Lesson1: Interpret Scatter Plots - Math
Semester B: Unit 2:Scatter PlotsLesson1: Interpret Scatter PlotsScatter 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 variablesParts of a Scatter Plot: 60960047625000If 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 increasesExample: As the number of people in a family increases, the time spent cleaning the house decreasesFind more help here: and Notes from Class:Lesson 2: Draw Scatter PlotsFirst 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 Plot4. Plot the points on the graphExample: Find more help here: from Class: Lesson 3: Correlation of Scatter PlotsPositive Correlation: both variables are increasingExample: As temperature increases, sales of ice cream cones increasesNegative Correlation: one variable increases and one variable decreasesExample: as the cost of an ice cream cone increases, the number sold decreasesNo Correlation: there is no relationship between the 2 variablesExample: there is no relationship between and number of flavors of ice cream and the number of cones sold Determine the Correlation from a Table: follow the pattern for the x and y valuesExample: Chart A: x values are increasing in a pattern of 1; y values show no patternNo CorrelationChart C: x values increasing in a pattern of 1; y values decreasing in a pattern of 2Negative CorrelationFind more help here: and Examples from ClassLesson 4: Linear and Non-Linear Scatter PlotsPerfect 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: 70485080962500Non-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 linearExample:x variable: increases by 1y variable: increases at first, then decreases Find more help here: and Examples from ClassLesson 6: Clusters and OutliersCluster: group of points that are close together70485052641500Example: most of the points are in a group near each other. This scatter plot shows a negative correlationExample: there is 1 cluster. This scatter plot shows a positive correlationOutlier: 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: and Examples from Class: Lesson 7: Identify a Line of Best Fit for a Scatter PlotLine of Best Fit: line that shows the general direction of the points on a scatter plotExample:Examples of Poorly drawn Lines of Best Fit: Find more help here: and Examples from Class: Lessons 8: Define the Equation for the Line of Best Fit for a Scatter PlotStep 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 canStep 2: choose 2 points on the line of best fit the go directly through the line orthe 2 points closest to the lineStep 3: use the coordinates of the 2 points chosen in step 2 and the slope formulato find the slope of the lineStep 4: substitute the slope and the x and y values of 1 point into y = mx + b. Solve the equation for bStep 5: write the equation of the line in slope intercept form, substituting the slope for m and the y-intercept for b: y = mx + bExample: 21145506477000Steps 1 and 2: Draw the Lineof Best Fit & choose2 points on the line60007534226500Step 3: Find theslope using2 points chosen instep 22362200135255Step 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 bStep 5: Write the equation of the line of best fit in slope-intercept form: y = mx +bm = 150, b = 800y = 150x + 800Find more help here: and Examples from Class: 2000250210820Lesson 9: Calculate the Correlation Coefficient for a Data SetCorrelation 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 TableExample: 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 b2Step 4: find the sums of a ? b; a2 and b2Step 5: use the formula to calculate the correlation coefficient295275017018000Formula for the Correlation Coefficient: 160020048133000Substitute 51 for a ? b, 10 for a2 and 329.2 for b2 51 ÷ 57.38 = .89Correlation 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: and Examples from Class ................
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