HYPOTHESES FOR CORRELATION ANALYSIS

1.Hypothesis test about the value of correlation coefficient (in the cor function and correlation matrix)

  • Hypotheses
    • H0: rho = 0 [there is no correlation]
    • H1: rho ≠ 0 [there is correlation] !Applicable for both Pearson and Spearman correlation coefficient

HYPOTHESES FOR REGRESSION ANALYSIS

1.Breusch-Pagan heteroskedasticity test

  • Hypotheses
    • H0: the variance of errors is constant [not residuals] (homoscedasticity)
    • H1: the variance of errors isn’t constant (heteroskedasticity)

2.Shapiro-Wilc normality test

  • Hypotheses
    • H0: Errors are normally distributed
    • H1: Errors aren’t normally distributed

3.Test of partial regression coefficient

  • Hypotheses
    • H0: beta = 0 [we have found no effect of … on…]
    • H1: beta ≠ 0 [we have found statistically significant influence of… on…] ! and now its impact is actual for population

4.Test of significance of the regression model

  • Hypotheses
    • H0: roh^2 = 0 (beta1 = beta2 = … = 0) [the model doesn’t explain anything lol]
    • H1: roh^2 > 0 (at least one beta ≠ 0)[at least 1 explanatory variable explains the variability in the dependent variable]

!One sided test, because roh^2 is obviously always between 0 and +1

*roh^2 is the population coefficient of determination

5. ANOVA test for comparison of two models

  • Hypotheses
    • H0: ∆‘roh^2’ = 0 [the significance of both regression models is same, both models fit the data well]
    • H1: ∆‘roh^2’ > 0 [population multiple coefficient of the determination of the 2nd model is higher than of 1st model. 2nd model fits the data better]