**Grade 12 – Data Management – 2-Variable Analysis**

**Correlation**

**Scatter Plots**graph data and is used to determine if there is a relation between the 2 variables**Linear Correlation:**changes in one variable tend to be proportional to changes in other variables- The stronger the correlation, the more closely the data points cluster around the line of best fit.
**Correlation Coefficient ( r ):**a value between -1 and 1 that provides a measure of how closely data points cluster around the line of best fit.**-1 – -0.62:**negative, strong correlation**-0.61 – -0.33:**negative, moderate correlation**-0.32 – 0:**negative, weak correlation**0 – 0.32:**positive, weak correlation**0.33 – 0.61:**positive, moderate correlation**0.62 – 1:**positive, strong correlation**Regression:**finding a relationship that models the 2 variables

**Generating lines of best fit and Outliers**

**TI-83 Graphing Calculator:**- Turn diagnostics on (2
^{nd}, O, DiagnosticsOn, Enter) - Enter Data (STAT, 1:edit)
- Graph Data (2
^{nd}, y=, Turn Plot 1 on, zoom, 9:zoomStat) - Equation of line of best fit (STAT, Calc, 4: LinReg(ax+b), Vars, yvars, 1: functions, 1:y1)
**Microsoft Excel**- Enter data
- Highlight data and construct scatterplot (Insert, Charts, Scatter)
- Equation for line of best fit (Chart Tools, Layout, Trend line)
**Fathom**- Enter data (Copy/Type/Open)
- Construct scatterplot (drag variables to axes)
- Add “Movable Lines”
- Equation for line of best fit (Graph, least squares line)
- Show Squares, residual plot to identify outliers
- Determine value of correlation coefficients

- Turn diagnostics on (2

**Cause and Effect**

**Cause and Effect**- A change in X causes a change in Y
- Ie. Time and tree trunk diameter
**Common Cause**- An external factor causes two variables to change in the same way
- Ie. Correlation between ski sales, and video rentals
- Where it’s caused by colder weather
**Reverse Cause and Effect**- The dependent and independent variables are reversed in ascertaining which caused which.
- Ie. Correlation between coffee consumption and anxiety theorized that drinking coffee causes anxiety and it is found that anxious people drink coffee
**Accidental Relationships**- A correlation without any casual relationship between the variables
- Ie Increase in SUV sales causes increase in chipmunk population
**Presumed Relationship**- A correlation that does not seem to be accidental even though no cause-and-effect or common cause relationship is apparent
- Ie. A correlation between the person’s level of fitness and the number of action movies they watch.

- A correlation that does not seem to be accidental even though no cause-and-effect or common cause relationship is apparent

- A correlation without any casual relationship between the variables

- The dependent and independent variables are reversed in ascertaining which caused which.

- Ie. Correlation between ski sales, and video rentals

- An external factor causes two variables to change in the same way

- A change in X causes a change in Y

**Critically Thinking about Data**

- When analyzing data, we should ask:
**Source:**How reliable/current is the source?**Sample:**Does the sample reflect the opinions in the population?- Was the sampling technique free foam bias?

**Graph:**Is the graph accurately portrayed? (Axis starting at zero)**Correlation:**Is the correlation between the variables strong enough to make inferences?- Is the causation assumed just because there is a correlation?
- Are there extraneous variables impacting the results?

**Number Manipulation**

**Percentage Points:**means that it’s X percentage points / the value- Ie. 3 percentage points up from 75% is 75+(3/75*100) = 79%
**Making Numbers Larger:**In order to make better sense of numbers, sometimes people use smaller scales to make them seem bigger- Ie. 2,000,000 iPads sold in the first 3 months can be said as “2 iPads sold every second” to sound larger.