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Graphing with Computers

Graphing with Computers. Pressure and Density. What is Pressure?. Pressure = Force = lbs area in 2 Let me propose the following experiment. Pressure Experiment. A series of 1 lbs, 1 in 2 disks are placed on a scale. What would the data Look like?. Data From Experiment.

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Graphing with Computers

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  1. Graphing with Computers Pressure and Density

  2. What is Pressure? Pressure = Force = lbs area in2 Let me propose the following experiment

  3. Pressure Experiment • A series of 1 lbs, 1 in2 disks are placed on a scale What would the data Look like?

  4. Data From Experiment

  5. This is a direct proportion. The pounds varies directly as the in2 We can use a “best fit” line to describe the relationship

  6. R2 = correlation coefficient This tells us how well the Line is described. Perfect correlation = 1 Best Fit Line I use excel to determine the equation for the line. y = 1.0 x What units does y represent? x? So the equation really is lbs = in2

  7. Best Fit Line • The line describes the ratio or proportion • The ratio is the slope or pounds / in2 • In the is example it is equal to 1 • This means for every pound added, one in2 is added • R2 = 1 tells us there is perfect correlation in our data • Our accuracy and precision are perfect • Our data was unrealistic • Let’s throw in some error and see what happens

  8. Data From Experiment

  9. Notice the data is not in perfect line. We can draw in a best fit line, but it is more accurate to let the computer do it

  10. Notice the slope is not perfectly 1 any more! The equation of y = mx +b turns into pounds = .9956 in2 + 0 R2 , our correlation coefficient is close to one. Good enough!

  11. Let’s Review • Plot the data. • Determine the type of proportion (direct) • Draw a best fit line • Determine the slope of the line • The slope is the relationship • It describes the proportion or ratio of the two variables

  12. Density • What are the units of density? g/mL • Given an unknown material • We can measure the grams • We can measure the mL by displacement • We can determine the density by using a graph!

  13. Graphing with Computers • Plot the data • Determine the type of proportion • linear or direct • Draw a best fit line • Also called doing a linear regression • Determine the slope of the line

  14. g/ml What are the units of the slope? What are the units of density? g/ml

  15. Let’s Switch to Excel • Use excel to graph and draw best line • Linear regressions are really easy !

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