ECON 492, F18 Homework #4 Due Thursday, September 13, in class Total points: 100
ID: 1137114 • Letter: E
Question
ECON 492, F18 Homework #4 Due Thursday, September 13, in class Total points: 100 Question 1 (15 points) Consider the following equation: SIZE,-72.2+5.77PRICE, Where: SIZE, the size (in square feet) of the ith house, PRICE, the price (in thousands of S) of that house 1) Carefully explain the meaning of each of the estimated regression coefficients. 2) Suppose you are told that this equation explains a significant portion (more than 80 percent) of the variation in the size of a house. Have we shown that high housing prices cause houses to be large? If not, what have we shown? What do you think would happen to the estimated coefficients of this equation if we had measured the price variable in dollars instead of thousands of dollars? Be specific. 3) Question 2 (35 points) Your friend uses OLS to estimate an equation of the demand for gasoline in city ABC as a function of gasoline prices and the average household income D, 72.2-5.77 P+2.06 C, where D, is the quantity demanded (in thousands of gallons) in the i-th year, P? is the price (in S per gallon) in the i-th year, and C, is the city-average household income (in thousands of dollars) in the i-th year 1) What does "least-squares estimates" mean? What is being squared? In what sense are the squares "least"? 2) Explain the meaning of the 3 estimated coefficients. 3) Why is the left-hand variable in your friend's equation D and not D? 4) Didn't your friend forget the stochastic error term in the estimated equation? 5) What do you think would happen to the estimated coefficients of this equation if we had measured the city-average household income in dollars rather than in thousands of dollars? Be specific. 6) Your friend is thinking about reporting the equation to the city council so that the board of economic advisors can use it in predicting future demand for gasoline. Would you encourage your friend to do so? Why yes or why not?Explanation / Answer
1.1. when the price is 0, the size of the house is 72.2sq ft on average, keeping other things constant. When price increases by $1000, the size increases by 5.77 sq ft on average, keeping other things constant.
1.2. The regression coefficient of determination shows how well the price explains the size of the house i.e. the price can explain 80% of the variation in house size. It strictly does not imply causation.
1.3. If $1000 dollar increase in price leads to 5.77 sq ft increase in size on an average, then $1 increase in price would lead to 0.00577 sq ft increase in sixe. The coefficient of price would become 0.00577 instead of 5.77
2.1. It means the value of parameter that minimizes the sum of the squares of the differences between the actual values and the predicted values. The term squared is the differences between the actual values and the predicted values.
2.2. When price and income are zero, the demand is 72.2 thousand gallon on an average, keeping other things constant. When price per gallon incraeses by $1, the demand decreases by 5.77 thousand gallon, keeping other things constant. When household income increases by $1000, the demand increases by 2.06 thousand gallon, keeping other things constant.
2.3. It is because D is a combination of price, constant, income and an error term. However, we can predict only the deterministic part of this equation and not the stochastic part, i.e. we cannot predict error. SInce it is estimated demand and not actual demand, we use D hat.
2.4. The estimated equation is the expected value of demand given the explanatory variables and does not include the error term. The actual demand would have an error term. Hence the equation is correct.
2.5. As given in the explanation for 1.3, the coefficient for income would become 0.00206.
2.6. I would encourage given that all coefficients are significant, the overall fit is significant and it satisfies the Gauss Markov theorem.
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