Graphing with Computers

Pressure and Density

What is Pressure?

Pressure = Force = lbs

area in2

Let me propose the following experiment

Pressure Experiment

• A series of 1 lbs, 1 in2 disks are placed on a scale

What would the dataLook like?

Data From Experiment

Total Pounds Total Inches squared

1 1

2 2

3 3

4 4

5 5

6 6

Pounds vs Inches Squared

012345678

0 2 4 6 8

Inches Squared

Po

un

ds

This is a direct proportion. The pounds varies directly as the in2

We can use a “best fit” line to describe the relationship

Best Fit Line

Pounds vs Inches Squaredy =1.0 x

R2 = 1

0

2

4

6

8

0 2 4 6 8

Inches Squared

Po

un

ds

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

R2 = correlation coefficientThis tells us how well the Line is described. Perfect correlation = 1

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

Data From Experiment

Total Pounds Total Inches squared

1.2 1.00

1.8 2.00

3.0 3.00

4.2 4.00

4.8 5.00

6.0 6.00

Pounds vs inches squared with error

0

2

4

6

8

0 2 4 6 8

inches squared

po

un

ds

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

Pounds vs inches squared with error

y = 0.9956x

R2 = 0.9906

0

2

4

6

8

0 2 4 6 8

inches squared

po

un

ds

Notice the slope is not perfectly 1 any more!

R2 , our correlation coefficient is close to one. Good enough!

The equation of y = mx +b turns into pounds = .9956 in2 + 0

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

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!

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

Densityy =1.0 x

R2 = 1

012345678

0 2 4 6 8

Milliliters

gra

ms

What are the units of the slope? g/ml

What are the units of density? g/ml

Let’s Switch to Excel

• Use excel to graph and draw best line

• Linear regressions are really easy !