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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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.
Total Fat (g)
Quarter Pounder with Cheese
Arch Sandwich Special
Arch Special with Bacon
Grilled Chicken Light
Is there a relationship between the fat grams and the total calories in fast food?
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.
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)
rounded to three decimal places.
We calculate slope using the slope formula
y2 – y1
x2 – x1
(9 , 260) & (30 , 530)
Remember a linearequation is written y = mx + b or y = a + bx
y - intercept
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)
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.
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.
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.