Question

read the following description of a data set.
piquant candy company is testing a new additive designed to make its hard caramel candies dissolve more slowly. company scientists gave several taste testers pieces of candy with varying amounts of the additive.
the scientists recorded the amount of additive in each piece (in milligrams), x, and how long the taste tester said it took to dissolve completely (in minutes), y.
the least squares regression line of this data set is:
( y = 0.099x + 0.048 )
if a piece of candy has 56.05 milligrams of the additive, how long does the line predict it would take to dissolve completely?
round your answer to the nearest integer.
minutes

Explanation:

Step1: Substitute the value of \(x\) into the regression line equation

Given the regression line \(y = 0.099x+0.048\) and \(x = 56.05\).
Substitute \(x\) into the equation: \(y=0.099\times56.05 + 0.048\).

Step2: Calculate the value of \(y\)

First, calculate \(0.099\times56.05\):
\(0.099\times56.05=(0.1 - 0.001)\times56.05=0.1\times56.05-0.001\times56.05 = 5.605-0.05605=5.54895\).
Then add \(0.048\): \(y = 5.54895+0.048=5.59695\).

Step3: Round the result to the nearest integer

Since \(5.59695\approx6\) (rounding to the nearest integer).

Answer:

\(6\) minutes