Residuals From the Carnegie Foundation math.mtsac.edu/statway/lesson_3.3.1_version1.5A

Residual (or error) Formula Observed Data - Predicted Data (actual data from the chart – the value from the regression equation)

Determines the effectiveness of the regression model Analyzing Residuals Determines the effectiveness of the regression model

A scatterplot of Residuals vs. X Residual Plots A scatterplot of Residuals vs. X

Residual Plots Determine If the line of best-fit (or regression equation) is appropriate, the plot will have a random scatter. If another type of equation is necessary, the plot will have a pattern. Pattern = Problem

Example of Random Scatter

Examples Determine, just by visual inspection, if the linear model is appropriate or inappropriate.

Linear model appropriate or inappropriate?

The only way to know is to see the residual plot. 1. Does their appear to be a pattern in the residual plot? Yes, quadratic. 2. Does this support your original guess? You must now see that a linear model does NOT fit this data.

Linear model appropriate or inappropriate?

The only way to know is to see the residual plot. 1. Does their appear to be a pattern in the residual plot? Yes, it fans out as x increases. 2. Does this support your original guess? You must now see that a linear model does NOT fit this data.

Linear model appropriate or inappropriate?

The only way to know is to see the residual plot. 1. Does their appear to be a pattern in the residual plot? Yes, it looks quadratic. 2. Does this support your original guess? This was very tricky. The scale was very small. You must now see that a linear model does NOT fit this data.

Linear model appropriate or inappropriate?

The only way to know is to see the residual plot. 1. Does their appear to be a pattern in the residual plot? Yes, it seems decrease as x increases. 2. Does this support your original guess? This was tricky. You must now see that a linear model does NOT fit this data.

Example: Calculate Residual Tracking Cell Phone Use over 10 days Total Time (minutes) Total Distance (miles Predicted Total Distance Residuals (observed – predicted) 32 51 54.4 -3.4 19 30 31.9 28 47 36 56 17 27 23 35 41 65 22 37 73 54 Data from TI Activity for NUMB3RS Episode 202

Example: Calculate Residual Tracking Cell Phone Use over 10 days Total Time (minutes) Total Distance (miles Predicted Total Distance Residuals (observed – predicted) 32 51 54.4 -3.4 19 30 31.9 -1.9 28 47 47.5 -0.5 36 56 61.3 -5.3 17 27 28.5 -1.5 23 35 38.8 -3.8 41 65 70.0 -5 22 37.1 3.9 37 73 63.1 9.9 54 6.5 Data from TI Activity for NUMB3RS Episode 202

Good fit or not?

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