# Graphing

## Sketching Graphs by hand:

You may be required to graph by hand.

__Sketching a graph __

Sketched graphs are meant to just show trends, so you do not put data points, units or scale values. You should still have axes labels, possibly a zero y axis shown for reference, and a trendline.

See the examples of sketched graphs (as opposed to complete graphs below):

## Complete graphs drawn by hand

### Complete graphs should have the following elements, whereas sketches of graphs can be simpler.

- Axes titles (with units)
- Most often we graph dependent variables on the y axis and independent on x, but on occasion we find it useful to plot variations on this.

- Axes scales (numbers that tell how much each box is worth)
- Your data points should span at least 1/2 of the graph space on each axis. If not, you should consider changing your scale. I have a method for determining scale below.
- PLEASE do not just label your X values from your data set along the X axis. This will always make a linear graph, but it will always be meaningless.

- Data points
- each data point should be plotted as a dot. Be very careful in making sure that your read your scale correctly.

- If applicable, scale should be chosen so you should be able see x and y intercepts
- If linear draw a best fit line
- If there are asymptotes, they should be identified

**How to scale a graph by hand: **

- Find the spread you need to show on your graph.
- I often use zero and the maximum value. In the data set at shown by the good graph example I chose a spread of 27.5 on the Y axis and 7 on the X.

- Count the number of vertical and horizontal spaces on your graph.
- On the grid used to graph in the example I counted 15 spaces each way.

- Divide the spread by the number of spaces on each axis and then round up to a convenient number to work with.
- For the Y axis 27.5/15=1.8, I rounded up to 2 and made each box worth 2 s. I chose not to label every line because that would be too crowded.

Be careful: Do not take uneven intervals (like 0.15, 0.40, 0.65) and plot them evenly on an axis. (See y axis on bad example below)

## Digitizing Hand Completed Work to include in an online lab notebook or online assignment

## Using Google sheets to create graphs:

Before starting to graph you should have your data prepared - - this video shows how to calculate values needed and format them to make it easy to graph.

These steps will help you create a scatter plot with trend lines, labels, equations, and an R^2 value to compare precision.

Use the **Insert** menu and select **Chart** to start creating a graph. Follow the following steps to format the graph:

### 1. Select your data

Under the **Data** tab of the chart editor select the data by doing the following:

- set the
**chart type**to*scatter chart* - set the
**series**to the Y axis values (click**add series**and then highlight data with header; remove any excess series shown) - set the
**X-axis**to your X axis values (click**Add X-axis**and then highlight data with your header) - the only box needed to be checked below is
**Use column A as labels**

### 2. Add labels

3. Under the **Customize** tab of the chart editor expand the **chart & axis titles** settings to add axis labels:

- Add a chart title if desired
- Change the type to
**Horizontal axis title**and enter the measurement and unit for your x-axis values (example: time (s)) as the*horizontal axis title*. - Repeat with
**Vertical axis title**

### 3. Add trendline

4. Still on the **customize** tab, expand the **series** settings.

- Check the box for the
**trendline** - Change the type between
*linear, polynomial,*and*power*to find the best fit. - Change the
**label**to*Use Equation*to show the equation on the chart. - Check the box for
**Show R^2**to display the how well the line matches your data (closer to 1.000 is good, 0.995 and up indicates that the line is a good model for the data set).

### 4. Check scales

4. Still on the **Customize** tab, expand the **Horizontal Axis** settings

- Make sure the box
**Treat labels as text**is not selected. This will cause a non-linear scale - If the default zoom over-emphasizes differences or fails to show an intercept, adjust min or max values to represent your data better.
- Repeat with the
**Vertical axis**if needed.

### 5. Double check all required elements

Graphs need

- Labels with units for each axis
- Consistent scales that allow all data/analysis points to be seen
- Trendlines (if data displays a trend)
- Equation of trendline (if trendline is appropriate)
- R^2 value (if trendline is appropriate)

## Interpreting Graphs:

- You should be able to describe graphs relationships by looking at them and matching them to the above trends
- A
**dependent**relationship just means that one changes the other. This can describe all relationships except constant (not shown above, but where the y value does not change the X or vice versa). - A
**positive correlation**indicates that when one value increases the other does as well.- A
**linear r**elationship is represented by a linear function y=mx+b- A
**direct**also known as**proportional**relationship is a special kind of linear relationship in that the b value is zero. so, y=mx. It must pass through the origin.

- A

- A
- A
**negative correlation**indicates that when one value increases the other decreases.- An
**inverse**relationship (also called inversely proportional) follows the equation y=m/x or y=m(1/x).- There is debate about what indirect means and I would avoid it's use. Some people consider it the same as inverse while others use it for any negative correlation.

- An
**inverse square**relationship is tough to tell from a simple**inverse**relationship - you need to linearize it to tell the difference.

- An

- A