In mammals, the toxicity of drugs, pesticides and chemical carcinogens can be altered by inducing liver enzyme activity. In a study on chickens, five liver enzymes had their activity induced by butylated hydroxytoluene, and the resulting percent detoxification of malathion (an organophosphate insecticide) was recorded. The experimenters believed that the response (% detoxification, DT) could be modelled by a multiple linear regression based on the activities of the individual enzymes (EAi, i = 1 to 5, measured as a percentage of normal activity): DT = b0 + b1×EA1 + b2×EA2 + b3×EA3 + b4×EA4 +b5×EA5 The results from the experiment are contained in the screenshot, which contains six variables: Detox – DT, the % detoxification of malathion by liver. EA1 – EA1, activity of enzyme 1 (% of normal activity). EA2 – EA2, activity of enzyme 2 (% of normal activity). EA3 – EA3, activity of enzyme 3 (% of normal activity). EA4 – EA4, activity of enzyme 4 (% of normal activity). EA5 – EA5, activity of enzyme 5 (% of normal activity). Perform a multiple linear regression (or univariate General Linear Model) calculation on this data, and answer the following questions based on your results. Include any relevant output from the calculation. Explain whether the intercept, b0, is significantly different from zero. If enzyme activities were 110, 95, 89, 123 and 103 for EAi, i = 1 . . . 5 respectively, what value of % detoxification would the model predict? By producing suitable plots, comment on whether the model assumptions of (i) normality of error and (ii) homogeneity of variance are satisfied.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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In mammals, the toxicity of drugs, pesticides and chemical carcinogens can be altered by inducing liver enzyme activity. In a study on chickens, five liver enzymes had their activity induced by butylated hydroxytoluene, and the resulting percent detoxification of malathion (an organophosphate insecticide) was recorded. The experimenters believed that the response (% detoxification, DT) could be modelled by a multiple linear regression based on the activities of the individual enzymes (EA_i, i = 1 to 5, measured as a percentage of normal activity):

DT = b₀ + b₁×EA₁ + b₂×EA₂ + b₃×EA₃ + b₄×EA₄ +b₅×EA₅

The results from the experiment are contained in the screenshot, which contains six variables:

Detox – DT, the % detoxification of malathion by liver.
EA1 – EA₁, activity of enzyme 1 (% of normal activity).
EA2 – EA₂, activity of enzyme 2 (% of normal activity).
EA3 – EA₃, activity of enzyme 3 (% of normal activity).
EA4 – EA₄, activity of enzyme 4 (% of normal activity).
EA5 – EA₅, activity of enzyme 5 (% of normal activity).

Perform a multiple linear regression (or univariate General Linear Model) calculation on this data, and answer the following questions based on your results. Include any relevant output from the calculation.

Explain whether the intercept, b₀, is significantly different from zero.
If enzyme activities were 110, 95, 89, 123 and 103 for EA_i, i = 1 . . . 5 respectively, what value of % detoxification would the model predict?
By producing suitable plots, comment on whether the model assumptions of (i) normality of error and (ii) homogeneity of variance are satisfied.