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Linear Functions: Y = a + bX

Linear Functions: Y = a + bX. ^. B t = 37.54*** - 0.88***P t + 11.89***Yd t se (10.0402) (0.1647) (1.7622) R 2 = 0.6580, N = 28, SER = 6.0806. Example 1 : Linear functional form. B t : The per capita consumption of beef in year t (in pounds per person)

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Linear Functions: Y = a + bX

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  1. Linear Functions: Y = a + bX

  2. ^ Bt = 37.54*** - 0.88***Pt + 11.89***Ydt se (10.0402) (0.1647) (1.7622) R2 = 0.6580, N = 28, SER = 6.0806 Example 1: Linear functional form Bt : The per capita consumption of beef in year t (in pounds per person) Pt : The price of beef in year t (in cents per pound) Ydt : The per capita disposable income in year t (in thousand of dollars)

  3. Example 6.7: Double-log functional form ^ lnBt = 3.5944*** - 0.3444***lnPt + 1.0715***lnYdt se (0.1413) (0.0622) (0.1485) R2 = 0.7099, N = 28, SER = 0.0536 Bt : The per capita consumption of beef in year t (in pounds per person) Pt : The price of beef in year t (in cents per pound) Ydt : The per capita disposable income in year t (in thousand of dollars)

  4. Example 4: Left-side semi-log functional form ^ lnBt = 3.9970*** - 0.0083***Pt + 0.1139***Ydt se (0.0945) (0.0015) (0.0166) R2 = 0.6699, N = 28, SER = 0.0057 Bt : The per capita consumption of beef in year t (in pounds per person) Pt : The price of beef in year t (in cents per pound) Ydt : The per capita disposable income in year t (in thousand of dollars)

  5. ^ Bt = 227.888*** - 0.804***Pt – 758.093***(1/Ydt) se (11.7778) (0.0990) (69.9654) R2 = 0.8306, N = 28, SER = 4.2795 ^ lnBt = 3.5944*** - 0.3444***lnPt + 1.0715***lnYdt se (0.1413) (0.0622) (0.1485) R2 = 0.7099, N = 28, SER = 0.0536 Eg 2 and Eg 5 lnB  exp(lnB)  R2 = 0.6707

  6. ^ (1) Bt = 37.54*** - 0.88***Pt + 11.89***Ydt R2 = 0.66 ^ (2) lnBt = 3.59*** - 0.34***lnPt + 1.07***lnYdt R2 = 0.71 ^ (3) Bt = -71.75*** - 0.87***Pt + 98.87***lnYdt R2 = 0.77 ^ (4) lnBt = 4.00*** - 0.01***Pt + 0.11***Ydt R2 = 0.67 ^ (5) Bt = 227.89*** - 0.80***Pt – 758.09***(1/Ydt) R2 = 0.83

  7. Child Mortality Data: BE4_Tab0604.xls CM: Child mortality FLR: Female literacy rate PGNP:Per capita GNP in 1980 TFR: Total fertility rate

  8. Partial Data for the relation wage = f(educ, exper, gender, status)

  9. 7. The Dummy Variable Approach to the Chow Test Yi = 0 + 1X1i + 2X2i + i, i = 1,…,N You believe that the data can be classified into two groups, A and B. The Chow test  can test the hypothesis  cannot tell us the source of the difference.

  10. Define Di = 1 for group A Di = 0 otherwise. Consider the model Yi = 0 + 0Di + 1X1i + 1(DiX1i) + 2X2i + 2(DiX2i) + i For Di = 0, Yi = 0 + 1X1i + 2X2i + t For Di = 1, Yi = (0 + 0) + (1 + 1)X1i + (2 + 2)X2i + i

  11. Example 17: (HtWt_2008s) The dependent variable is “weight” in Kg. hh = height – 160cm.

  12. Example 7.9: ** Investment (INV) depends on value of the firm (V) and stock of capital (K). ** INV = 0 + 1 V + 2 K + . ** 2 firms: GE and Westinghouse ** Test whether they have the same investment function using the dummy variable approach?

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