Question

use the least squares regression line of this data set to predict a value.
jasmine is an editor reviewing short story submissions for a literary magazine.
she collected data showing that shes an efficient reviewer and wants to leverage
this to get a raise.
for a week, jasmine recorded the number of words in each short story
submission, x, and how long it took her to review that story (in minutes), y.
the least squares regression line of this data set is:
y = 0.005x + 17.299
how long does this line predict it would take jasmine to review a 5,525 - word story?
round your answer to the nearest thousandth.
minutes

Explanation:

Step1: Substitute \(x = 5525\) into the regression equation

Given the regression line \(y=0.005x + 17.299\), substitute \(x = 5525\) into it. So we get \(y=0.005\times5525+17.299\).

Step2: Calculate the product

First, calculate \(0.005\times5525\). Using the formula \(a\times b\) (where \(a = 0.005\) and \(b = 5525\)), \(0.005\times5525=\frac{5}{1000}\times5525=\frac{5\times5525}{1000}=\frac{27625}{1000}=27.625\).

Step3: Calculate the sum

Then, calculate \(y\). \(y=27.625 + 17.299\). Using the formula \(a + b\) (where \(a=27.625\) and \(b = 17.299\)), \(y=44.924\).

Answer:

\(44.924\)