Name:



Name: ___________________________

AP Statistics - Residuals Notes & Worksheet

|x |y |[pic] |[pic] |

|2 |1 | | |

|3 |4 | | |

|5 |6 | | |

|6 |5 | | |

|7 |9 | | |

|9 |8 | | |

|10 |11 | | |

1. Plot the scatterplot for the points above.

2. Find the LSRL and correlation coefficient. (Round to 4 decimal places)

[pic] = ______________________________ r = _________________

3. Use the LSRL to calculate the predicted (fitted) value for each x-value. Fill in the chart above.

4. Calculate the residuals ([pic]) and fill in the chart above.

5. Create a residual plot by plotting a scatterplot of the 6. Create another residual plot by plotting

x-values on the horizontal axis and the residuals on the the [pic]-values on the horizontal axis and

vertical axis. the residuals on the vertical axis.

7. What do you notice about these two residual

plots?

8. Is the LSRL from question 2 an appropriate

model for this data? Explain.

One measure of the success of knee surgery is post-surgical range of motion for the knee joint following a knee dislocation.

Age 45 40 31 28 26 16 14 20 21

Range of Motion 205 137 133 122 135 135 108 120 127

9. Sketch a scatterplot of this data and calculate the LSRL.

Plot the LSRL on your scatterplot.

[pic] = ______________________________

10. Does there appear to be an influential point? IF so, which one?

11. Remove the point from your list. Sketch a scatterplot of this

data and calculate the LSRL. Plot the LSRL on your scatterplot.

[pic] = ______________________________ r = _____ r2 = ______

12. Would you consider this point influential? Explain.

13. Write interpretations, in context, for the slope, r & r2 for question 11.

14. Which of these measures would be considered resistant? (LSRL, correlation coefficient (r), or coefficient of

determination (r2))

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_________________________ is the vertical distance that a point on a scatterplot is from the LSRL.

The sum of the residuals is ALWAYS equal to ______________________________.

Residuals = [pic]

x

Residuals

Residuals

[pic]

Residual Plots

• A scatterplot of the residuals plotted against the

x-values or the predicted or fitted values ([pic]).

• The purpose of a residual plot is to determine if the

model (equation) is an appropriate fit for the data.

o The residual plot should look like a random

scatter of points.

o If no pattern exists between the points in the

residual plot, then the model is appropriate.

o If a pattern does exist, then the model is not

appropriate for the data.

Coefficient of determination (r2)

• gives the proportion of variation in y that can be attributed to an approximate linear relationship between x & y

• remains the same no matter which variable is labeled x

In a regression setting, an outlier is a data point with a large residual.

An influential point is a point that influences where the LSRL is located. If removed, it will significantly change the slope of the LSRL.

Age

Range of Motion

Age

Range of Motion

Interpretations: (replace the underlined items with correct values or words in context)

Slope: For each unit increase in x, there is an approximate increase/decrease of b in y.

Correlation coefficient: There is a direction, strength, linear of association between x and y.

Coefficient of determination: Approximately r2% of the variation in y can be explained by the LSRL of x & y.

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