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Read the following description of a data set. $\newline$ A French car company wants to cut costs by using cheaper low-carbon steel in its car frames. To determine how varying the carbon content will affect strength, company engineers manufactured several car frames.For each car frame, the engineers noted the percentage of carbon, $x$ , as well as the weight it could support (in kilograms), $y$ .The least squares regression line of this data set is: $y = 370.966x + 282.742$ $\newline$ Complete the following sentence: $\newline$ If a car frame has one additional percentage point of carbon, the least squares regression line predicts it can support ___ more kilograms.

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Interpret regression lines

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Q. Read the following description of a data set.

\newline

A French car company wants to cut costs by using cheaper low-carbon steel in its car frames. To determine how varying the carbon content will affect strength, company engineers manufactured several car frames.For each car frame, the engineers noted the percentage of carbon,

x

, as well as the weight it could support (in kilograms),

y

.The least squares regression line of this data set is:

y = 370.966x + 282.742

\newline

Complete the following sentence:

\newline

If a car frame has one additional percentage point of carbon, the least squares regression line predicts it can support ___ more kilograms.

Identify coefficient of $x$ : Identify the coefficient of $x$ in the regression equation to determine the increase in weight support per percentage point increase in carbon content.
Interpret coefficient of $x$ : Interpret the coefficient of $x$ as the increase in weight (in kilograms) that the car frame can support for each additional percentage point of carbon.

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