Question

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Consider a binary response variable y and an explanatory variable x that varies between 0 and 4. The linear model is estimated as yˆy^ = −1.19 + 0.53x.

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.) Estimated probability negative Estimated probability greater than one

Answer 1

y^ = -1.19 + 0.53 * x

a) x = 2

y^ = -1.19 + 0.53 * 2 = -0.13 (ans)

x = 3

y^ = -1.19 + 0.53 * 3 = 0.4

b) Estimated probability negative,

y^ < 0

or, -1.19 + 0.53 * x < 0

or, 0.53 * x < 1.19

or, x < 2.25 (ans)

Estimated probability greater than one,

y^ > 1

or, -1.19 + 0.53 * x > 1

or, 0.53 * x > 1 + 1.19

or, x > 4.13 (ans)