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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: $y = 416.595x + 395.776$ $\newline$ 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 = 416.595x + 395.776

\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.

Determine Effect of Carbon: We need to determine the effect of one additional percentage point of carbon on the weight a car frame can support. The slope of the regression line represents the change in the dependent variable ( $y$ , the weight the car frame can support) for each one-unit change in the independent variable ( $x$ , the percentage of carbon). The slope of the given regression line is $416.595$ .
Calculate Increase in Weight: To find the increase in weight supported for one additional percentage point of carbon, we simply take the slope of the regression line, which is $416.595$ , and understand it as the increase in kilograms for each one percentage point increase in carbon content.
Predicted Increase in Kilograms: Therefore, if a car frame has one additional percentage point of carbon, the least squares regression line predicts it can support $416.595$ more kilograms.

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