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Scatterplots and a line of best fit. When data is displayed with a scatterplot , it is often useful to attempt tp represent the data with a straight line so we could predict values not displayed on a scatterplot. Such a line is called “ line of best fit ”.

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Presentation Transcript
slide2

When data is displayed with a scatterplot, it is often useful to attempt tp represent the data with a straight line so we could predict values not displayed on a scatterplot.

Such a line is called “line of best fit”.

A line of best fit is a straight line that best represents the data on a scatterplot.

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

Its best to try to get your line to pass through at least two of the points, but in the middle of all of them.

slide3

Sandwich

Total Fat (g)

Total Calories

Hamburger

9

260

Cheeseburger

13

320

Quarter Pounder

21

420

Quarter Pounder with Cheese

30

530

Big Mac

31

560

Arch Sandwich Special

31

550

Arch Special with Bacon

34

590

Crispy Chicken

25

500

Fish Fillet

28

560

Grilled Chicken

20

440

Grilled Chicken Light

5

300

Is there a relationship between the fat grams and the total calories in fast food?

slide4

Can we predict the number of total calories based upon the total fat grams? Lets see!

First, create a scatterplot of the data on a piece of graph paper.

slide5

1.  Prepare a scatter plot of the data.

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’re going to choose the two point (9,260) & (30,530)

slide6

5.  Calculate the slope of the line through your two points.

rounded to three decimal places.

We calculate slope using the slope formula

y2 – y1

x2 – x1

(9 , 260) & (30 , 530)

x1

y1

x2

y2

Remember a linearequation is written y = mx + b or y = a + bx

slope

y - intercept

slide7

6.  Write the equation of the line.

Remember we write equations as y =mx + b or y = a + bx

Use the point-slope formula

y – y1 = slope (x – x1)

Our 2 points

( 9 , 260) & ( 30 , 530)

x1

y1

x2

y2

slide8

Now we have the equation:

y = 12.87(x – 9) + 260

Multiply 12.87 by both x and –9 to get this equation

y = 12.87x – 115.83 + 260

y = 12.87x + 144.17

Now add 260 with –115.83 to get this equation

This is the equation of the line we just made to fit the data!

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

slide9

Predicting: - If you are looking for values that fall within the plotted values, you are interpolating.

- If you are looking for values that fall outside the plotted values, you are extrapolating.Be careful when extrapolating.  The further away from the plotted values you go, the less reliable is your prediction.

Using your best fit line, predict the total calories based upon 22 grams of fat.

y = 12.87x + 144.17

y = 12.87 (22) + 144.17

Substitute 22 for x

y = 427.141

This means that if you have a sandwich that has 22 grams of fat, it will have 427.141 calories.

so who has the correct line of best fit
So who has the Correct line of best fit

In step 4 above, we chose two points to form our line-of-best-fit.  It is possible, however, that someone else will choose a different set of points, and their equation will be slightly different.  Your answer will be considered CORRECT, as long as your calculations are correct for the two points that you chose.