Fig. 2

Hypothesis testing for the multivariate linear regression model diagnosis. 1) Residuals vs Fitted figure (upper left) was used to explore the linearity between fitted values and residuals. Data points were uniformly distributed on the both side of y = 0 and the line presented a stationary curve without obvious shape feature, which suggested the linearity was good. 2) Normal Q-Q figure (upper right) was used to examine the normality of standardized residuals. Data points were arranged in diagonal lines, tending to a straight line, and passing diagonally through it, which indicated the residuals were normally distributed. 3) Square root of standardized residuals and fitted figure (lower left) was used to examine the homoscedasticity of standardized residuals. Data points were uniformly distributed on the both side of y = 0 and the line presented a stationary curve without obvious shape feature, which suggested that the residual values of all predicted dependent variables are approximately equal. 4) Standardized residuals vs leverage figure (lower right) was used to check the outlier. There were no significant outliers that can affect the regression results in this model