Question

# You are studying the relationship between the verbal ability of children and the number of working...

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?

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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)

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