Exercise 2 (Total: 20 points) Suppose a hypothetical study analyzes the factors that explain the extent of extramarital affairs in a marriage, and estimates the following multiple linear regression using data on married individuals: (equation 2-1) ex_m_affairs, = 5.180 - 0.039 age; - 0.132 yrs_married; - 0.032 m_satisfaction; + 0.081 income; (2.610) (0.015) (0.041) (0.015) (0.052) N = 928, R2 = 0.22, RSE = 800 Variable Description of Variable (Units) ex_m_affairs Number of extramarital affairs an individual had in the past year age Age of the individual (Yrs) yrs_married Number of years the individual has been in current marriage m_satisfaction Subjective satisfaction index (0 ~100); higher number represents higher satisfaction with current marriage income Couple's combined income (10,000 USD a. [3pts] Interpret the estimated intercept of 5.180. Does it make sense? Explain - Max 3 sentences. (For interpretation, rather than SSS, describe what the intercept represents in the research context.) b. [3.5pts] Write down an extension of the above regression model that would allow men and women to have different intercepts, using the usual notations, Bo, B1, ..., BK, to denote the intercept and the regression coefficients. Define any new variable used. What is your benchmark group? What are the intercepts for each group? c. [3.5pts] Write down an extension of the model from part (b) that would allow you to test whether the number of years in current marriage has differential impact on the number of extramarital affairs in the past year, depending on gender. Which coefficient(s) should we test for statistical significance