Question

sandeep wants to determine how much bottled water he should stock in his store on any given day. he believes that sales of bottled water are much higher on hotter days. to test this hypothesis, sandeep tracked his water bottle sales over several days. he recorded the high temperature (in celsius), x, and the number of bottles sold, y, each day. temperature (in celsius) | bottles: 31.12 | 179; 31.30 | 162; 33.77 | 194; 35.95 | 196; 38.63 | 191 the least squares regression line of this data set is: y = 3.116x + 77.976 how many bottles of water does this line predict sandeep would sell on a day with a high temperature of 35.15 degrees celsius? round your answer to the nearest integer.

Explanation:

Step1: Identify the regression equation

The least squares regression line is given by \( y = 3.116x + 77.976 \), where \( x \) is the temperature (in Celsius) and \( y \) is the number of bottles sold.

Step2: Substitute the given temperature into the equation

We need to find the number of bottles sold when the temperature \( x = 35.15 \) degrees Celsius. Substitute \( x = 35.15 \) into the equation:
\[
y = 3.116 \times 35.15 + 77.976
\]

Step3: Calculate the product

First, calculate \( 3.116 \times 35.15 \):
\[
3.116 \times 35.15 = 3.116 \times (35 + 0.15) = 3.116 \times 35 + 3.116 \times 0.15 = 109.06 + 0.4674 = 109.5274
\]

Step4: Add the constant term

Now, add \( 77.976 \) to the result from Step 3:
\[
y = 109.5274 + 77.976 = 187.5034
\]

Step5: Round to the nearest integer

Round \( 187.5034 \) to the nearest integer, which is \( 188 \).

Answer:

188