Problem 1 (20 pts). A researcher is using data for a sample of 3570 Hong Kong citizens 25 years of age and over to investigate the relationship between the monthly housing rental value per unit area Yi (measured in HKD per square foot) and their hourly wage Xi (measured in HKD/hour). The regression model takes the forms Yi = a + bXi + ui . Information of the sample data is summarized as follows: N = 3570; X N i=1 Xi = 96000; X N i=1 (Xi ? X) 2 = 498517; X N i=1 X2 i = 3080030; X N i=1 Yi = 34000; X N i=1 (Yi ? Y ) 2 = 15118; X N i=1 Y 2 i = 338927; X N i=1 (Xi ? X)(Yi ? Y ) = 75498; X N i=1 XiYi = 989783; X N i=1 u 2 i = 3728; Use the above sample information to answer all the following questions. Show your calculations. (a) Compute the least-square estimators of a and b. Explain in words what the numeric value your calculated for ?b means. (b) Calculate an estimate of the error variance ? 2 . (c) Compute the value of R2 , the coefficient of determination for the regression model. Briefly explain what R2 means in words.

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