Q2 This dataset discuss a study of the ozone layer over the Antarctic. Scientist

Question

Q2 This dataset discuss a study of the ozone layer over the Antarctic. Scientists developed a mea- sure(INHIBIT) of the degree to which oceanic phytoplankton production is inhibited by exposure to ultraviolet radiation (UVB). Another categorical variable SURFACE is the depth below the ocean's surface from which the sample was taken. The data is shown in Table 2 a) The first model treats the INHIBIT as the response and SURFACE as the regressor. Below is the R output: Call: 1n (formula Inhibit Surface, data dat) Residuals: Min 1Q Median 3q Max 18.350 -8.350 3.643 1.857 40.650 Coefficients: Intercept) SurfaceSurface7.707 Estimate Std. Error t value Pr( ) 4.6453.950 0.00128 7.239 1.065 0.30384 18.350

Explanation / Answer

a) Model 1

what is the average degree of Inhibit for each surface level .

See here model is not significant because P-value is greater tahn 0.05.

so the average degree of Inhibit for each surface level is 13.72 ( mean of all inhibit because surface variable not singnificant ).

See surface variable is qualitative

So we cansider indicator variable Deep =0

Surface =1  

b) Model 2

what is the average degree of Inhibit for each surface level when the UVB = 0.025

For Surface level = surface (1) , VUB= 0.025

Inhibit = 5.425 - 21.159 * surfacesurface + 923.185*UVB

= 5.425 - 21.159 * 1 + 923.185 * 0.025

= 7.345625

For Surface level = Deep(0) , VUB= 0.025

Inhibit = 5.425 - 21.159 * surfacesurface + 923.185*UVB

= 5.425 - 21.159 * 0 + 923.185 * 0.025

= 28.50463

c) Model 3

what is the average degree of Inhibit for each surface level when the UVB = 0.025

For Surface level = Deep(0) , VUB= 0.025

Inhibit = 1.181 + 1.278 * surfacesurface +1226.389*UVB - 939.931 * surfacesurface *UVB

= 1.181 + 1.278 * (0) +1226.389* 0.025 - 939.931 * 0 * 0.025

=31.84072

For Surface level = surface (1) , VUB= 0.025

Inhibit = 1.181 + 1.278 * surfacesurface +1226.389*UVB - 939.931 * surfacesurface *UVB

= 1.181 + 1.278 * (1) +1226.389* 0.025 - 939.931 * 1 * 0.025

= 9.62045

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