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Residuals, outliers, influential observations

Residuals, outliers, influential observations. AP Statistics. Rediduals. A residual is the difference between an ovserved value of the response variable and the value predicted by the regression line. That is, Residual = observed y – predicted y Or

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Residuals, outliers, influential observations

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  1. Residuals, outliers, influential observations AP Statistics

  2. Rediduals • A residual is the difference between an ovserved value of the response variable and the value predicted by the regression line. That is, • Residual = observed y – predicted y • Or • THE MEAN OF THE LEAST SQUARES RESIDUALS IS ALWAYS ZERO.

  3. Example 3.14 Here is a scatterplot of the data with the regression line Predicted y = 109.8738-1.1270 ( Age at first word)

  4. 3.45 p. 166-167 Beavers and BeetlesEcologists sometimes find rather strange relationships in our environment. One study seems to show that beavers benefit beetles. The researchers laid out 23 circular plots, each four meters in diameter, in an area where beavers were cutting down cottonwood trees. In each plot they counted the number of stumps from trees ct down by beavers and the number of clusters of beetle larvae. Here are the data:Example 3.14 Continued • Here is a scatterplot of the data with the regression line • Predicted y = 109.8738-1.1270 ( Age at first word) • For child 1, who first spoke at 15 months, we predict the score: • Predicted score = 109.8738 – 1.1270 (15) = 92.97 • The child’s actual score was 95. The residual is • Residual = observed y – predicted y = 95 – 92.97 = 2.03 • This residual is positive because it lies above the line.

  5. Residual Plot • a scatter plot of the regression residuals against the explanatory variable. Residual plots help us assess the fit of the regression line.

  6. INTERPRETING RESIDUAL PLOTS: • The following residual plot is in a curved pattern and shows that the relationship is not linear. A straight line is not a good summary for such data.

  7. INTERPRETING RESIDUAL PLOTS: • Increasing or decreasing spread about the line as x increases indicates that prediction of y will be less accurate for larger x. The following is an example of this sort of situation:

  8. INTERPRETING RESIDUAL PLOTS: • The following shows a residual plot that has a uniform scatter of points about the fitted line with no unusual ovservations. This tells us that our linear model (regression line) will give us a good prediction of the data.

  9. Outliers and Influential points • Outlier: an observation that lies outside the overall pattern of the other observations • Influential points: Points that when removed would markedly change the result of your calculations. Points that are outliers in the x direction of a scatterplot are often influential for the least squares regression line.

  10. Residual plots on the calculator: • 3.45 p. 166-167 Beavers and BeetlesEcologists sometimes find rather strange relationships in our environment. One study seems to show that beavers benefit beetles. The researchers laid out 23 circular plots, each four meters in diameter, in an area where beavers were cutting down cottonwood trees. In each plot they counted the number of stumps from trees ct down by beavers and the number of clusters of beetle larvae. Here are the data: • Stumps: 2 2 1 3 3 4 3 1 2 5 • Beetle: 10 30 12 24 36 40 4 3 11 27 56 Larvae • Stumps: 1 3 2 1 2 2 1 1 4 1 • Beetle 18 40 25 8 21 14 16 6 54 9 Larvae: • Stumps: 2 1 4 • Beetle 13 14 50 • NOW, Calculate the LSRL • Highlight List 3 • 2nd STAT • Go down to the RESID List and hit enter • 2nd y=, turn plot 1 on scatterplot • For x list use List 1, but for y list use List 3 • Zoom 9 (Zoom Stat)

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