Question

Read the following description of a data set. Janelle wants to determine how much bottled water she should stock in her store on any given day. She believes that sales of bottled water are much higher on hotter days. To test this hypothesis, Janelle tracked her water bottle sales over several days. She recorded the high temperature (in Celsius), x, and the number of bottles sold, y, each day. The least squares regression line of this data set is: y=77.823x–2,440.061 How many bottles of water does this line predict Janelle would sell on a day with a high temperature of 38.89 degrees Celsius? Round your answer to the nearest integer. bottles

Answer 1

To find the predicted number of bottles Janelle would sell on a day with a high temperature of 38.89 degrees Celsius using the least squares regression line equation:

\[
y = 77.823x - 2,440.061
\]

we need to substitute \(x\) with 38.89:

\[
y = 77.823(38.89) - 2,440.061
\]

Now, calculate \(77.823 \times 38.89\):

\[
77.823 \times 38.89 \approx 3,030.81847
\]

Next, plug this value into the equation:

\[
y \approx 3,030.81847 - 2,440.061
\]

Now, perform the subtraction:

\[
y \approx 3,030.81847 - 2,440.061 \approx 590.757
\]

Rounding this result to the nearest integer gives:

\[
y \approx 591
\]

Therefore, the predicted number of bottles Janelle would sell on a day with a high temperature of 38.89 degrees Celsius is **591 bottles**.