Estimate the model Y = 1 + 2X2 + 3X3 + 4X4 + 5X5 + u for the data given for wild

Question

Estimate the model Y = 1 + 2X2 + 3X3 + 4X4 + 5X5 + u for the data given for wildcat oil well development in the Canvas data set. Wildcats are wells drilled to find and produce oil and/or gas in an unproved area or to find a new reservoir in an existing field. The number of wildcat wells drilled (wildcats) is the dependent variable. The independent variables are price per barrel of oil (price) in constant dollars, U.S. oil production (output) as measured in millions of barrels of oil per day, U.S. Gross National Product (GNP), and time. Test the significance of the overall regression and the individual parameter estimates, interpret the value of R2, interpret the parameter estimates, and then explain your findings with respect to the potential relationship between the dependent and independent variables. Use = .05. WILDCATS PRICE OUTPUT GNP TIME 8.01 4.89 5.52 487.67 1 9.06 4.83 5.05 490.59 2 10.31 4.68 5.41 533.55 3 11.76 4.42 6.16 576.57 4 12.43 4.36 6.26 598.62 5 13.31 4.55 6.34 621.77 6 13.1 4.66 6.81 613.67 7 14.94 4.54 7.15 654.8 8 16.17 4.44 7.17 668.84 9 14.71 4.75 6.71 681.02 10 13.2 4.56 7.05 679.53 11 13.19 4.29 7.04 720.53 12 11.7 4.19 7.18 736.86 13 10.99 4.17 7.33 755.34 14 10.8 4.11 7.54 799.15 15 10.66 4.04 7.61 830.7 16 10.75 3.96 7.8 874.29 17 9.47 3.85 8.3 925.86 18 10.31 3.75 8.81 980.98 19 8.88 3.69 8.66 1,007.72 20 8.88 3.56 8.78 1,051.83 21 9.7 3.56 9.18 1,078.76 22 7.69 3.48 9.03 1,075.31 23 6.92 3.53 9 1,107.48 24 7.54 3.39 8.78 1,171.10 25 7.47 3.68 8.38 1,234.97 26 8.63 5.92 8.01 1,217.81 27 9.21 6.03 7.78 1,202.36 28 9.23 6.12 7.88 1,271.01 29 9.96 6.05 7.88 1,332.67 30 10.78 5.89 8.67 1,385.10 31

Explanation / Answer

The regression equation is
WILDCATS = - 9.80 + 2.70 PRICE + 3.05 OUTPUT - 0.0160 GNP - 0.023 TIME

Predictor Coef SE Coef T P
Constant -9.799 8.931 -1.10 0.283
PRICE 2.7002 0.6986 3.87 0.001
OUTPUT 3.0451 0.9411 3.24 0.003
GNP -0.01599 0.0082 -1.95 0.062
TIME -0.0233 0.2734 -0.09 0.933

S = 1.64289 R-Sq = 0.578 R-Sq(adj) = 0.514

The significance test of the overall regression and the individual parameter estimates is given in the above table. The estimated value of R2 is 0.578. Hence, 57.8% of total variance of the number of wildcat wells drilled (wildcats) is explained by the four covariates variables price per barrel of oil (price) in constant dollars, U.S. oil production (output) as measured in millions of barrels of oil per day, U.S. Gross National Product (GNP), and time.

The price and output are the only significant covariates in this model at 0.05 level of significance. Hence, a unit increase in price and output increases the mean WILDCATS by 2.7002 and 3.0451 respectively.

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