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Semester B: Unit 2:Scatter Plots Lesson1: Interpret Scatter Plots Scatter Plot: a graph in which 2 variables are plotted along the x and y axis. The purpose of a scatter plot is to show the relationship between the 2 variables Parts of a Scatter Plot: 1 If you are given a table, you can plot the points on a graph to create a scatter plot. The first point is the x coordinate and the second point is the y coordinate. Example: Relationships on a Scatter Plot: you can determine what kind of relationship exists (if there is one) between the 2 variables. Example: As the tree gets older, the height increases 2 Example: As the number of people in a family increases, the time spent cleaning the house decreases Find more help here: https://docs.google.com/a/agora.org/viewer?a=v&pid=sites&srcid=YWdvcmEub3JnfG5leHQtZ2VuLWxlc 3Nvbi1kb2N1bWVudHN8Z3g6Nzk2OTRhZWU4NDYyYjhhMg Examples and Notes from Class: 3 Lesson 2: Draw Scatter Plots First Variable: plot on the x axis. Second Variable: plot on the y axis Draw a Scatter Plot: 1. Determine the label for the x and y axis. 2. Determine a scale for each axis (the scale does NOT have to be the same on each axis) The scale is the number you count by and label on the axis 3. Determine a title for the Scatter Plot 4. Plot the points on the graph Example: 4 Find more help here: https://docs.google.com/a/agora.org/viewer?a=v&pid=sites&srcid=YWdvcmEub3JnfG5leHQtZ2VuLWxlc 3Nvbi1kb2N1bWVudHN8Z3g6ODg1ZjRkMmZlODMxNmNk Notes from Class: 5 Lesson 3: Correlation of Scatter Plots Positive Correlation: both variables are increasing Example: As temperature increases, sales of ice cream cones increases Negative Correlation: one variable increases and one variable decreases Example: as the cost of an ice cream cone increases, the number sold decreases 6 No Correlation: there is no relationship between the 2 variables Example: there is no relationship between and number of flavors of ice cream and the number of cones sold 7 Determine the Correlation from a Table: follow the pattern for the x and y values Example: Chart A: x values are increasing in a pattern of 1; y values show no pattern No Correlation Chart C: x values increasing in a pattern of 1; y values decreasing in a pattern of 2 Negative Correlation Find more help here: https://docs.google.com/a/agora.org/viewer?a=v&pid=sites&srcid=YWdvcmEub3JnfG5leHQtZ2VuLWxlc 3Nvbi1kb2N1bWVudHN8Z3g6M2E3OWNlMzk3OWUyMGM1Ng Notes and Examples from Class 8 Lesson 4: Linear and Non-Linear Scatter Plots Perfect Linear Association: when variables change at a constant rate. The pattern of change is constant for both variables. When you connect the points, it will be a straight line. (This does NOT mean that the pattern is the same for both variables, just constant) Example: Non-Perfect Linear Association: the points will generally fall in a straight line, but not exactly. Example: 9 Non-Linear Association: the data appears as a curved instead of a straight line. The pattern of both variables is not constant (it may be constant for 1 variable). There is a relationship between the 2 variables, but it is not linear Example: x variable: increases by 1 y variable: increases at first, then decreases Find more help here: https://docs.google.com/a/agora.org/viewer?a=v&pid=sites&srcid=YWdvcmEub3 JnfG5leHQtZ2VuLWxlc3Nvbi1kb2N1bWVudHN8Z3g6Nzg0ZTc0OGI0YTk3ZDU1Yw Notes and Examples from Class 10 Lesson 6: Clusters and Outliers Cluster: group of points that are close together Example: most of the points are in a group near each other. This scatter plot shows a negative correlation Example: there is 1 cluster. This scatter plot shows a positive correlation 11 Outlier: a point that does not fall in the main pattern of a scatter plot. On a graph, an outlier is not close to the other points. Example: Find more help here: https://docs.google.com/a/agora.org/viewer?a=v&pid=sites&srcid=YWdvcmEub3JnfG5leHQtZ2VuLWxlc 3Nvbi1kb2N1bWVudHN8Z3g6NTkwNGFiZDVjMmM0NzFhMQ Notes and Examples from Class: 12 Lesson 7: Identify a Line of Best Fit for a Scatter Plot Line of Best Fit: line that shows the general direction of the points on a scatter plot Example: Examples of Poorly drawn Lines of Best Fit: 13 Find more help here: https://docs.google.com/a/agora.org/viewer?a=v&pid=sites&srcid=YWdvcmEub3JnfG5leHQtZ2VuLWxlc 3Nvbi1kb2N1bWVudHN8Z3g6NjI4MDgyNTk4NGJlMDFmNQ Notes and Examples from Class: 14 Lessons 8: Define the Equation for the Line of Best Fit for a Scatter Plot Step 1: draw the line of best fit: a straight line that falls in the middle of the data and represents the data as best it can Step 2: choose 2 points on the line of best fit the go directly through the line or the 2 points closest to the line Step 3: use the coordinates of the 2 points chosen in step 2 and the slope formula to find the slope of the line Step 4: substitute the slope and the x and y values of 1 point into y = mx + b. Solve the equation for b Step 5: write the equation of the line in slope intercept form, substituting the slope for m and the y-intercept for b: y = mx + b 15 Example: Steps 1 and 2: Draw the Line of Best Fit & choose 2 points on the line Step 3: Find the slope using 2 points chosen in step 2 16 Step 4: Use the point (1, 950) for x and y and the slope 150 for m. Substitute into y = mx + b to find the value of b Step 5: Write the equation of the line of best fit in slope-intercept form: y = mx +b m = 150, b = 800 y = 150x + 800 17 Find more help here: https://docs.google.com/a/agora.org/viewer?a=v&pid=sites&srcid=YWdvcmEub3JnfG5leHQtZ2VuLWxlc 3Nvbi1kb2N1bWVudHN8Z3g6NjUxNWNhN2MyNmQxMWZiMQ Notes and Examples from Class: 18 Lesson 9: Calculate the Correlation Coefficient for a Data Set Correlation Coefficient: shows how closely two sets of data are related. It uses a value between -1 and +1. Values closer to +1 (like 0.9 or 0.88) show the data has a positive correlation: (both variables are increasing) Values closer to -1 (like -0.95 or -0.89) show the data has a negative correlation: (one variable is increasing, one variable is decreasing) Value of 0 means there is no correlation between the variables To find the Correlation Coefficient, you must complete a Correlation Table Example: Step 1: find the mean (average) of the x and y values Step 2: subtract each x value from the mean (represented by the variable a) subtract each y value from the mean (represented by the variable b) Step 3: calculate a • b; a2 and b2 Step 4: find the sums of a • b; a2 and b2 Step 5: use the formula to calculate the correlation coefficient 19 Formula for the Correlation Coefficient: Substitute 51 for a • b, 10 for a2 and 329.2 for b2 51 ÷ 57.38 = .89 Correlation Coefficient = .89 shows a strong, positive relationship. You can see that from the scatter plot as well. The dots are relatively close together. Find more help here: https://docs.google.com/a/agora.org/viewer?a=v&pid=sites&srcid=YWdvcmEub3JnfG5leHQtZ2VuLWxlc 3Nvbi1kb2N1bWVudHN8Z3g6N2M0NTI2NjNmMjRjNjU2MA Notes and Examples from Class 20 21