5. Residuals and significance testing with a regression equation Aa Aa Experienc

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5. Residuals and significance testing with a regression equation Aa Aa Experienced observers use aerial survey methods to estimate the number of snow geese in their summer range area west of Hudson Bay, canada. Asmall aircraft fies over the range, and when a flock of geese is spotted, the observer estimates the number of geese in the flock. To investigate the reliability of the estimates, an airplane carrying two goose observers fies over 45 flocks. Each observer makes an independent estimate of the number of geese in eadn flock. A photograph is taken of each flock and a count made of the number of geese in the photograph. The sample data for the 45 focks appear in the Dataview too. [Data source: These data were obtained from Lunneborg, E. (1994). Modeling experimental and observational data. Padfic Grove, CA: Duxbury Press.] Geese Variables 3 Phele Al 1 40 50 12 152 13 205 You will work with goose observer B's estimates in this problem to examine how wel observer B's estimates predict counts from the would Photographs for the same flock. The photographs provide a highly acourate count of geese optimally, the observer's estimate predict the photo-based count for a specific Frst, use the regression equation to predict Y values based on observer B's estimates. The rogression equation, in the format bx 0.77 x 16.16 where goose observer B's estimate an estimate f the goose count from the photograph How to Print you are rrent students Use your Hunter All other Hunter issued cards: the when the number on the left "Peak to

Explanation / Answer

Predicted y for flock 2,17,35
31.56
46.96
50.81
Actual y for flock 2,17,35
26
73
48

Residual = Actual y - Predicted y
26-31.56 = -5.56
73-46.96 = 26.04
48-50.81 = -2.81

1st option is correct - The regression equation does not account for a significant portion of the variance in the Y scores.

r = Sxy/sqrt(SSx * SSy)
Sxy = r * sqrt(SSx * SSy) = 0.9245 * sqrt(490692.44*339559.64) = 377372
SS(Regression) = Sxy*Sxy/SSx = 377372*377372/490692.44 = 290221.8
SS(Residual) = SSy - Sxy*Sxy/SSx = 339559.64 - 290221.8 = 49337.84

The number of degree of freedom for F test is 1 and 45-1 = 44
Critical value of F for alpha = 0.1 is 2.82
F = (R^2/1-R^2) * (n-k-1)/k
= (0.9245/(1-0.9245)) * (45-1-1)/1 = 526.5363
Null Hypothesis is rejected
You can conclude that the regression equation accounts for a significant portion of variation of Y scores.

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