Unit 4.3 Correlation

Correlation coefficient is a numerical value that ranges between what numbers? What does it indicate?

• -1 and +1

• Indicates correlation

What can the correlation coefficient between two variable not necessarily indicate?

The relationship

“A line of best fit is a line that passes most closely through-”

“-all the points in a set of two-variable data”

Describe the relationship between line of best fit and the correlation coefficient

• Lines of best fit are representative of the data

• Correlation coefficient is a numerical derived value to indicate how well the line fits the data

What are the other 2 names the correlation coefficient is known by?

• Pearson product-moment

• r-value

If the line of best fit has a positive slope, will it have a positive r-value?

Yes

If the line of best fit has a negative slope, will it have a negative r-value?

Yes

As the r-value gets closer to 1, this indicates-

A stronger positive correlation

As the r-value gets closer to -1, this indicates-

A stronger negative correlation

As the r-value gets closer to 0, this indicates-

A weaker correlation

If the r-value is 1, this indicates-

A perfect positive correlation

If the r-value is -1, this indicates-

A perfect negative correlation

If the r-value is 0, this indicates-

No correlation

In GeoGebra Spreadsheets, how would you find the exact values for line of best fit, r-value, slope etc.?

• Click back into your data and highlight

• From the top toolbar, choose the one that looks like a bar graph and click two variable regression analysis

• At the bottom, make sure linear is selected

• From the toolbar at the top right, click the tab that looks like “Ex”

• At the bottom of the page you will be able to see the equation and from the stats section you can see the r-value

What are 2 things to remember when interpreting results of data analyses?

• Sample size

• Outliers

Define outlier

• A point that lies away from the pattern established by the rest of the data points

• An outlier may skew both the line of best fit and the r-value

When are 2 times that an outlier could be removed/disregarded?

• Outlier occurs form an error in recording the data (e.g. a height of 167cm was recorded as 67cm)

• Outside factors affected the data (e.g. data was collected every day but there was a power outage on Tuesday and nothing was recorded)

To determine if a sample size is too small, what are 3 things to think about?

• Does the size of the sample seem appropriate to the size of the population?

• Is the size of the sample large enough to predict the relationship between the variables?

• Is the range of the independent variable appropriate for meaningful predictions to be made using the line of best fit?

What percentage of a population is generally okay for a sample?

Usually around 10%

When using GeoGebra Spreadsheets, if you have the scatter plot and have found all the equations, what would you do if the question as for a quadratic equation?

Same pathway as last time except instead of “linear” choose “polynomial - 2”

When considering correlation for a quadratic equation instead of a linear one, do you use r-value still?

Close - use r²

When extrapolating, could there be a problem with having a linear line of best fit vs. a quadratic one?

YES.