# 1. Loading Package

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# 2.Cleaning Data

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# 3. Building Model

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# 4. Get the best degree for regression

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# 5. Apporach the Model (evluate the model performance)

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# 6. Draw the Difference between prediction and real

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# 7. Anova & P-values & R-Squared

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The regression results depict the relationship of multiple predictors to the return rate. With an value of 0.115, the model explains approximately 11.5% of the variance in the return rate. This suggests that while the predictors do have some explanatory power, a significant portion of the return rate's variability remains unexplained by the model. Among the predictors, variables labeled as x1 and x3 stand out as statistically significant at conventional levels (with p-values less than 0.05), implying a robust relationship with the return rate. Notably, the coefficients suggest that x1 has a positive correlation and x3 a negative correlation with the return rate. Conversely, other predictors such as x2, x4, x5, and x6 have high p-values, which denotes that their individual effects are not statistically distinguishable from zero within the model. The non-significant constant and high p-values for several predictors underscore the necessity for model refinement, potentially incorporating additional relevant predictors or considering other modeling techniques to enhance explanatory power.

# 8. Test if the differences between actual and predicted are significant

## i). Draw The Difference

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ii). See the significant

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Given the t-statistic and p-value (more than 0.05 significant level), there's no statistically significant evidence to suggest that the parameters affecting the return rate are different before and after COVID-19, supporting your alternative hypothesis. However, always remember that "failing to reject" the null hypothesis doesn't prove the alternative hypothesis; it simply means that based on your data, the two periods (before and after COVID) are not statistically different in the context of return rates

# 9. View the equation

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### Here is the equation then:

Return rate = -0.0002 + 1.2444(GDP growth rate) + -0.2153(Interest rate) + -2.7065(Inflation rate) + 0.9683(Unemployment rate) + -0.0000(Residential property prices) + -0.0032(Loans to private sector)

# 10. Effect Size of Parameters

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The effect sizes derived from the model shed light on the magnitudes of the relationships between predictors and the return rate. The GDP growth rate, with an effect size of 0.0637, indicates a relatively moderate positive relationship with the return rate. Conversely, the Inflation rate demonstrates a negative effect, suggesting that as inflation rises, the return rate tends to decrease. Unemployment rate and Residential property prices too exert negative pressures on the return rate, but their magnitudes are comparatively smaller. The interaction term between GDP and Interest rate showcases a negative effect size of -0.0236, implying that the combined influence of GDP growth and Interest rate has a dampening effect on the return rate. Interestingly, while the Interest rate and Loans to private sector both have effect sizes close to zero, suggesting minimal individual impact, their combined interaction reveals a more profound influence. This underscores the complexity of the relationships and the significance of understanding not just individual factors but also their interactions when predicting return rate

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# 11. Time Series (AMRA) forcast future trend

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