Line of Best Fit

Sometimes points on a scatter plot are represented by a trend line or a ___________________. You can study the line to see how the data behaves. You may have a basis predict what the data might be for values not given. line of best fit

Line of Best Fit Line of Best Fit is a line that approximates a trend for the data in a scatter plot. It shows pattern and direction

Line of Best Fit a line that approximates a trend for the data in a scatter plot shows pattern and direction

How to Find the Line of Best Fit The line of best fit should: pass through as many points as possible allow remaining points to be grouped equally above and below the line

Draw the line of best fit for the following scatter plots:

Draw the line of best fit for the following scatter plots:

Why make a Line of Best Fit? Helps us to make predictions by INTERPOLATING EXTRAPOLATING

Interpolating: Estimating a value BETWEEN two measurements in a set of data Extrapolating: Estimating a value BEYOND the range of a set of data Helps us determine if it is a weak or strong correlation.

Interpolating – what would the wife’s age be of a husband who is 57? Extrapolating - what would the wife’s age be of a husband who is 84?

If the data points are close to the line of best fit, it is said to have a ___________correlation. strong strong positive weak positive strong negative weak negative

Use the line of best fit to predict how many tornadoes may be reported in the United States in 2015 if the trend continues. 1200 1000 800 600 If the trend continues we predict that there will be 1200 tornadoes reported in 2015. 400 200 1950 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010 2015

Finding the Line of BEST Fit Usually there is no single line that passes through all the data point, so you try to find the line that best fits the data. Step 1: using a ruler, place it on the graph to find where the edge of the ruler touches the most points. Step 2: Draw in the line. Make sure it touches at least 2 points.

Finding the Line of BEST Fit (continued) Step 3: Find the slope between two points Step 4: Substitute that into slope- intercept form of an equation and solve for “b.” Step 5: Write the equation of the line in slope-intercept form.

Let’s try one: SANDWICH Total Fat (g) Total Calories Grilled Chicken 5 300 Hamburger 9 260 Cheeseburger 13 320 Quarter Pounder 21 420 Quarter Pounder with Cheese 30 530 Big Mac 31 560 Arch Sandwich Special 550 Arch Special with Bacon 34 590 Crispy Chicken 25 500 Fish Fillet 28 Grilled Chicken with Cheese 20 440