Question

percent carbon weight supported (in kilograms)
1.03 1,066
1.11 1,186
1.18 1,123
1.23 1,102
1.30 1,208
1.48 1,265
1.69 1,194
1.71 1,301
the correct least squares regression line for the data set is:
y = 239.903x + 858.855
use it to complete the following sentence:
if a car frame has one additional percentage point of carbon, the least squares regression
line predicts it can support more kilograms.

Explanation:

Step1: Recall the form of a linear regression equation

The general form of a linear regression equation is \(y = mx + b\), where \(m\) is the slope and \(b\) is the y - intercept.

Step2: Interpret the slope in the context of the problem

In the equation \(y = 239.903x+858.855\), \(x\) represents the percent carbon and \(y\) represents the weight supported. The slope \(m = 239.903\). The slope of a regression line \(m=\frac{\Delta y}{\Delta x}\). Here, \(\Delta x = 1\) (since we are looking at an increase of one percentage point of carbon).

Answer:

\(239.903\)