Question

read the following description of a data set. meteorologists in a seaside town wanted to understand how their annual rainfall is affected by the temperature of coastal waters. for the past few years, they monitored the average temperature of coastal waters (in celsius), x, as well as the annual rainfall (in millimeters), y. the least squares regression line of this data set is: y = 19.405x + 296.234 how much rainfall does this line predict in a year if the average temperature of coastal waters is 13 degrees celsius? round your answer to the nearest integer. millimeters

Explanation:

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

Given the regression line \(y = 19.405x+296.234\) and \(x = 13\).
Substitute \(x = 13\) into the equation: \(y=19.405\times13 + 296.234\).
First, calculate \(19.405\times13\):

$$
LATEXBLOCK0
$$

Then \(y = 252.265+296.234\).

Step2: Calculate the value of \(y\)

\(y=252.265 + 296.234=548.499\).

Step3: Round the result

Round \(548.499\) to the nearest integer. Since the decimal part \(0.499\lt0.5\), we round down.

Answer:

\(548\)