Question
Use the least squares regression line of this data set to predict a value.
Jerry has trouble getting his math homework done on time, and his mother suspects it is due to lack of sleep.
For the next few nights, Jerry's mother notes the number of hours he sleeps, x, and the number of minutes it takes him to do his math homework the following day, y.
Hours slept Minutes needed to finish math homework
4.1 95
4.4 98
5.1 75
6.3 85
6.4 63
The least squares regression line of this data set is:
y=
–
10.298x+137.369
If Jerry sleeps 4.5 hours one night, how many minutes does this line predict it will take him to do his math homework the next day?
Round your answer to the nearest integer.
minutes
Jerry has trouble getting his math homework done on time, and his mother suspects it is due to lack of sleep.
For the next few nights, Jerry's mother notes the number of hours he sleeps, x, and the number of minutes it takes him to do his math homework the following day, y.
Hours slept Minutes needed to finish math homework
4.1 95
4.4 98
5.1 75
6.3 85
6.4 63
The least squares regression line of this data set is:
y=
–
10.298x+137.369
If Jerry sleeps 4.5 hours one night, how many minutes does this line predict it will take him to do his math homework the next day?
Round your answer to the nearest integer.
minutes
Answers
Answered by
GPT-4o mini
To predict the number of minutes it will take Jerry to do his math homework, we can use the least squares regression line equation provided:
\[ y = -10.298x + 137.369 \]
We need to substitute \( x = 4.5 \) into the equation:
\[ y = -10.298(4.5) + 137.369 \]
Calculating that:
1. First, calculate \( -10.298 \times 4.5 \):
\[
-10.298 \times 4.5 = -46.341
\]
2. Then, add this result to 137.369:
\[
y = -46.341 + 137.369 = 91.028
\]
Now we round \( 91.028 \) to the nearest integer:
\[
y \approx 91
\]
Thus, if Jerry sleeps 4.5 hours, the least squares regression line predicts it will take him approximately **91 minutes** to do his math homework the next day.
\[ y = -10.298x + 137.369 \]
We need to substitute \( x = 4.5 \) into the equation:
\[ y = -10.298(4.5) + 137.369 \]
Calculating that:
1. First, calculate \( -10.298 \times 4.5 \):
\[
-10.298 \times 4.5 = -46.341
\]
2. Then, add this result to 137.369:
\[
y = -46.341 + 137.369 = 91.028
\]
Now we round \( 91.028 \) to the nearest integer:
\[
y \approx 91
\]
Thus, if Jerry sleeps 4.5 hours, the least squares regression line predicts it will take him approximately **91 minutes** to do his math homework the next day.