Oct. 11 - Scatter Plots Day 2

1. national farmers day! 10.11.22 Open your chromebook to Brightspace. In the content section, locate your scatterplot practice activity. Agenda: • Warm-up/Graded Classwork • Lesson: Linear Regressions Is cereal soup? Pencil, Calculator, Notebook, Chromebook

2. Warm - up • Open your Chromebook to Brightspace • Content section • 10/10 Practice

3. Place the graphs in order from lowest correlation coefficient to highest correlation coefficient. Place Lowest Here Second Lowest Third Lowest Third Highest Second Highest Place Highest Here

4. Scatter Plots and Lines of Best Fit Day 2 - Linear Regressions

5. I can: • calculate a linear regression equation • determine the correlation coefficient • interpret slope and y-intercept • use the regression equation to predict Scatter Plots and Lines of Best Fit

6. I can: • calculate a linear regression equation • determine the correlation coefficient • interpret slope and y-intercept • use the regression equation to predict Scatter Plots and Lines of Best Fit

7. I can: • calculate a linear regression equation • determine the correlation coefficient • interpret slope and y-intercept • use the regression equation to predict Scatter Plots and Lines of Best Fit

8. I can: • calculate a linear regression equation • determine the correlation coefficient • interpret slope and y-intercept • use the regression equation to predict Scatter Plots and Lines of Best Fit

9. I can: • calculate a linear regression equation • determine the correlation coefficient • interpret slope and y-intercept • use the regression equation to predict Scatter Plots and Lines of Best Fit

10. Correlation Coefficient: The value between -1 and 1 that describes the direction and strength of the data set. (Also called the r-value) Vocabulary

11. Linear Regression Equation: An equation used to make predictions using scatter plot data. (Also called the line of best fit or trend line) Vocabulary

12. The table shows data collected from an ice cream shop for five different dates in a given year. Example - Scatter Plots and Lines of Best Fit

13. Plotting the data gives us this scatter plot. Example - Scatter Plots and Lines of Best Fit

14. Notice there is a strong positive correlation with no outliers. Example - Scatter Plots and Lines of Best Fit

15. We will use technology to calculate the linear regression equation. Example - Scatter Plots and Lines of Best Fit

16. Example - Scatter Plots and Lines of Best Fit

17. This is how we type our usual y=mx+b into the calculator so that it will give us the regression equation information. Example - Scatter Plots and Lines of Best Fit

18. The slope (m) and y-intercept (b) as calculated by the Desmos calculator.

19. Here is our correlation coefficient (r-value). Very strong positive as we thought.

21. Use the slope (m) and y-intercept (b) to write the equation. Round as directed or to make sense in the problem.

22. The line for the regression equation might pass through some data points, but often will not.

23. Analysis: What is the slope of the regression equation and what does it mean? What is the y-intercept of the regression equation and what does it mean?

24. What is the slope of the regression equation and what does it mean? The slope is 4.09. It means that for each one degree increase in temperature, there are $4.09 more ice cream sales. The sales increase $4.09 per degree.

25. What is the y-intercept of the regression equation and what does it mean? The y-intercept is (0,-111.56). It means if the temperature is 0 degrees, there are -$111.56 in ice cream sales. **This does not make sense in the context of the problem.

26. The regression equation can be used to make predictions. If a prediction is made within the given data set, it is called interpolation. If a prediction is made outside of the data set, it is called extrapolation. Notes - Scatter Plots and Lines of Best Fit

27. Interpolation: Making predictions inside a set of data. Vocabulary

28. Extrapolation: Making predictions outside a set of data. Vocabulary

29. Let’s Interpolate! y = 4.09x - 111.56

30. Predict the total ice cream sales when the temperature is 80 degrees. y = 4.09x - 111.56 Interpolation

31. Predict the total ice cream sales when the temperature is 80 degrees. y = 4.09x - 111.56 This is interpolation because our data temperatures range from 25 to 102 degrees. 80 falls between those numbers, or inside of the data. Interpolation

32. Predict the total ice cream sales when the temperature is 80 degrees. y = 4.09x - 111.56 y = 4.09x - 111.56 y = 4.09(80) - 111.56 y = 327.2 - 111.56 y = 215.64 Interpolation

33. Predict the total ice cream sales when the temperature is 80 degrees. y = 4.09x - 111.56 y = 4.09x - 111.56 y = 4.09(80) - 111.56 y = 327.2 - 111.56 y = 215.64 Interpolation

34. Predict the total ice cream sales when the temperature is 80 degrees. y = 4.09x - 111.56 y = 4.09x - 111.56 y = 4.09(80) - 111.56 y = 327.2 - 111.56 y = 215.64 Interpolation

35. Predict the total ice cream sales when the temperature is 80 degrees. y = 4.09x - 111.56 y = 4.09x - 111.56 y = 4.09(80) - 111.56 y = 327.2 - 111.56 y = 215.64 Interpolation

36. Predict the total ice cream sales when the temperature is 80 degrees. y = 4.09x - 111.56 y = 4.09x - 111.56 y = 4.09(80) - 111.56 y = 327.2 - 111.56 y = 215.64 (80, 215.64) When the temperature is 80 degrees, the ice cream shop should have $215.64 in sales. Interpolation

37. Let’s Extrapolate! y = 4.09x - 111.56

38. Predict the total ice cream sales when the temperature is 105 degrees. y = 4.09x - 111.56 Extrapolation

39. Predict the total ice cream sales when the temperature is 105 degrees. y = 4.09x - 111.56 This is extrapolation because our data temperatures range from 25 to 102 degrees. 105 falls above 102, or outside of the data. extrapolation

40. Predict the total ice cream sales when the temperature is 105 degrees. y = 4.09x - 111.56 y = 4.09x - 111.56 y = 4.09(105) - 111.56 y = 429.45 - 111.56 y = 317.89 Extrapolation

41. Predict the total ice cream sales when the temperature is 105 degrees. y = 4.09x - 111.56 y = 4.09x - 111.56 y = 4.09(105) - 111.56 y = 429.45 - 111.56 y = 317.89 Extrapolation

42. Predict the total ice cream sales when the temperature is 105 degrees. y = 4.09x - 111.56 y = 4.09x - 111.56 y = 4.09(105) - 111.56 y = 429.45 - 111.56 y = 317.89 Extrapolation

43. Predict the total ice cream sales when the temperature is 105 degrees. y = 4.09x - 111.56 y = 4.09x - 111.56 y = 4.09(105) - 111.56 y = 429.45 - 111.56 y = 317.89 Extrapolation

44. Predict the total ice cream sales when the temperature is 105 degrees. y = 4.09x - 111.56 (105, 317.89) y = 4.09x - 111.56 y = 4.09(105) - 111.56 y = 429.45 - 111.56 y = 317.89 When the temperature is 105 degrees, the ice cream shop should have $317.89 in sales. Extrapolation

45. Let’s learn how to find a linear regression equation!! Day 2 - Linear Regressions

47. Your Your table should look like this.

48. Click the magnifying glass to make the graph zoom in on your data.

49. Your graph should resemble this one. Remember, x is the number of hours studying and y is the test score.

50. Next, click inside box 2 to type a new equation.