Question
Read the following description of a data set.
Turner hangs his laundry outside every Saturday and has noticed that his clothes dry faster on some days than others. He is curious to know how the daily temperature influences the time it takes for his clothes to dry.
Over the last several Saturdays, he recorded the temperature (in Celsius), x, and the time it had taken for his clothes to dry (in hours), y.
The least squares regression line of this data set is:
y=
–
1.042x+41.444
How long does this line predict Turner's clothes will take to dry when it is 22 degrees Celsius?
Round your answer to the nearest integer.
hours
Turner hangs his laundry outside every Saturday and has noticed that his clothes dry faster on some days than others. He is curious to know how the daily temperature influences the time it takes for his clothes to dry.
Over the last several Saturdays, he recorded the temperature (in Celsius), x, and the time it had taken for his clothes to dry (in hours), y.
The least squares regression line of this data set is:
y=
–
1.042x+41.444
How long does this line predict Turner's clothes will take to dry when it is 22 degrees Celsius?
Round your answer to the nearest integer.
hours
Answers
GPT-4o mini
To predict how long Turner's clothes will take to dry at 22 degrees Celsius, we can substitute \( x = 22 \) into the regression equation:
\[
y = -1.042(22) + 41.444
\]
Calculating the right side:
\[
y = -1.042 \times 22 + 41.444
\]
\[
y = -22.924 + 41.444
\]
\[
y = 18.52
\]
Rounding to the nearest integer, we find that the predicted time for Turner's clothes to dry at 22 degrees Celsius is:
\[
\boxed{19} \text{ hours}
\]
\[
y = -1.042(22) + 41.444
\]
Calculating the right side:
\[
y = -1.042 \times 22 + 41.444
\]
\[
y = -22.924 + 41.444
\]
\[
y = 18.52
\]
Rounding to the nearest integer, we find that the predicted time for Turner's clothes to dry at 22 degrees Celsius is:
\[
\boxed{19} \text{ hours}
\]