Felipe is preparing for the national spelling bee and is following a strict study plan. To create the plan, he timed how long it had taken him to memorize several words.
Felipe recorded the number of letters in each word, x, and how many minutes, y, it had taken him to memorize it.
The least squares regression line of this data set is:
y=3.477x–50.707
How many minutes does this line predict Felipe would need to memorize a 17-letter word?
Round your answer to the nearest thousandth.
minutes
1 answer
To predict how many minutes Felipe would need to memorize a 17-letter word using the least squares regression line \( y = 3.477x - 50.707 \), we simply need to plug in \( x = 17 \) into the equation.
\[ y = 3.477(17) - 50.707 \]
Calculating \( 3.477 \times 17 \):
\[ 3.477 \times 17 = 59.109 \]
Now we will subtract \( 50.707 \):
\[ y = 59.109 - 50.707 = 8.402 \]
Thus, the predicted time for Felipe to memorize a 17-letter word is:
\[ \boxed{8.402} \text{ minutes} \]
