Question

You are studying the relationship between the verbal ability of children and the number of working hours for their parents. You collected data from two different cities A and B (N = 100, for each city). You found that the slopes (when predicting children’s verbal ability from the number of parents’ working hours) for cities A and B were .61 and .89, respectively. However, the correlation coefficients were exactly the same (r = .32). Do you think that it is possible or that it is just an error? If it is possible, what happened?

Answer 1

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It is entirely possible. It' not an error. The regression slope gives a useful quantity interpreted as the estimated change in the expected value of Yi for a given value of Xi, which is different for the 2 equations, but the correlation gives you a bounded measurement that can be interpreted independently of the scale of the two variables, which in our case are same, implying how linear the relation is! ( in our case they are equally linear)