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

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

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

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

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

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

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

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