Warm-Up 8/50 = .16 10/20 = .50 18/50 = .36 Math Social Studies P.E.   Math Social Studies P.E. Women 16 6 8 Men 2 10 What is the probability that a randomly selected person is a woman who likes P.E.? 2. Given that you select a man, what is the probability that he likes Social Studies? 3. What is the probability that you select a person who likes Math? 8/50 = .16 10/20 = .50 18/50 = .36

Correlation, Linear Regression, & Exponential Regression Skills Check Correlation, Linear Regression, & Exponential Regression

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

Residual is another word for ERROR Residuals Residual is another word for ERROR

Residuals To find the residual you take the ACTUAL data and SUBTRACT the PREDICTED data.

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

Residual Plots A residual plot is another type of SCATTERPLOT that shows the relationship of the residual to the x value.

Residual Plots Determine If it the regression model is appropriate, then the residual plot will have a RANDOM scatter. If the residual plot creates a pattern then the regression model is NOT A GOOD FIT. 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 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 Total Time (minutes) Total Distance (miles) Predicted Total Distance Residuals (observed – predicted) 32 51 54.4 -3.4 19 30 31.9 28 47 47.5 36 56 61.3 17 27 28.5 23 35 38.8 41 65 70.0 22 37.1 37 73 63.1 54 Data from TI Activity for NUMB3RS Episode 202

Example: Calculate Residual 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? Residual Total Time

Good fit or not? Residual Total Time

Residuals Task – Carnival Classwork Residuals Task – Carnival

Residuals CW worksheet Homework Residuals CW worksheet