I know the correct answer is number 4, but can someone explain why?
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2 Answers
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None of those appear to be qqplots. the p like symbol (rho) represents correlation. If correlation is high (near 1), as one variable goes up, the other variable goes up a roughly equal amount.
The middle one, look across the horizontal axis, as x increases, do the values of y tend to increase an equal amount? No, in fact there is no correlation there, so the correlation coefficient is 0.
The first and last ones, as x goes up, y also goes up. But if you look closely, the first one is curvy x's increase is not followed exactly with an increase in y. So its correlation is less than the third one.
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From the third plot, we can say $\rho_{XY_3}$ is positive and near to one as the relation of $X$ and $Y_3$ are increasing linearly. Hence, statement 2 and 5 cannot be true because they said $\rho_{XY_3}$ is negative.
From the second plot, we can say $\rho_{XY_2}$ is near zero because we can't see any linear pattern between $X$ and $Y_2$. Hence, they are not correlated anymore. Hence, statement 3 cannot be true.
From the first plot, we can say the correlation of $X$ and $Y_1$ is positive because they change like $Y_1 = X^2$, and it should be more than $0.5$. Hence, the statement 5 cannot be true.
Therefore, just the fourth statement could be true.