Final answer:
To estimate the probability for x = 15 cm using the given fitted model, substitute the value of x into the model and calculate the logit probability. Then, use the logistic function to convert the logit probability to a regular probability. Don't forget to consider the coefficients for other variables in the model if they are given.
Step-by-step explanation:
To estimate the probability for x = 15 cm, we can substitute the value of x into the fitted model. So, the logit probability is logit π = -12.75 + 1.330c₁ + 1.402c₂ + 1.106c₃ + 0.468(15). Simplifying the equation gives us a value for the logit probability.
Once we have the logit probability, we can convert it to a regular probability using the logistic function. The formula for converting the logit probability to a regular probability is P(X = x) = 1 / (1 + e^(-logit π)). Substituting the logit probability we found earlier, we can calculate the estimated probability for x = 15 cm.
Remember to plug in the values for c₁, c₂, and c₃ if they are given, as they represent the coefficients for other variables in the fitted model.