(MCC9-12.S.ID.6; MCC9-12.S.ID.6a; MCC9-12.S.ID.6b; MCC9-12.S.ID.6c)

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(MCC9-12.S.ID.6; MCC9-12.S.ID.6a; MCC9-12.S.ID.6b; MCC9-12.S.ID.6c) The Wandering Point Retrieved from stat.scareyjones.com Adapted by Dr. Jennifer L. Brown, Columbus State University, ©2012 (MCC9-12.S.ID.6; MCC9-12.S.ID.6a; MCC9-12.S.ID.6b; MCC9-12.S.ID.6c)

difference between observed and predicted y values What is a residual? difference between observed and predicted y values How do you find the residual? length of vertical line from predicted to observed. y - ŷ

Procedures: Use your wikki stick to “eyeball” a line of best fit. Find ŷ (predicted y value) for each x value. Find the informal residual for each x value. Find y - ŷ (exact residual) for each x value.

ŷ = 0.4x + 2.8 x y 1 2 6 4 5 + - 1.

ŷ = 0.4x + 2.8 x y ŷ Informal Residual y - ŷ 1 2 3.2 -1 -1.2 6 3.6 2.5 2.4 4 4.4 -2.5 -2.6 5 4.8 1.5 1.2

ŷ = 0.8x + 1.8 x y 1 2 6 4 5 8 9 2.

ŷ = 0.8x + 1.8 x y ŷ Informal Residual y - ŷ 1 2 2.6 -0.5 -0.6 6 3.4 3.0 4 5 -3.0 5.8 0.5 0.2 8 9 8.2 0.8

ŷ = 0.4x + 3.6 x y 1 2 6 4 5 3 8 3.

ŷ = 0.4x + 3.6 x y ŷ Informal Residual y - ŷ 1 2 4 -2.0 6 4.4 1.5 1.6 5.2 -3.0 -3.2 5 5.6 0.5 0.4 3 8 4.8 3.5 3.2

ŷ = -0.06x + 4.8 x y 1 2 6 4 5 7 4.

ŷ = -0.06x + 4.8 x y ŷ Informal Residual y - ŷ 1 2 4.74 -2.5 -2.74 6 4.68 1.5 1.32 4 4.56 -2.56 5 4.5 7 2.5 2.26

Extension Activity Purpose: To determine the influence of one more point on the correlation and the slope. MCC9-12.S.ID.7; MCC9-12.S.ID.8)

Slope of the regression line Fifth Point Correlation Slope of the regression line Size of the residual None 0.3162 0.4 N/A (3,4) (8,6) 0.5 (10,7) 0.6157 0.4228 0.033 (small) (3,8) 0.2357 3.2 (large) (1,7) -0.0457 -0.06 2.3 (medium) (8,9) 0.7303 0.8 0.8 (small) (10,0) -0.4888 -0.3740 -1.1 (small)

(MCC9-12.S.ID.6; MCC9-12.S.ID.6a; MCC9-12.S.ID.6b; MCC9-12.S.ID.6c) Residual Plot Purpose: Determine if a linear model is an appropriate fit for the data. (MCC9-12.S.ID.6; MCC9-12.S.ID.6a; MCC9-12.S.ID.6b; MCC9-12.S.ID.6c)

Graph the x values and the residual values.

Linear or Non-linear?

Templates/Handouts

x y 1 2 6 4 5

1. 2. 3. 4. x y ŷ Informal Residual y - ŷ 1 2 6 4 5 x y ŷ