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Get out your Interpretation WS! You will be able to predict values based on a regression line. You will be able to communicate the risk in extrapolation. You will be able to define and find a residual. Today’s Objectives:

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Warm Up Number of people (x)5791113 Cost ($)200340410490560

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Homework Check.99 0.16; when the meal cost increases by $1 then the tip increases by $0.16 $1.35 -0.3; if there is no meal cost there is no tip

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Homework Check.99 6.09; for every hour extra spent studying, then exam grade increases by 6.09%. 100.47% 63.93; if you do not study you will make a 63.93%

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Homework Check.9992 or 1 4.36; so if the length of the shark goes up by 1 then the weight goes up by 4.36 170.86 -156.14; no statistical significance

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Homework Check.997 or 1.42; if a man grows one inch taller, then his shoe size will increase by.42 of a size 72.17 inches -19.81; no statistical significance

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Extrapolation Predicting Y values for X values outside the range of X values observed in the data is extrapolation. This is risky, because you have no evidence that the linear relationship you have seen in the scatterplot continues to hold in the new X region. Extrapolated values can be entirely wrong.

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Why is Extrapolation Risky? # of Years Old2345678 Height (inches)31333740424445

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Extrapolation

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Conclusion You can see now that you have no evidence that the linear relationship between the boy’s heights between 2 and 8 years continues to hold in the new X region, 55 years. What do you expect to happen to the scatterplot? To the regression line? # of Years Old23456781755 Height (inches)31333740424445 6972

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Extrapolation

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The second line you see graphed is the regression line that CAN be used to predict the height of any man ages 2-55. And still, you cannot predict the height of a 74 year old man because you have no evidence that the linear relationship you have seen in the scatterplot continues to hold in the new X region.

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Residuals Worksheet Get out your calculator and a pencil/pen. Everyone will get a worksheet. Keep your notebooks open so that you can continue to take notes.

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Residuals On your worksheet make a scatterplot (by hand) of the following female height data. Now make a scatterplot on your calculator and draw a regression line. Write the equation on your worksheet. # of Years Old68101113151720 Height (in)4145515260636465

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Residual Notes

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Finding the Residual

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Plotting Residual Points

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Final Residual Plot Connect each plotted point to the zero line with a vertical line. This plot help you visualize the variation of the predictions vs. the actual data points. The zero line represents the actual data.

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Residual Notes Points underneath the residual’s zero line have a negative residual. So, these points are under-predicted. Points underneath the residual’s zero line have a positive residual. So, these points are over-predicted.

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Residual Plot on the Calculator

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Another Residual Problem Use your calculator to make a scatterplot of the summary of the cost of a catered dinner for different numbers of people. Draw the regression line. Find the equation. Find each predicted prices. Find each residual. Draw the zero line. Plot all residuals on a residual plot. # of People, x1215182021263235 Cost ($), y100110125132135141149155

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Answers Predicted $ 107.85 114.51 121.16 125.60 127.82 138.92 152.24 158.90 Residuals -7.85 -4.51 3.84 6.4 7.18 2.08 -3.24 -3.9 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 8 7 6 5 4 3 2 1 0 -2 -3 -4 -5 -6 -7 -8

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Ticket Out The Door On a 3x5 card please write your name and answer the following… 3 - things you learned today 2 - questions you still have 1 - summarize the lesson in ONE sentence

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HOMEWORK Residuals Worksheet Due next Monday HAPPY THANKSGIVING!

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