How to interpret coefficient of determination, and coefficient of correlation, fisher test of hypothesis?
The coefficient of determination, often denoted as R-squared (R²), measures the proportion of the variance in the dependent variable that is predictable from the independent variable(s). It indicates how well the regression model fits the observed data points. R-squared ranges between 0 and 1, with 0 indicating that the model does not explain any variation in the dependent variable and 1 indicating a perfect fit.
Interpreting R-squared involves understanding the proportion of the variance explained by the independent variable(s). A higher R-squared value suggests that a larger proportion of the variability in the dependent variable can be explained by the independent variable(s). However, it does not necessarily imply that the model is the best or that the relationship between the variables is causal. Therefore, it is essential to consider other factors and evaluate the overall significance and accuracy of the model.
The coefficient of correlation is often denoted as r and measures the strength and direction of the linear relationship between two variables. It can take values between -1 and 1, where -1 indicates a perfect negative correlation, 1 indicates a perfect positive correlation, and 0 indicates no correlation.
Interpreting r involves understanding the direction and strength of the relationship between the two variables. If r is positive, it suggests a positive correlation, meaning that as one variable increases, the other tends to increase as well. Conversely, if r is negative, it implies a negative correlation, indicating that as one variable increases, the other tends to decrease. The closer the absolute value of r is to 1, the stronger the correlation. However, like R-squared, correlation does not imply causation, and other factors should be considered before drawing conclusions.
The Fisher test of hypothesis, also known as Fisher's exact test, is a statistical test used to determine the independence of two categorical variables. It is commonly applied when the sample size is small or when the expected cell frequencies are insufficient for using a chi-square test.
Interpreting the Fisher test involves assessing the p-value generated by the test. If the p-value is less than a pre-determined significance level (e.g., 0.05), it suggests evidence against the null hypothesis of independence. This implies that the two categorical variables are likely to be dependent. Conversely, if the p-value is greater than the significance level, it suggests insufficient evidence to reject the null hypothesis, indicating that the variables are likely to be independent.