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Positive correlation means that as one variable increases, the other tends to increase as well. Height and weight fit this pattern because generally, as a person’s height increases, their weight tends to rise too, since a larger body typically requires more mass. Of course there are individual differences due to muscle, fat, and fitness, but the overall trend is that bigger size goes along with greater weight.

The other pairs don’t show a reliable positive link. Temperature and distance don’t have a consistent upward relationship: distance from a reference point doesn’t determine temperature in a general, universal way. Age and IQ aren’t reliably positively correlated across the lifespan; IQ can improve with development in childhood but tends to level off or vary in adulthood. Shoe size and GPA are unrelated; shoe size relates to height, not academic achievement.