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Scatter Plots, Spaghetti , and Predicting the Future

Scatter Plots, Spaghetti , and Predicting the Future. Image used with permission from commons.wikimedia.com. Warming up for the lesson. What is the slope of the line that contains the points (-3, 7) and (6, 1) ?

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Scatter Plots, Spaghetti , and Predicting the Future

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  1. Scatter Plots, Spaghetti, and Predicting the Future Image used with permission from commons.wikimedia.com

  2. Warming up for the lesson • What is the slope of the line that contains the points (-3, 7) and (6, 1) ? • What is the equation of the line referred to in #1? Write the equation in slope-intercept form. • Sketch a graph of this line. Explain what the slope means and how the slope of the line is related to how the graph looks.

  3. Solutions and discussion • What is the slope of the line that contains the points (6, 1) and (-3, 7) ? 2. What is the equation of the line in slope-intercept form? Use y = mx + b, solve for b: 1 = (-2/3)(6) + b 1 = (-4) + b b= 5 y = (-2/3)(x) + 5 Use point-slope form: y – 1 = (-2/3)(x – 6) y– 1 = (-2/3)x + 4 y = (-2/3)x + 5 3. Sketch the graph:

  4. What have we learned in the past about scatter plots?

  5. Scatter plots show a graph of a set of points. Scatter plots help us to see if there is a relationship between the two variables. Positive Correlation As x increases, y increases. No Correlation x and y are not related Negative Correlation As x increases, y decreases. How is correlation related to slope of a line?

  6. Reviewing the vocabulary of Scatter plots • x-axis • y-axis • independent variable • dependent variable • correlation: positive, negative, or none

  7. Lost Jeremy decided to go on a diet and start exercising in order to lose weight. His goal was to lose 20 pounds. At the end of every week he weighed himself and recorded his weight in a chart. We can make a scatter plot and use it to organize and analyze this information, and maybe even predict the future!

  8. Lost Do the points appear to have a positive or negative correlation, or neither? Explain your answer.

  9. “Trend line” When the points in a scatter plot seem to be in a pattern of a line, we can sketch a line that is near as many of the points as possible. This is called a “Trend Line”. There should be about the same number of points above as below the line.

  10. Spaghetti without the sauce Let’s all decide on a good Trend Line together. Using a piece of spaghetti, locate a line that you think is as close as possible to as many of the points as possible. Your line should pass through at least two of the points in the scatter plot. Let’s all use the points (7, 261) and (10, 257). Use a straight edge and draw the line, being sure it contains the two points we selected.

  11. Complete question 4 on your papers Let’s review our work. slope: Using the points (7, 261) and (10, 257) So the slope equals about -1.3

  12. Slopes and Trend lines Slope is a very important value. It explains the rate of change that is occurring with the variables. Slope includes information about how the variables are increasing or decreasing in relation to each other. In this example about Jeremy, how would you describe or explain the slope as a rate of change?

  13. A closer look at SlopeWhat does slope mean in this example????? Assign units to the slope. Since slope compares the change in y with the change in x, we will use the units of y and xalong with the value for slope. If m = -1.3, what does that mean?

  14. The equation of the trend line We can use our slope (-1.3) and either one of the two points on our trend line ((7, 261) or (10, 257)) to find the equation of the line. y = mx + b 261 = -1.3(7) + b 261 = -9.1 + b 270 ≈ b y = -1.3x + 270 y = mx + b 257 = -1.3(10) + b 257 = -13 + b 270 = b y = -1.3x + 270

  15. The equation of the trend line Our trend line has the equation y = -1.3x + 270 What is the y-intercept of this line? What does the y-intercept tell us about Jeremy? (hint: what value of x corresponds to the y-intercept?) Does this match the data that we were given? Explain why or why not.

  16. Predicting the future using the trend line Using the equation for our trend line y = -1.3x + 270, we can predict the future! Questions: What if Jeremy continued his diet for another week? How could you use the equation of the trend line to predict his weight?

  17. How can we use the equation of the trend line to predict Jeremy’s weight after 14 weeks? Do you think you can use the equation of the trend line to predict Jeremy’s weight a year from now? Why or why not?

  18. How can we use the equation of the trend line to predict Jeremy’s weight after 14 weeks? Substitute 14 in place of x: y = (-1.3)(14) + 270 y = 251.8 pounds Do you think you can use the equation of the trend line to predict Jeremy’s weight a year from now? Why or why not? It depends on if Jeremy continues his diet and exercising for that length of time.

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