Question

To see whether a widely used food preservative contributes to the hyperactivity of preschool children, a dietitian chose a random sample of 10 four-year-olds known to be fairly hyperactive from various nursery schools and observed their behavior 45 minutes after they had eaten measured amounts of food containing the preservative. here variables were x, the amount of food consumed containing preservative (in grams) and y, a subjective rating of hyperactivity (on a scale from 1 to 20). the least-squares equation is y = 1.5 + 0.16x. if a child's hyperactivity rating is predicted to be 18, how many grams of food containing preservatives did he consume?

Answer 1

Answer : If a child's hyperactivity rating is predicted to be 18, he consumed 103.125 grams of food containing preservatives.

The regression (least-squares) equation given in the question is:

$y = 1.5 + 0.16x$

In the equation above, y is the predicted variable. Here the predicted variable is the subjective hyperactivity rating (on a scale of 1 to 20).

The independent variable, x, is the quantity of food containing preservatives (in grams) consumed by hyperactive children.

The question tells us that the subjective hyperactivity rating of a child is 18.

Substituting the value of y in the equation above, we have,

$18 = 1.5 +0.16x$

$\frac{16.5}{0.16} =x$

$x = 103.25$