Read the following description of a data set.

Question

Eliana 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, Eliana 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=3.981x+39.029
How many bottles of water does this line predict Eliana would sell on a day with a high temperature of 35 degrees Celsius?
Round your answer to the nearest integer.
bottles

Answer 1

To find the predicted number of bottles Eliana would sell on a day with a high temperature of 35 degrees Celsius, we can substitute \( x = 35 \) into the least squares regression line equation:

\[ y = 3.981x + 39.029 \]

Substituting \( x = 35 \):

\[ y = 3.981(35) + 39.029 \]

Calculating \( 3.981 \times 35 \):

\[ 3.981 \times 35 = 139.335 \]

Adding \( 39.029 \) to this result:

\[ y = 139.335 + 39.029 = 178.364 \]

Now, rounding \( 178.364 \) to the nearest integer gives:

\[ y \approx 178 \]

Therefore, the predicted number of bottles Eliana would sell on a day with a high temperature of 35 degrees Celsius is 178 bottles.