A scatter plot Used to display values for typically for a set of

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1 Name: MPM 1D Lesson Date: U4-L3 Trends & Lines of Best Fit A scatter plot Used to display values for typically for a set of used to determine if a or exists between two variables if a trend exists, we can use a or a to best represent the data In many cases, plotted data points do not lie on a (scatter plot), however, the points may be close to a straight line i.e. Line of Best Fit: line that best describes the points on the scatter plot should be can be used for between two variables on each side of the line of values not recorded or plotted Examples NOTE: LoBF does NOT have to pass through any points in your data set but when we draw them by hand it MUST pass through at least two actual points so we can determine the equation of the LoBF Outlier A data point that significantly defers from the rest.

2 Extrapolating vs. Interpolating 2 predictions made the given data set is called predictions made the given data set is called The Analysis Stage A. Correlations: Is there a correlation? Is the relation positive or negative? Positive correlation: as the independent variable (x) increases as the dependent variable (y) increases Negative correlation: as the independent variable (x) increases, the dependent variable (y) decreases Example State whether the following scatterplots suggest a linear or non-linear correlation. For those that are linear, is it a positive or negative correlation? a) b) c) d)

3 3 B. Define the correlation in words. Example As the number of hours of watching TV the test scores., Source: C. Is the data best represented by a line of best fit or curve of best fit? D. Discrete vs Continuous data: Does the data between the given points realistically have meaning?

4 E. Making predictions: Interpolating and Extrapolating 4 predictions made the known values is called predictions made the known values is called Examples 1. A skateboarder starts from various points along a steep ramp and practices coasting to the bottom. The table lists the skateboarder s initial height above the bottom of the ramp and his speed at the bottom of the ramp. a) Draw a scatterplot. Be sure to label your axes and give your graph a title. b) Draw the line of best fit. c) Describe the relationship between the two variables d) Identify any outliers. What might cause an outlier in this data set? Initial Height (m) Speed (m/s) In your binder: e) Find the equation of the line of best fit. i. Locate 2 points ON your line of best fit and write them as ordered pairs. ii. Calculate the slope of the line using the appropriate formula. iii. Write the equation of the line of best fit. iv. How does the initial height relate to the speed? Explain in words. v. Correlation: Is there a relation? Is there a positive or negative correlation? vi. Correlation with variables: Define the relation in words. vii. Linear or Non-Linear: Is the data best represented by a straight line or a curve? viii. Discrete or Continuous: Does the data between the given points have any meaning? To compare your graph and equation, go to desmos.com. Enter the data into a table. Go to a new relation and type in y1~mx1+b.

5 Definitions: a) estimate a value BEYOND the range of a data set 5 b) measurement that differs significantly from the rest c) relationship between two variables d) conclusion based on reasoning and data e) estimate a value BETWEEN two measurements in a data set Homework & Practice 2. The table below shows the number of fruit flies after they have been sprayed: Time (hours) Number of Fruit Flies a) Create a scatter plot for this data. Be sure to label all parts of your graph. b) Draw the line of best fit. c) Write the equation of the line of best fit. Provide a complete algebraic solution. d) Determine algebraically, how long after spraying, the fruit fly population is 20 fruit flies. e) What does the slope represent in the context of the problem? Explain. f) What does the y-intercept represent in the context of the problem? Explain. g) Using your graph and/ or equation, state an example of each of the following: (i) interpolation (ii) extrapolation h) Describe the correlation. Is the data continuous or discrete? Explain.

6 6 3. The table below shows the measures of the length of a bird and its wingspread. a) Draw the scatter plot on grid paper and draw the line of best fit b) Write the equation of the line of best fit. Length (cm) Wingspread (cm) Lengths and Wingspreads of Birds c) Analyze the data by answering the following questions: How does the length of a bird relate to the wingspread? Explain in words. Correlation: Is there a relation? Is there a positive or negative correlation? Correlation with variables: Define the relation in words. Linear or Non-Linear: Is the data best represented by a straight line or a curve? Discrete or Continuous: Does the data between the given points have any meaning? 4. Tall Buildings: The table gives the number of stories and heights of seven buildings in Canadian cities. Building City Number of Stories Height (m) First Canadian Place Toronto Manulife Place Edmonton PetroCan Center Calgary Place de Ville Ottawa Royal Center Vancouver Rue de la Gauchetiere Montreal Toronto Dominion Center Winnipeg a) Draw a scatter plot of number of stories versus height. b) Draw the line of best fit. c) Write the equation of the line of best fit. d) How does the height of a building seem to be related to the number of stories? Explain in words. e) Correlation: Is there a relation? Is there a positive or negative correlation. f) Correlation with variables: Define the relation in words. g) Linear or Non-Linear: Is the data best represented by a straight line or a curve? h) Discrete or Continuous: Does the data between the given set of points have any meaning?