In a simulation exercise, regression model (1.1) applies with f30 = 100, f31 = 20, and a 2 = 25. an observation on y will be made for x = 5.
a. can you state the exact probability that y will fall between 195 and 205? explain.

We can not state the exact probability that y will fall between 195 and 205

Step-by-step explanation:

* Lets explain how to solve the problem

- Regression model applies with f(30) = 100 and f(31) = 20

- The variance = 25

- An observation on y will be made for x = 5

- Suppose that the regression model is

∵

∵

∵ x = 5

∴ Y = 100 + 20(5) = 100 + 100 = 200

∴ Y = 200

- But the regression model is without error term

∵ We do not know the probability distribution of y for each value

  of x we only know the value of y at one value of x

∵ We know that the mean of distribution is 100 + 20x

∵ We know the variance of distribution is 25

∵ We don not know the shape of the distribution

- We can not  find the exact value of probability of y without the

  Normal error and the regression model must be

  to know that it has a normal distribution

∴ We can not calculate the exact value of probability of y

∴ We can not state the exact probability that y will fall between 195

  and 205

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step-by-step explanation: