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ARE106SU09HW3 - 1 University of California Davis Managerial...

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1 University of California, Davis Managerial Economic(ARE) 106, Summer 2009 Instructor: John H. Constantine Problem Set #3: Due Monday, August 24, 2009 Problem 1 : This problem requires the use of SHAZAM. Consider the problem of estimating a production function that expresses the relationship between the level of output of a product ( y ) and the level of an input, or factor of production ( x ). The SHAZAM command file is given below. When necessary, assume α = 5%. sample 1 15 read(are106/table3-2.dat) x y print x y plot ols y x stop (a) Assume that the data can be described the simple linear regression model: y = β 1 + β 2 x + e . Use SHAZAM estimate b 1 and b 2 . State the associated t statistics. (b) Give an economic interpretation of the estimated parameters. (c) Draw your estimated OLS line through the data plot. (d) (i) Find the confidence interval for b 2 . (ii) Draw a picture and show the regions of “Reject H 0 ” and “Do Not Reject H 0 ”. (iii) Clearly explain what this confidence interval means. (e) Using the Confidence Interval approach, you are to test the following hypotheses. Draw β 2 HO on your picture in part (d, ii) for each hypothesis. (i) H 0 : β 2 = 0 (ii) H 0 : β 2 = 0.30 (iii) H 0 : β 2 = 0.50 (f) Now, conduct the three hypotheses of part (e), but this time using the t-test approach.
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