Question

the weight (in pounds) and height (in inches) for a child were measured every few months over a two - year period. the results are given in the table.
weight(x) height(y)
8 22
12 23
18 26
24 30
30 32
32 33
35 35
37 36
using technology, what is the y - intercept and what is its interpretation?
the y - intercept is - 34.13. when the weight is 0 pounds, the height will be - 34.13 inches.
the y - intercept is 17.37. when the weight is 0 pounds, the height will be 17.37 inches.
the y - intercept is - 34.13. when the weight is 0 pounds, the height is predicted to be - 34.13 inches.

Explanation:

Step1: Recall y - intercept concept

In a linear regression model $y = mx + b$, the y - intercept $b$ is the value of $y$ when $x = 0$. Here $x$ is weight and $y$ is height.

Step2: Analyze the physical meaning

Physically, when the weight $x = 0$ pounds, we are looking at the height value which is the y - intercept. A negative height like - 34.13 inches is not physically possible in this context. A positive value makes more sense for height when weight is 0.

Answer:

The y - intercept is 17.37. When the weight is 0 pounds, the height will be 17.37 inches.