Final answer:
For calculating inferential statistics of a regression, the required assumptions include homoscedasticity, linearity, and normal distribution of residuals. Not all points need to lie on the regression line and heteroscedasticity is not a required assumption.
Step-by-step explanation:
In the context of computing inferential statistics for a regression analysis, certain assumptions about the data must be met to ensure the validity of the results. Let's address which assumptions are required:
- Homoscedasticity: This assumption states that the variance around the regression line should be the same for all values of X, ensuring that the spread of residuals is consistent across levels of the predictor variable.
- Linearity: The relationship between the two variables must be linear, meaning the change in the dependent variable is proportional to the change in the independent variable.
- Normality of residuals: The errors of prediction should be distributed normally. This means the residuals, which are the differences between the observed and predicted values of Y, should form a normal distribution when plotted.
It's important to note that not all points need to lie on the regression line; in fact, this is never the case with real-world data. Homogeneity of variances is not a requirement per se for regression, as it is more associated with ANOVA tests. However, the concept is similar to the equal variance assumption. Heteroscedasticity, which implies increasing variance of residuals as X increases, is contrary to the homoscedasticity condition and is therefore not a required assumption.