Question

Use the least squares regression line of this data set to predict a value.
Doug 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.
Temperature Drying time
17 19
22 13
28 16
31 13
33 12
The least squares regression line of this data set is:
y=
–
0.324x+23.084
How long does this line predict Doug's clothes will take to dry when it is 26 degrees Celsius?
Round your answer to the nearest integer.
hours

Answer 1

To predict the drying time when the temperature is 26 degrees Celsius, we will use the least squares regression line given by the equation:

\[ y = -0.324x + 23.084 \]

Substituting \( x = 26 \) into the equation:

\[
y = -0.324(26) + 23.084
\]

Calculating:

\[
y = -8.424 + 23.084
\]

\[
y = 14.66
\]

Rounding to the nearest integer, the prediction for how long Doug's clothes will take to dry at 26 degrees Celsius is:

\[
\boxed{15} \text{ hours}
\]