Question
Use the least squares regression line of this data set to predict a value.
Pedro 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.
Pedro recorded the number of letters in each word, x, and how many minutes, y, it had taken him to memorize it.
Letters Minutes
9 3.4
10 4.3
11 3.7
13 5.4
20 6.9
The least squares regression line of this data set is:
y=0.309x+0.842
How many minutes does this line predict Pedro would need to memorize an 18-letter word?
Round your answer to the nearest thousandth.
minutes
Pedro 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.
Pedro recorded the number of letters in each word, x, and how many minutes, y, it had taken him to memorize it.
Letters Minutes
9 3.4
10 4.3
11 3.7
13 5.4
20 6.9
The least squares regression line of this data set is:
y=0.309x+0.842
How many minutes does this line predict Pedro would need to memorize an 18-letter word?
Round your answer to the nearest thousandth.
minutes
Answers
Answered by
GPT-4o mini
To predict the time it would take Pedro to memorize an 18-letter word using the least squares regression line \( y = 0.309x + 0.842 \), we need to substitute \( x = 18 \) into the equation.
\[
y = 0.309(18) + 0.842
\]
Calculating \( 0.309 \times 18 \):
\[
0.309 \times 18 = 5.562
\]
Now, add \( 0.842 \):
\[
y = 5.562 + 0.842 = 6.404
\]
Thus, the predicted time for Pedro to memorize an 18-letter word is approximately:
\[
\boxed{6.404} \text{ minutes}
\]
\[
y = 0.309(18) + 0.842
\]
Calculating \( 0.309 \times 18 \):
\[
0.309 \times 18 = 5.562
\]
Now, add \( 0.842 \):
\[
y = 5.562 + 0.842 = 6.404
\]
Thus, the predicted time for Pedro to memorize an 18-letter word is approximately:
\[
\boxed{6.404} \text{ minutes}
\]