although personal, social, and contextual factors also play vital roles.

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