1. Number of vacations in past 5 years
Minds On…
Describe the correlation shown below
Do you think it’s reasonable to assume that there is a ‘causal’ relationship between these variables?
Number of vacations in past 5 years
Number of Pets in household

2. LG: I can assess the reliability of a linear model
Line of Best Fit
LG: I can sketch a line of best fit, determine an equation for the line, and use this equation to make predictions
LG: I can assess the reliability of a linear model

3. Lines of Best Fit
A line of best fit is a line drawn through data points to best represent a linear relationship between the two variables
Also called a trend line or regression line
The line is not just ‘through the middle’, it should be as close as possible to all data points
A line of best fit doesn’t work for all data; sometimes a curve of best fit is a better option

4. Outliers
Any point that lies far away from the main cluster of points is an outlier
May be caused by inaccurate measurements, or may be unusual but still valid
The line of best fit should reflect all valid data points, including outliers

5. Effect of Outliers on Line of Best Fit
Which trend line best represents the data? Why?
Suggests there are NO outliers
Gives too much importance to the outliers
Is affected by the outliers, but is affected MORE by the larger cluster of data

6. Recall: Find the equation of this line
y = mx + b
STEP 1: Choose 2 points on the line
STEP 2: Find slope
STEP 3: Find y-intercept
STEP 4: state equation

7. Using a Line of Best Fit to Make Predictions
Interpolation – Predictions WITHIN data point
Extrapolation – Predictions BEYOND data points

8. Reliability
Some factors make predictions from a line of best fit less reliable
Data spread over small range
Small sample size
Nonlinear data