bivariate statistical measures of regression and correlation
linear regression
It is used to analyze the relationship between two continuous variables.
objective: predict one variable in another
use the regression formula: y=mx+b
correlation coefficient
measures the degree of relationship between two continuous variable variants
range between -1 and 1
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correlation coefficient: r
-r= 1: perfect positive correlation
-r= 0: no correlation
-r= -1 perfect negative correlation
determination coefficient
(R-squared)
measures what proportion of the variance of the dependent variable is explained by the independent variable
range between 0 and 1
rΛ2=1: 100% of the variance is explained
rΛ2=0: no variance is explained
variance analysis(ANOVA)
It is used to compare the means of more than two groups.
evaluates whether there are significant differences between the means of the groups
calculates the total variance, variance between groups, and variance within groups
standard regression coefficient
measures how many standard deviations the dependent variable changes when the independent variable changes one standard deviation
It is calculated by dividing the covariance by the standard deviation of the independent variable.
significance test
determines the relationship between the variables is statistically significant
uses the significance level (generally 0.05)
If the p value is less than the significance level, the relationship is significant.
If the p value is greater than the significance level, the relationship is not significant.