Question

Rejecting the null hypothesis that the population slope is equal to zero or no relationship and concluding that the relationship between x and y is significant does not enable one to conclude that a cause-and-effect relationship is present between x and y. Explain why. In replies to peers, provide support of the ideas presented by peers or refute the ideas by providing evidence to the contrary.

can someone answer this in your own words and if you get this from a book can you list a refrence please.

Answer 1

For solving such problems, we have

Null hypothesis-

H​​​​​​0 : A population slope is equal to zero i.e., = 0

Or

H​​​​​​0 : There is no significant relationship between X and Y

Or

H​​​​​​0 : The coefficient of X in the model is zero i.e., = 0

Similarly, alternative hypothesis-

H : A population slope is not equal to zero i.e., 0

Or

H : There is significant relationship between X and Y

Or

H : The coefficient of X in the model is non-zero i.e., 0

The null hypothesis is always of no relationship. Once it is rejected, we accept the alternative hypothesis which denotes significant relationship between X and Y.

For, linear regression models, the relationship between X and Y is linear or Y is related to X through linearly.

Any other relationship form, be it quadratic, exponential, logarithmic, will not be considered in this scenario and will always be prooved for no relationship due to the lack of linear relationship in the model.

Also, correlation and causations are two different things.Causation explicitly applies to cases where action A causes outcome B. We cannot simply assume causation even if we see two events happening, seemingly together, before our eyes. the other hand, correlation is simply a relationship. Action A relates to Action B—but one event doesn’t necessarily cause the other event to happen.

There are so many other possibilities for an association, including:

• The opposite is true: B actually causes A.
• The two are correlated, but there’s more to it: A and B are correlated, but they’re actually caused by C.
• There’s another variable involved: A does cause B—as long as D happens.
• There is a chain reaction: A causes E, which leads E to cause B (but you only saw that A causes B from your own eyes).

I'm attaching two links for further explanation:

https://amplitude.com/blog/2017/01/19/causation-correlation

https://clevertap.com/blog/correlation-vs-causation/