How to write an equation for line of best fit

Asked by admin @ 27/11/2021 in Mathematics viewed by 331 People

How do you write an equation for the line of best fit?

Answered by admin @ 27/11/2021

Answer:

A line of best fit (or "trend" line) is a straight line that best represents the data on a scatter plot.

This line may pass through some of the points, none of the points, or all of the points.

Step-by-step explanation:

1. Prepare a scatter plot of the data on graph paper.

2. Using a strand of spaghetti, position the spaghetti so that the plotted points are as close to the strand as possible.

3. Find two points that you think will be on the "best-fit" line.

4. We are choosing the points (9, 260) and (30, 530).

You may choose different points.

5. Calculate the slope of the line through your two points (rounded to three decimal places).

$\frac{530-260}{30-9} =\frac{270}{21} =12.857$

6. Write the equation of the line.

$y-y_{1} m(x-x_{1} )\\y-260=12.857(x-9)\\y=12.857(x-9)+260$

7. This equation can now be used to predict information that was not plotted in the scatter plot.

Question: Predict the total calories based upon 22 grams of fat.

y=12.857(22-9)+260

y=12.857(13)+260

y=427.141

ANS: 427.141 calories

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