An association that supports people who research, design, and evaluate the user experience of products and services periodically conducts a salary survey of its members. One of the authors of the report investigated how much having a Ph.D. affects salaries of people in the profession. The author fit a first-order multiple regression model for salary $\hat{y}$ (in dollars) as a function of years of experience $(x_1)$, Ph.D. status $(x_2 = 1$ if Ph.D., 0 if not), and manager status $(x_3 = 1$ if manager, 0 if not). The following prediction equation was obtained:

\[
\hat{y} = 56,832 + 3,264x_1 + 17,099x_2 + 10,379x_3
\]

a. Predict the salary of a member of the association with 14 years of experience, who does not have a Ph.D. and is not a manager.
$ _ (Round to the nearest dollar as needed)

b. Predict the salary of a member of the association with 14 years of experience, who does have a Ph.D. and is a manager.
$ _ (Round to the nearest dollar as needed)

The predicted salary for a member with 14 years of experience, no Ph.D., and not a manager is $295,618. The predicted salary for a member with 14 years of experience, a Ph.D., and is a manager is $309,261.

Explanation:

In this problem, we are given a multiple regression model for predicting salaries based on years of experience, Ph.D. status, and manager status. The prediction equation is:

ŷ = 56,832 + 3,264x4 + 17,099x1 + 10,379x3

where ŷ represents the predicted salary, x1 represents years of experience, x2 represents Ph.D. status (1 if Ph.D., 0 if not), and x3 represents manager status (1 if manager, 0 if not).

a. To predict the salary of a member with 14 years of experience, no Ph.D., and not a manager, we substitute the values into the equation:

ŷ = 56,832 + 3,264(0) + 17,099(14) + 10,379(0)

ŷ = 56,832 + 0 + 238,786 + 0

ŷ = 295,618

Therefore, the predicted salary is $295,618 (rounded to the nearest dollar).

b. To predict the salary of a member with 14 years of experience, a Ph.D., and is a manager, we substitute the values into the equation:

ŷ = 56,832 + 3,264(1) + 17,099(14) + 10,379(1)

ŷ = 56,832 + 3,264 + 238,786 + 10,379

ŷ = 309,261

Therefore, the predicted salary is $309,261 (rounded to the nearest dollar).

Learn more about predicting salaries based on years of experience, ph.d. status, and manager status here:

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