How to interpret the results of multiple regression analysis in R?

After conducting multiple regression analysis in R language, you can view the results of the analysis using the summary() function.

In the output of the summary() function, our main focus is on the following aspects:

1. Coefficient estimates: provide the estimated coefficients for each independent variable, indicating that a higher coefficient value suggests a greater impact of the independent variable on the dependent variable.
2. Significance level (p-value): Indicates the significance level of each independent variable. A p-value less than the significance level (usually 0.05) indicates a significant impact of the independent variable on the dependent variable.
3. R-squared: Indicates the goodness of fit of a model by showing the proportion of variability in the dependent variable that is explained by the independent variables. It ranges from 0 to 1, with values closer to 1 indicating a better fit of the model.
4. F statistic: used to test the significance of the overall model. A larger F statistic indicates a higher overall significance of the model.

In addition to the summary() function, you can also use other functions to obtain more detailed analysis results, such as:

1. Anova() function: used to obtain an analysis of variance table, which allows you to see the results of the variance analysis for each independent variable.
2. vif() function: used to calculate multicollinearity between independent variables, if some of the independent variables are highly correlated, variable selection or transformation may be necessary.

In conclusion, by observing the estimated coefficients, significance levels, and model fit indices, it is possible to make preliminary interpretations and judgments of the results of multiple regression analysis. It is important to note that the interpretation of the results should be based on specific research purposes and backgrounds.