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 = 31 lakes to obtain the estimated regression equation y 3.89 0.033x1 +0.024x2 0.023x3 0.0080x4 - 0.13x5 0.72x6 where y species richness, x1 = watershed area, x2 = shore width, x3 = poor drainage (%), x4 = water color (total color units), x5 sand (%), and X = alkalinity. The SSR and SSE have been calculated to be: SSR = 768 and SSE 307.2. What percent of the variation in y can be explained by the model? R2 = %. (Give your value in percent and round to two decimal places.) Carry out the model utility F test. State the appropriate hypotheses. Ho: B1 B1 = ... = B6 = 0 Ha: no Bi 0 Ha: at least one among B1, .., B6 is zero Ho: B1# B1 ... B6 0 Hai B1 = B1 = ..= B6 = 0 OHo: B1 = p1 = ... = ß6 = 0 Ha: at least one among B1, ..., ß6 is not zero Round your test statist decimal plac alue and obtai Compute the decin places.(Hint: You can us to your p-value to p-va p-value f= test statistic State the conclusion in the problem context. Use a = 0.05. OReject Ho. There is no evidence at least one explanatory variable is a significant predictor of species richness. Reject Ho. There is significant evidence at least one explanatory variable is a significant predictor of species richness. Fail to reject Ho. There is significant evidence at least one explanatory variable is a significant predictor of species richness. Fail to reject Ho. There is no evidence at least one explanatory variable is a significant predictor of species richness.

Answer 1

SSE = 307. 2 SSR= 768 , SST= 768 307.2 075.2 En= 31] DFT = 3| - { = 30 [no. of estimator] k 6 DFE= 30- 6=24 OFR = 6 89 t 075.2 SSR x 00 SST 7' 43 option (D Ha: at leant one among f.-P is not zeYo SSR 768 = ( 2 8 MSR = DFR SE 307. 2 DFE MSE = = |2:8 24 | 2 8 MSR . test statistic ', f= MSE 2. 8 P-Value ** O. 000015 - OO000 * Conclusion : Option (B Reject Ho There is significant evidence at ex planatory var iable is a teant One significant predictor of species richness