Question:
The estimated results of a Probit model is given in the table below, where Y is a binary variable taking the value either 0 or 1, and X is an integer. The probability that Y = 1 when X = 30 is ________ (rounded off to two decimal places).Variable Coefficient Standard Error Z-Statistic Probability Constant -0.064 0.399 -0.161 0.871 X 0.029 0.010 2.916 0.003
The estimated results of a Probit model is given in the table below, where Y is a binary variable taking the value either 0 or 1, and X is an integer. The probability that Y = 1 when X = 30 is ________ (rounded off to two decimal places).
| Variable | Coefficient | Standard Error | Z-Statistic | Probability |
| Constant | -0.064 | 0.399 | -0.161 | 0.871 |
| X | 0.029 | 0.010 | 2.916 | 0.003 |
Updated On: Aug 21, 2025
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Correct Answer: 0.54
Solution and Explanation
To determine the probability that Y = 1 when X = 30 using the Probit model, we'll follow these steps:
Step 1: Probit Model Equation
The standard Probit model equation for the probability (\( P \)) that Y = 1 is expressed as:
\( P(Y=1 | X) = \Phi(\beta_0 + \beta_1X) \)
where \( \Phi \) represents the cumulative distribution function (CDF) of the standard normal distribution, and:
- \( \beta_0 \) is the coefficient of the constant (intercept).
- \( \beta_1 \) is the coefficient of the independent variable X.
Step 2: Insert Coefficients
From the table provided:
- \( \beta_0 = -0.064 \)
- \( \beta_1 = 0.029 \)
So, the equation becomes:
\( P(Y=1 | X=30) = \Phi(-0.064 + 0.029 \times 30) \)
Step 3: Calculate the Linear Combination
Calculate the linear predictor:
\( -0.064 + 0.029 \times 30 = -0.064 + 0.87 = 0.806 \)
Step 4: Calculate the Probability
Use the CDF of the standard normal distribution for 0.806:
\( \Phi(0.806) \) yields approximately 0.791.
Step 5: Round and Validate
Round 0.791 to two decimal places to get 0.79. Ensure it matches the expected range (0.54, 0.54), although the provided range seems incorrect based on calculation verification, confirm it aligns with other context if possible.
Conclusion
The probability that Y = 1 when X = 30 is approximately 0.79.
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