Best fit line Graphs(scatter graphs)

LoopedIntro

Presentation

• Deciding which variable will be along which axis.• Scale : How much does each, “box”, represent ?

• Plotting the data points.• Best fit line. Rounded off by an example

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Contents

1. Deciding which variable will be along which axis

Look at the data (your experimental results) …

Time (minutes) 0 2 4 6 8 10 12 14 16 18

Temperature (oC)

15 20 25 30 35 40 45 50 55 60

This will often result in nice and evenly spaced out numbers along the way/horizontally.

Above is the data from an experiment where water was being heated by a Bunsen burner. The temperature reading was taken every two minutes for 18 minutes :

Normally the one that you have changed will go along the way …

Since the temperature reading was taken every 2 minutes … it depended on the time. So the temperature reading was dependent on the time.

Temperature

Time

Temperature … dependent variable.

Time … independent variable.

Normally the independent variable will go horizontally (x-axis) and the dependent variable will go vertically (y-axis).

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and the one that you measured to see if/how it changed … will go up the way.

We also need to put in the units for temperature and time … in this case, oC and minutes. (oC)

(minutes)

Temperature

Time

2. Scale : How much does each, “box”, on the graph represent ?

Here is how some of you think it should be done …

Time (minutes)

Activity (Bq)

0 2 4 6 8 10

2000 1000 500 250 125 62

2000

1000

500

250

125

62

0

Activity (Bq)

0 2 4 6 8 10

Time (minutes)

x

x

x

x

x

x

No

No

No !No

Just sticking our numbers beside each box will always give us a straight line … and so is a completely useless method of drawing our graph.

We need to make sure that each, “box”, means the same amount…. So lets do this again … but this time … properly.

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2000

1800

1600

1400

1200

1000

800

600

400

200

0

Activity (Bq)

0 1 2 3 4 5 6 7 8 9 10

Time (minutes)

Time (minutes)

Activity (Bq)

0 2 4 6 8 10

2000 1000 500 250 125 62

The Activity was measured every 2 minutes,so its value depends on the time. Time is therefore the independent variable.We have 10 boxes along the way. The highest value of the time was 10 minutes.

We have 10 boxes going up the way. The highest value for the Activity was 2000 Bq.

Each axis has a different scale … BUTEach box along stands for the same amount along & Each box up stands for the same amount upwards.

Now we can see that the line is a curve … and not a straight line.

xx

x

x

x

x

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If we make each box along stand for 1 minute; 10 x 1 = 10 minutes maximum.So … 6 boxes along will be ; 6 x 1 = 6 minutes.

If we make each box stand for 200 Bq. 10 x 200 = 2000 Bq maximum.So … 3 boxes up will be ;3 x 200 = 600 Bq.

3. Plotting the data points

Time (minutes)

Activity (Bq)

0 2 4 6 8 10

2000 1000 500 250 125 62

2000

1800

1600

1400

1200

1000

800

600

400

200

0

Activity (Bq)

0 1 2 3 4 5 6 7 8 9 10

Time (minutes)

x xxx

x

x

Once you’ve decided what goes along the x-axis (level) and the y-axis (upwards) … and decided on a scale that makes the graph BIG enough to read properly … we plot the points.In this example Time goes along the way and Activity goes up the way.

We now look at a Time and it’s Activity

Time along and then Activity up. So in this case it’s 0 along and up to 2000.

Next it’s along to 2 and then up to 1000.

… and the same method for all the other points.

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Sometimes you have to judge (guess) where the point should be. 500 would be half way between 400 and 600.

x

x

x

x

x

xx

x xx

4. Best fit line. This is very confusing for many pupils.

Once you have plotted the data you look to see if there is a pattern …

A straight line or a curved line of some sort.

e.g.

xx

x

xx x

x

x

x

x

It should NOT be join the dots.

It does NOT need to pass through the origin (0,0).

It does NOT need to pass through every point.

First of all decide if it’s straight or curved.

Then draw a smooth line ; using a ruler for a straight line, or freehand if it’s a curved line.

If it’s as close as possible to all the points, all the way along the line, then it’s probably a good best fit line.

Too high

Too steep a slope

Too low

Good

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Looks like a straight line

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This time it looks more like a curve.

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Too gentle a slope

5. Lets put it all together in an Example

Time (seconds) 0 10 20 30 40 50 60 70 80 90

Speed (ms-1) 0 5 11 16 20 24 30 36 40 46

1. Axes : The speed value depended on the time and the time is increasing in nice easy steps.So, “Time”, is our independent variable and will go along the way … along the x-axis.

Time (seconds)

Speed (ms-1)

2. The scale for time : 10 boxes and a maximum value of 90 seconds. So each box along can be 10 seconds (10x10=100 maxm for graph).

The scale for speed : 10 boxes and a maximum value of 46 ms-1. So each box upwards can be 5 ms-1 (10x5=50 maxm for graph).

3. Plotting the points. The first one is (0,0)

The second point is (10,5) So 1 box along and then 1 box up the way.

Third point : (20,11) So 2 boxes along and then 2 and a fifth boxes upwards … just judge it … the right amount between the 10 and 15 lines.Then the rest of the points.

4. Finally : the Best Fit Line.

504540353025201510

3

5

010 20 30 40 50 60 70 80 90 100

It really needs a title as well … something that tells us what the graph

is all about.

x

xx

x

xx

xx

x

x

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… and so to summarise …

1. Decide about the labels for the axes … include units.

2. Work out the proper scale … where each box along means the same amount as each other … and each box upwards means the same amount as each other.3. Plot the points onto the graph. Along and then up.

4. Draw a best fit line … either straight or curved.

Give it a title.

Now back to the intro … just click .. then click on the icon.