CAS Exam MAS-I Fall 2019, Question 35

Study guide: Exam MAS-I

Two variables, X and Y, exhibit the following relationship:

Y_i = 1.5X_i + 2 + \varepsilon_i

where \varepsilon_i is a standard normal random variable, and each \varepsilon_i is mutually independent.

For some sample of data, an actuary uses ordinary least squares regression of the form:

Y_i = \hat{\beta}_1 X_i + \hat{\beta}_0 + e_i

to estimate the relationship. The following parameter estimates were formed:

Calculate the bias of the estimate.

• A) Less than -0.1
• B) At least -0.1, but less than 0.1
• C) At least 0.1, but less than 0.3
• D) At least 0.3
• E) There is not enough information provided to calculate the bias.

Answer this question and see the worked solution

Concepts tested

• Unbiasedness
• Bias
• Linear Regression
• Ordinary Least Squares

More questions from this set

• CAS Exam MAS-I Fall 2019, Question 34
• CAS Exam MAS-I Fall 2019, Question 36