Exercise 2 (Total: 20 points) Suppose a hypothetical study analyzes the factors that explain the extent...

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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 agei (2.610) (0.015) 0.132 yrs married (0.041) 0.032 m_satisfaction; + 0.081 income (0.015) (0.052) N = 928, R2 = 0.22, RSE = 800 Description of Variable (Units) Number of extramarital affairs an individual had in the past year Variable ex_m_affairs age Age of the individual (Yrs) yrs_married m_satisfaction income Number of years the individual has been in current marriage Subjective satisfaction index (0-100); higher number represents higher satisfaction with current marriage 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, B, ..., k, 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? d. [4pts] The researcher omits the variable, age, from equation 2-1 and observes the estimated coefficient on m_satisfaction changes to -0.011. According to what we know about the omitted variable bias, what should be the sign of correlation between age and m_satisfaction? e. [6pts] In conducting the test of joint significance (F-test) on multiple variables in a linear regression model, we can estimate the generalized restricted and unrestricted models as follows: Unrestricted Model: = B + B + B2x2 + B3x3 + 4x4 Restricted Model: y = 0 + +2x2 Sign the relationship between SSR_restricted and SSR_unrestricted. ( 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 agei (2.610) (0.015) 0.132 yrs married (0.041) 0.032 m_satisfaction; + 0.081 income (0.015) (0.052) N = 928, R2 = 0.22, RSE = 800 Description of Variable (Units) Number of extramarital affairs an individual had in the past year Variable ex_m_affairs age Age of the individual (Yrs) yrs_married m_satisfaction income Number of years the individual has been in current marriage Subjective satisfaction index (0-100); higher number represents higher satisfaction with current marriage 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, B, ..., k, 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? d. [4pts] The researcher omits the variable, age, from equation 2-1 and observes the estimated coefficient on m_satisfaction changes to -0.011. According to what we know about the omitted variable bias, what should be the sign of correlation between age and m_satisfaction? e. [6pts] In conducting the test of joint significance (F-test) on multiple variables in a linear regression model, we can estimate the generalized restricted and unrestricted models as follows: Unrestricted Model: = B + B + B2x2 + B3x3 + 4x4 Restricted Model: y = 0 + +2x2 Sign the relationship between SSR_restricted and SSR_unrestricted. (