Researchers at a cognitive psychology lab are studying how children develop their color vocabulary. In a recent study, the researchers showed children of various ages different colored objects and asked them to name the colors.
They recorded each child's age (in months), x, and the number of colors the child could name, y.
The least squares regression line of this data set is:
y = 0.106x+5.814
How many colors does this line predict a 25-month-old child would be able to name?
Round your answer to the nearest integer.
_______ colors
The least squares regression line equation is y = 0.106x + 5.814
Plugging in x = 25 into the equation:
y = 0.106(25) + 5.814
y = 2.65 + 5.814
y ≈ 8.464
Therefore, the line predicts that a 25-month-old child would be able to name approximately 8 colors.