Final answer:
If x and y are unrelated in a regression model, it indicates that there is no significant linear relationship between them, making them bad candidates for linear regression. The correlation coefficient would be close to zero, which necessitates rejection of the alternate hypothesis of a non-zero population correlation coefficient.
Step-by-step explanation:
If x and y in a regression model are totally unrelated, this means that there is insufficient evidence to conclude there is a significant linear relationship between x and y. The correlation coefficient would be not significantly different from zero, indicating no linear trend in the data. When variables show no significant linear relationship, they are not good candidates for linear regression analysis. In such cases, the regression line cannot be used to accurately model or predict the relationship between x and y in the population.
However, it's important to consider whether a different type of relationship exists, such as a curvilinear relationship, before concluding that the variables have no relationship at all. In some instances, other types of statistical methods may be more appropriate to analyze the relationship between x and y.
As per our hypothesis testing, the alternate hypothesis Ha: The population correlation coefficient is significantly different from zero, would be rejected, which supports the finding that there is no significant linear relationship between the variables.