Question

at a family reunion, parents recorded each child’s age and height. (from lesson 3.11)
a. fully describe the association. include whether it is positive or negative, linear or nonlinear, and whether there are any outliers.
b. draw a trend line. use your trend line to predict the height of a 14 - year - old in this family.

Explanation:

Part a: Describe the Association

1. Direction: As age (x - axis) increases, height (y - axis) generally increases, so the association is positive.
2. Form: The points roughly follow a straight - line pattern, indicating a linear association.
3. Strength: The points are relatively close to a potential trend line, so the association is moderately strong.
4. Outliers: No obvious points that deviate far from the general pattern.

Step 1: Draw the Trend Line

Visually fit a straight line through the scatter plot, balancing the number of points above and below the line.

Step 2: Find the x - value (Age = 14)

Locate \( x = 14 \) on the age (x - axis) of the scatter plot.

Step 3: Find the Corresponding y - value (Height)

From the trend line at \( x = 14 \), read the corresponding \( y \) (height) value. By visually estimating, if the trend line at age 14 aligns with a height around 60 - 62 inches (this depends on the exact scatter plot, but a reasonable estimate from typical child growth and the plot’s scale: age 8 - 50 inches, age 12 - ~58 inches, so age 14 would be ~61 inches).

Answer:

The association between age and height is positive, linear, and moderately strong with no outliers.

Part b: Predict Height for 14 - Year - Old