Question

run a linear regression analysis on the data table to the right. use that information to answer the following questions.
note: write each answer as an equation. round all values to 3 decimal places.
write the linear equation that models this data:
y = -3.489x + 219.453
use this equation to predict y when x = 38.7. enter the prediction as an equation in the form y =.

Explanation:

Step1: Substitute x value

We are given the linear - equation $y=-3.489x + 219.453$ and $x = 38.7$. Substitute $x = 38.7$ into the equation.
$y=-3.489\times38.7+219.453$

Step2: Calculate the product

First, calculate $-3.489\times38.7=-3.489\times(38 + 0.7)=-3.489\times38-3.489\times0.7=-(3.489\times38+3.489\times0.7)$.
$3.489\times38=(3 + 0.4+0.08 + 0.009)\times38=3\times38+0.4\times38+0.08\times38+0.009\times38=114 + 15.2+3.04+0.342 = 132.582$.
$3.489\times0.7=(3 + 0.4+0.08 + 0.009)\times0.7=3\times0.7+0.4\times0.7+0.08\times0.7+0.009\times0.7=2.1+0.28+0.056+0.0063 = 2.4423$.
$-3.489\times38.7=-(132.582 + 2.4423)=-135.0243$.

Step3: Calculate the final y - value

Then, calculate $y=-135.0243+219.453$.
$y = 84.429$.

Answer:

$y = 84.429$