Question

use the least squares regression line of this data set to predict a value.
roy teaches a standardized test prep course. students take a diagnostic test at the beginning of the course and then take the real test at the end. roy wanted to know how well the diagnostic test predicts a students score on the real test.
he recorded each students score on the diagnostic test, x, and on the real test, y. both tests were graded on a scale from 120 to 180.
the least squares regression line of this data set is:
y = 0.463x + 82.822
if a student got a 132 on the diagnostic test, how many points does this line predict the student would get on the real test?
round your answer to the nearest integer.
points

Explanation:

Step1: Identify the regression line and x - value

The least squares regression line is given by \(y = 0.463x+82.822\), and the value of \(x\) (diagnostic test score) is \(x = 132\).

Step2: Substitute x into the regression line

Substitute \(x = 132\) into the equation \(y=0.463x + 82.822\).
We calculate \(y=0.463\times132 + 82.822\).
First, calculate \(0.463\times132\):
\(0.463\times132=(0.4 + 0.06+0.003)\times132=0.4\times132+0.06\times132 + 0.003\times132=52.8+7.92 + 0.396 = 61.116\)
Then, add \(82.822\) to the result: \(y=61.116 + 82.822=143.938\)

Step3: Round to the nearest integer

Rounding \(143.938\) to the nearest integer gives \(144\).

Answer:

\(144\)