Question

For each of the following pairs of variables, indicate whether you would expect a positive correlation, a negative correlation, or a correlation close to \(0 .\) Explain your choice. a. Weight of a car and gas mileage b. Size and selling price of a house c. Height and weight d. Height and number of siblings

Short answer

a) Negative correlation: As car weight increases, gas mileage decreases. b) Positive correlation: As house size increases, its selling price also increases. c) Positive correlation: As height increases, weight usually also increases. d) Correlation is close to 0: There is no systematic increase or decrease between a person's height and the number of siblings they have.

Step-by-step solution

Correlation of weight of a car and gas mileage

Generally, the heavier a vehicle is, the more gas it consumes to move, hence the lesser the mileage it offers. Therefore, the correlation between the weight of a car and gas mileage could be considered negative. As car weight increases, gas mileage decreases.

Correlation of size and selling price of a house

Usually, bigger houses tend to cost more because they offer more living space. Therefore, the correlation between the size of a house and its selling price could be considered positive. As house size increases, its selling price also increases.

Correlation of height and weight

Typically, taller individuals tend to weigh more because they have a larger body mass. This leads to a positive correlation. As height increases, weight usually also increases.

Correlation of height and number of siblings

There seems to be no logical relation between a person's height and the number of siblings they have, therefore, the correlation can be considered close to 0. One variable does not increase or decrease systematically with the other.