Are there ever any circumstances when a correlation such as Pearson's r can be interpreted as evidence for a causal connection between two variables?

For this project you will collect at least 10 pairs of quantitative data and conduct a hypothesis test for linear correlation and also give the best predicted value of y for a given value of x. Below is my example:(you can't use my example, you have to come up with your own) I am collecting data to see if there is correlation between a person's age and how many hours they use the phone I will also give the best predicted value for a person who is 40 years old. My data age hours 19 7.3 25 6.5 31 4.6 18 3.2 25 5.2 27 2.9 26 3.7 39 6.5 47 4.1 55 3.9 A)l will test the claim that there is no correlation (start with the Claim and finish with the conclusion) C: Ho HA etc B) will give the best estimate for how many hours a person who is 35 years old uses the phone. (make sure to use the write y and x and include the P value in your answer and decide if you will plug in x or find the average of the y's) The P value is (big/small) so I have to (either give the average of the y's or plug in the x…

1. People often think that correlation implies causation. In other words, if two variables are correlated, then one must be causing the change in the other. Explain how two variables can be correlated yet one does not cause the other to change. Give an example.

What information is provided by calculations of a Pearson’s Correlation Coefficient?