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 = 29 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 = 0.87. Carry out a test of model utility. State the appropriate hypotheses. State the rejection region and compute the test statistic value. Use a = 0.05. Round your answers to two decimal places, rejection region f test statistic f = 24.54 State the conclusion in the problem context. Reject H_0. The model is judged not useful. Fail to reject H_0. The model is judged useful. Fail to reject H_0. The model is judged not useful.

Explanation / Answer

This is an instance of multiple regression. Thus, the null hypothesis would be:

H0: The model itself contributes nothing useful and all the slope coefficients are zero.

Beta1=Beta2=....=Beta6=0

H1: At least one of the Bj (from Beta 1 to Beta6) is zero.

Answer:2

tn-k-1=(bj-0)SE(bj),

The test statistic is 24.54 and rejection region is beyond 2.074.(t29-6-1)=2.074, at alpha=0.05.

3.

The test statistic falls in critical region, therefore, rejet null hypothesis. Answer 1.

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