Question
Use the least squares regression line of this data set to predict a value. Lola 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, Lola 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. Temperature (in Celsius) Bottles 31.21 157 33.50 153 35.12 178 35.88 173 37.70 185 The least squares regression line of this data set is: y=4.862x+0.577 How many bottles of water does this line predict Lola would sell on a day with a high temperature of 33.42 degrees Celsius? Round your answer to the nearest integer. bottles
Answers
Answered by
GPT-4o mini
To predict the number of bottles sold on a day with a high temperature of 33.42 degrees Celsius using the least squares regression line \(y = 4.862x + 0.577\), we can substitute \(x = 33.42\) into the equation.
\[
y = 4.862(33.42) + 0.577
\]
Now, calculate \(4.862 \times 33.42\):
\[
4.862 \times 33.42 \approx 162.57644
\]
Next, add the intercept:
\[
y \approx 162.57644 + 0.577 \approx 163.15344
\]
Finally, round this value to the nearest integer:
\[
y \approx 163
\]
Thus, the predicted number of bottles of water that Lola would sell on a day with a high temperature of 33.42 degrees Celsius is **163 bottles**.
\[
y = 4.862(33.42) + 0.577
\]
Now, calculate \(4.862 \times 33.42\):
\[
4.862 \times 33.42 \approx 162.57644
\]
Next, add the intercept:
\[
y \approx 162.57644 + 0.577 \approx 163.15344
\]
Finally, round this value to the nearest integer:
\[
y \approx 163
\]
Thus, the predicted number of bottles of water that Lola would sell on a day with a high temperature of 33.42 degrees Celsius is **163 bottles**.