Correlation Coefficient - statements

Question

This is in relation to a scatterplot of 400 data points, with a very strong negative correlation.

For the statements, state whether they are correct or incorrect and why.

1. If each value of the y variable is divided by four, then the value of the correlation coefficient will also be divided by four. - Assume this one is true? As the correlation coefficient then wouldn't change?

2. The scatterplot shows that the variable x causes the variable y to take the values it does. - not too sure about this one?

Thanks

Answer 1

For (1): As the covariance and the standard deviation of $y$ are changed by the same positive factor the correlation remains unchanged.

For (2): A high correlation alone doesn’t establish any causality.