Investigating Scatter Plots Scatter plots – show correlations (relationships) between two different pieces of data.  dependent variable (y’s or range) are affected by the independent variable  independent variable (x’s or domain) cause the change in dependent variable

Investigating Scatter Plots Data is collected and plotted on a graph A pattern may be generally linear, but not form a perfect straight line.

Investigating Scatter Plots Positive correlations occur when two variables or values move in the same direction.  As the number of hours that you study increases your overall class grade increases

Investigating Scatter Plots – Positive Correlation Study TimeClass Grade

Investigating Scatter Plots Negative Correlations occur when variables move in opposite directions  As the number of days per month that you exercise increases your actual weight decreases

Investigating Scatter Plots – Negative Correlation Work out timeWeight

Investigating Scatter Plots No correlation exists if there is no noticeable pattern in the data  There is no relationship between the number of shirts someone owns and their annual salary

Investigating Scatter Plots – No Correlation number of shirts ownedsalary

Line of Best Fit A line of best fit is a line that best represents the trend of the data on a scatter plot. A line of best fit may also be called a trend line  An equation of this line can be used to make predictions  The slope of the line is the average increase or decrease in y for every x  The y intercept is the value of y when x =0  The line may pass through some of the points, none of the points, or all of the points.

Use the data to create a scatter plot Sandwich Total Fat (g) (X) Total Calories (y) Hamburger9260 Cheeseburger13320 Quarter Pounder21420 Quarter Pounder with Cheese30530 Big Mac31560 Arch Sandwich Special31550 Arch Special with Bacon34590 Crispy Chicken25500 Fish Fillet28560 Grilled Chicken20440 Grilled Chicken Light5300

Scatter Plot of the Data

Using Graph Calculator for scatter plots and line of best fit Reset your calculator 2 nd, +, 7, 1, 2 See “STAT PLOT” above Y= 2 nd, Y =, enter, enter ( this turns plotter on ) STAT, Enter, L1 are x’s, L2 are y’s Enter in your data for fat and calories

Using Graph Calculator for scatter plots and line of best fit See “STAT PLOT” above Y= 2 nd, Y =, enter, enter ( this turns plotter on ) STAT, Enter, L1 are x’s, L2 are y’s Enter in your data for fat and calories Press Graph, (why cant I see anything?)

Using Graph Calculator for scatter plots and line of best fit 2 nd, Y =, enter, enter ( this turns plotter on ) STAT, Enter, L1 are x’s, L2 are y’s Enter in your data for fat and calories Press Graph, (why cant I see anything?) Window, adjust settings Xmin = 0 Xmax = 35 Ymin = 0 Ymax = 600 Graph

Using Graph Calculator for scatter plots and line of best fit We can have the calculator find an equation for line of best fit, using linear regression. STAT, CALC, #4, Store the equation using ALPHA TRACE Graph Now that we have an equation that models the data’s behavior, we can make predictions. How many calories would expect a food item to have if it had 35 grams of fat? about 604

Y = 11.73x C = 11.73f The slope is the average increase in Calories for every gm of fat (slope is average change in y for every x) The y intercept is the number of calories when a food item has no fat (y intercept is the value of y when x equals 0)

Things to remember positive correlation has X and Y values that rise together. negative correlation has X values that rise as Y values decrease no correlation has no visible relationship line of best fit is the line that best shows the trend of the data An equation of the line of best fit is a model of the data’s behavior and can be used to make predictions Slope if average increase in y for every x Y intercept is value of y when x = 0