Exercise 17-27 Algo Consider a binary response variable y and an explanatory var

Question

Exercise 17-27 Algo Consider a binary response variable y and an explanatory variable x that varies between 0 and 4. The linear model is estimated as y -1.03 + 0.62x a. Compute the estimated probability for x = 2 and x-3. (Negative values should be indicated by a minus sign. Round your answers to 2 decimal places.) Estimated probability x=2 x=3 b. For what values of x is the estimated probability negative or greater than one? (Round your answers to 2 decimal places.) values of x Estimated probability negative Estimated probability greater than one Rook& RASsOurces

Explanation / Answer

a.) Here value of y can be treated as the probabilities

For X = 2

Probability = -1.03 + 0.62*2 = 0.21

For X = 3

Probability = -1.03 + 0.62*3 = 0.83

(b) for estimated probbaility to be negative

-1.03 + 0.62*x < 0

x < 1.03/0.62 = 1.66

Thus for X < 1.66, probbaility is negative

For probability to be greater than 1

-1.03 + 0.62*x > 1

x > (2.03)/0.62 = 3.27

for X > 3.27, probability > 1

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