The ability of ecologists to identify regions of greatest species richness could

Question

The ability of ecologists to identify regions of greatest species richness could have an impact on the preservation of genetic diversity, a major objective of the World Conservation Strategy. A study used a sample of n = 27 lakes to obtain the estimated regression equation y = 3.89 + 0.033x_1 + 0.024x_2 + 0.023x_3 - 0.0080x_4 - 0.13x_5 - 0.72x_6 where y = species richness, x_1 = watershed area, x_2 = shore width, x_3 = poor drainage (%), x_4 = water color (total color units), x_5 = sand (%), and x_6 = alkalinity. The coefficient of multiple determination was reported as R^2 = 0.85. Carry out a test of model utility. State the appropriate hypotheses. H_0:beta_1 beta_1... beta_6 0 H_a: at least one among beta_1,..., beta_6 is zero H_0:beta_1 = beta_1 =... beta_6 0 H_a: at least one among beta_1,..., beta_6 is not zero H_0:beta_1 beta_1... beta_6 0 H_a: beta_1 = beta_1 =... = beta_6 = 0 H_0:beta_1 = beta_1 =... beta_6 0 H_a: no beta_i = 0 State te rejection region and compute the test statistic value. Use alpha = 0.05. Round your answers to two decimal places.

Explanation / Answer

Find critical value of F at a=.05 for a hypothesis test with 27 subjects with 6 independent variables

Degrees of freedom for total = 27-1=26

Degrees of freedom for regression=6

Degrees of freedom for error =26-6=20

F critical value =2.60

Test statistic f=18.89

F= (R2 / ( 1- R2) * ( (n-k-1)/k)

=(0.85/0.15) *(20/6)

=18.89

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