Question

2. (20 pts) Suppose that a researcher is interested in how variables such as CONCENTRA- TION and STRAIN in an environment affect reproduction of Ceriodaphnia organisms For this purpose, some study was conducted. In the study, the variable CERIODAPH- NIA indicates the number of Ceriodaphnia organisms that are counted in a controlled environments (fixing levels of CONCENTRATION and STRAIN ) in which reproduction occurs among the organisms. The study considers a regression analysis of the loga- rithm of CERIODAPHNIA (for response variable) on CONCENTRATION and STRAIN (for regressors). Here is some output results of the analysis Model log (Ceriodaphnia) Concentration + Strain Coefficients: Estimate Std Error (Intercept) 4.4546 0.0391 Ceriodaphnia -1.5431 0.0466 Strain -0.2750 0.0484 (b) After dropping the regressor variable ConcentraTiON, we run a regression again It is called a reduced model. Let Np and NR be the predicted number of Cerio- daphnia from the full model and reduced model, respectively. Predict the incre- ment of the log ratio, log(NF NR) when ConcentratiOn increases from x to x and STRAIN is fixed.

Answer 1

Ansaen GINen mode Concentation St9nain Coefficient Estimate std. Pioic Internet 54 G O-039i 0.ot46 Ceniodaphnia -.53 o.o48 -o.2750 Stnain t tra ion) (st Jai'h) Noc log eridaphmia) - O.a150 a) Given Conce ntonation= CeniodaPhnia ahen To fredict the numbesr of amd stain Noa togtniedaphnia) 0.2150x(t) 4.4546.5431 X1- us46-(2.3145)- O 55 .456.8646 log (cesiodaphmic tog (eriodaphmia) I.59 51) Ceoiodaphmi a Noc the numben of Numbe of Ceniodafhnia - 39

mumber Stonain henrethe ven oncentnation and of Ceoiodaphnia ais 30 Noco e loeiodaphni a = ff2' strain of find the numben Fom gvem Ymodel need Ceaiodaphnia the model ai-) NF No og 445 6- 1S431 (onrentjaio - 0.215stsnan N - 1-5 431 (once n ta ti'on NR St9nain 40.215t A) bermes model Hear Concentuatian at the Cue Censideo the 543 ancentojation NF (4-456-F.') stonain o.315+ e do nothave Sedured mod el e2ua tion. f eduæd Because Values aJe unknoGn model A NF = (4.4s4c-' )- (s431) )- (6.2157-AAstn NR

LO3NF NR 24N15-.5431) - (0.2754 0)- 1.s43c0.2754 Pi) stömn A trtom above The Concentatiom iS to left at Constant Strain NF fsrom the above definihon of log NR