y do we sometimes take the logarithm of the variables before adding them to the regression model? How to properly interpret the coefficient estimate on ln(salary)? 7. We estimated a linear model (shown below) with interaction terms. Spending = a + b * ln(salary) + c * gender + d * ln(salary) * gender + e, where gender is a binary variable which is set to 1 if the current observation is from a male object (0 otherwise). We use the estimated model to draw the relationship between the spending and ln(salary), and here is what we get: Please infer the signs of the parameters (if the estimated a, b, c, and d are positive or negative)? 8. We collected a dataset about the investment in public security and the crime rate in each USA states over the past 15 years. Then we run the following regression model: Crime_rate = a + b * police_force_investment + e We find that the coefficient b is estimated to be positive. Can we claim that the investment in police force increases the crime rate? Why? Please propose a linear model to correct.