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In recent years environmentalists and health professionals have been concerned about the ill effects onthe environment of the widespread use of insecticides. If human beings...

      

In recent years environmentalists and health professionals have been concerned about the ill effects on
the environment of the widespread use of insecticides. If human beings are to cope with the problem
and make decisions about how to deal with it, they must understand the effect of insecticides on humans
and other animals. In the kind of study often done to promote such understanding, two professors at
University of Nairobi investigated the effect of a commonly used insecticide on sheep. Among other
statistical analyses, they derived the following linear regression equation (n = 16):
linear1120191008c.png
This equation describes the relationship between the activity of a certain enzyme in the
sheep's brain (Y)and the time (in hours) after the sheep has been exposed to the insecticide (X).
Required:
i) Suppose 30 hours have elapsed since a sheep has been exposed to the insecticide, what is the
predicted value of Y?
ii) How would you describe the relationship between the two variables?linear1120191008ci.png
iii) The professors computed a coefficient of determination (r2) of 0.86 from the data. What
conclusion can be drawn about the true relationship between the two variables?
iv) What assumption are necessary to solve part (iii) above?

  

Answers


Mutiso
linear1120191008cia.png
iv) Assumptions include:
- Relationship is linear
- Independent variable x is known, so used to predict y
- Errors are normally distributed with expected value of zero for any value of x
- Variance of errors is a constant
- Errors are independent
Mutiso answered the question on January 1, 2019 at 19:22


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