In the first case, r makes no sense since one can only create perform linear regression on numerical ordered paired data. As stated, the notion of gender is not a numerical quantity and thus cannot (for example) create a scatter plot. One might however “randomly” assign a numerical value to gender (such as 1 = woman and 0 = man) but that is not part of this exercise.

For the second case, adjusting the scale of the data points will not affect the correlation coefficient. Indeed, suppose all the x’s are scaled larger by a factor of 1000. Then, the mean and the standard deviation of x-values will also be 1000 times larger (convince yourself of this) and the covariance will be 1000 times larger. Indeed, for covariance

and one can easily see that the 1000 factors out. So, 1000 will factor out of both numerator and denominator and hence cancel in the covariance formula.