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 overall multiple linear regression model is significant. Explain which slope parameter, if any, in the model is not Explain which enzyme activity causes the % detoxification to decrease.
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 overall multiple linear regression model is significant.
- Explain which slope parameter, if any, in the model is not
- Explain which enzyme activity causes the % detoxification to decrease.
![1
2
3
4
5
6
7
8
9
10
11
12
13
XEMENT
Detox
146.104
152.597
168.831
178.571
191.558
113.636
188.312
94.156
159.091
142.857
DEMEDEN
EA1
348.475
233.220
287.458
152.542
276.271
78.644
196.949
101.695
194.576
325.424
LINE
EA2
337.500
260.417
273.958
310.417
818.750
156.250
260.417
112.500
280.208
326.042
EA3
108.122
82.234
74.619
86.802
122.843
112.690
79.188
127.919
239.594
173.096
CENE
EA4
106.667
80.000
66.667
73.333
86.667
93.333
80.000
93.333
106.667
113.333
EXEREMETTR
EA5
107.692
88.889
87.179
96.581
97.436
94.872
106.838
80.342
91.453
100.000
var
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