Question

There is a ___ correlation between the number of doughnuts Homer eats and his weight. If Homer wants to lose weight, he should eat ___doughnuts. If Homer graphed this relationship on a scatterplot, an increase on the y axis would lead to ___on the x axis.

Answer 1

Answer:

There is a linear correlation between the number of doughnuts Homer eats and his weight. If Homer wants to lose weight, he should eat less doughnuts. If Homer graphed this relationship on a scatterplot, an increase on the y axis would lead to an increase on the x axis.

Step-by-step explanation:

Given that doughnuts have a high content of fat and sugar, they are well proved to be fattening foods. Indeed, one would expect that the more doughnuts are consumed per time unit, the more body weight will increase.

Mathematically, both variables (amount of doughnuts consumed and body weight) will behave the same way: an increase in one of them will led to an increase in the other one. The independent variable is the amount of doughnuts consumed by Homer (per unit time), as this is independent on anything else for this given problem, while the body weight is the dependent variable for its will respond to the increase in the amount of doughnuts consumed.

Graphically, the independent variable is plotted on the "y" axis, while the dependent variables is placed on the "x" axis.

Thus, when the relation between both variables is plotted, a straight-line relationships is expected. This is called a linear correlation, and it is interpreted as mentioned above: when the independent variable increases, the dependent variable increases as well, while a decrease in the independent variable leads to a decrease in the dependent one.