how to transform a model into one that could be estimated using ols 6

Only these first 4 questions. Analytical Exercises: 1) For the following models, label each as either i) linear in both parameters and variables, ii) linear in parameters but not linear in variables, iii) linear in variables but not in parameters, or iv) neither linear in parameters nor linear in variables. a) = 1 + 2 log( 2 ) + 3 log( 3 ) + b) = 1 + 2 2 2 + 3 3 + c) = 1 (1 − 2 ) + 2 log( 2 ) + 3 log( 3 ) + d) = log( 1 ) + 2 3 2 + 4 log( 3 ) + e) = 1 + 2 2 + 3 3 + f) = 1 + 2√ 2 + 3 3 3 + 2) Consider the following model of the relationship between a dependent variable and two independent variables, 2 and 3 : = 1 2 2 3 3 a) Transform this model into one that could be estimated using OLS. b) Give an interpretation of the parameters 2and 3. 3) Stock market investors give considerable attention to a firm’s quarterly “earnings announcement,” at which the firm releases its quarterly accounting earnings. Suppose we are interested in estimating a model to measure the stock market’s response to the information contained in the earnings announcement. We settle on the following model: = 1 + 2 + 3 + 4 + 5 + 6 + 7 + where: : the percentage change in the stock price of company in a short window (24 hours) around the time of the earnings announcement. : the earnings “surprise”, measured as the deviation of the firm’s accounting earnings from the average expectations of Wall Street analysts. This is measured in cents per share of stock outstanding. 2 : a dummy variable that is 1 if firm had negative accounting earnings (a loss) and is 0 otherwise. : a dummy variable that is 1 if firm had accounting earnings in excess of the average expectations of Wall Street analysts (i.e. is positive), and is zero otherwise. (a firm can have a positive accounting earnings that does not beat expectations, i.e. = 0) : a dummy variable that is 1 if firm i is in industry B, and is zero otherwise. : a dummy variable that is 1 if firm i is in industry C, and is zero otherwise. : a dummy variable that is 1 if firm i is in industry D, and is zero otherwise. All firms in the sample are in either industry A, B, C, or D. Estimation of this model yields the following fitted model: ̂ = 0.1 + 0.5 − 2 + 0.4 + 0.1 + 0.2 − 0.3 a) What is the reference category for this regression? b) What is the effect on of moving from industry A to industry B, all else held equal? c) What is the effect on of moving from industry C to industry B, all else held equal? d) Define a new variable , which is 1 if firm is in industry A and is zero otherwise. Using this variable and the other variables defined above, write down a regression that would fall into the “dummy variable trap”. 4) Data was collected from a random sample of 220 home sales from a community in 2003. Let denote the selling price (in $1000), denote the number of bedrooms, denote the size of the house (in square feet), denote the age of the house (in years), denote a dummy variable that is equal to 1 if the condition of the house is reported as “poor” and is zero otherwise, and denote a dummy variable that is 1 if the house has a view of a nearby mountain range and is zero otherwise. An estimated regression yields the following fitted regression line: ̂ = 119.2 + 0.485 + 0.156 + 0.090 − 48.8 + 25.5 − 0.005 ∗ + 0.005 ∗ a) Suppose that a homeowner of a 2500 square foot house removes a row of tall trees that is blocking the view of the mountains from the house. What is the regression’s prediction for the increase in the value of the house? (Don’t forget the interaction term!) b) Consider a house that has a view of the mountains and is in poor condition. Suppose the homeowner adds 100 square feet to the house. What is the regression’s prediction for the increase in the value of the house? (Don’t forget the interaction term!)
 
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