Which statement is false regarding a simple linear regression model?

In the context of a simple linear regression model, the statement about the choice of the explanatory variable affecting the total sum of squares is indeed correct. The total sum of squares (SST) quantifies the total variability in the response variable around its mean. This measure can be influenced by the variability explained by the model, which is in turn determined by the choice of the explanatory variable. Different explanatory variables can lead to different models, which can result in different levels of explained variability and, consequently, different total sum of squares.

The statement regarding the response variable being continuous holds true, as traditional simple linear regression assumes a continuous response variable. Categorial response variables would require different regression approaches, such as logistic regression.

The assertion that the relationship between the explanatory and response variables is linear is a fundamental assumption of simple linear regression. This linearity implies that any change in the explanatory variable leads to a proportional change in the response variable.

Residuals having constant variance, also known as homoscedasticity, is another key assumption of regression analysis. Ideal residuals should not show patterns or inequalities in variance; this implies that the spread of residuals should be consistent across all levels of the explanatory variable.

Thus, focusing on the influence of the explanatory variable