Homework #1

The data file DATA01. xlsx contains monthly data for the period Jan-1991 through Dec-2019.

There are three data series, RIGS, WTI, and CPI-U.

RIGS is the total rig count in the lower 48 states for oil and gas wells.

WTI is the underlying commodity of the New York Mercantile Exchange's oil futures contracts. It is the marker price for oil in the U.S.

CPI-U is the consumer price index for all urban consumers.

Rigs are the large apparatus you will find in oil and gas fields that explore for oil and natural gas.They are very expensive and are usually leased on a daily or weekly basis.

In this first exercise

1.Start by regressing RIGS on WTI and CPI-U

a.What sign would you expect for WTI? Why?

b.What is the interpretation of the WTI coefficient?

c.Is the WTI coefficient significant at the .05 level? At the .01 level?

2.What purpose is served by including CPI-U?

3.Is the regression significant?

a.Would you use a t test or an F test to answer this question?

b.What is the probability the relationship is not significant?

c.Can you think of an alternative way for CPI-U to enter the equation?

4.Graph the error with Date on the x-axis

a.Does the error seem to have a pattern?

b.What is the correlation between the error term and itself lagged one month?

c.Does this correlation suggest a problem with the regression?

5.Graph the squared error vs Date.

a.Does there appear to be a pattern with the variance?

b.Add WTI to this graph (graph WTI on the secondary y-axis)

c.Does this graph suggest a problem with the regression?

6.Rig counts represent the sum of all rigs active during any month

a.Can you think of a reason we might want to express the RIGS variable in natural logs?

b.How about WTI and CPI-U?Can you think why they might be better expressed in logs?

7.Run the same regression, but with all three variables expressed in natural logs

a.How does the log-log structure change the interpretation of the coefficients?

b.After graphing the error and the squared error with Date on the x-axis, do you still see any issues with patterns in either the error term or the variance of the error term?

c.Is it valid to compare the R² of this regression with the R² of the previous regression?

Date RIGS WTI

Jan-91 1068 24.70

Feb-91 984 20.55

Mar-91 925 19.90

Apr-91 854 20.80

May-91 819 21.25

Jun-91 867 20.20

Jul-91 844 21.45

Aug-91 803 21.70

Sep-91 775 21.85

Oct-91 795 23.25

Nov-91 808 22.60

Dec-91 796 19.55

Jan-92 710 18.80

Feb-92 669 19.00

Mar-92 648 18.95

Apr-92 642 20.25

May-92 638 21.00

Jun-92 621 22.35

Jul-92 676 21.75

Aug-92 686 21.30

Sep-92 717 21.90

Oct-92 803 21.70

Nov-92 882 20.35

Dec-92 926 19.40

Jan-93 824 19.05

Feb-93 684 20.05

Mar-93 614 20.35

Apr-93 609 20.30

May-93 637 20.00

Jun-93 695 19.15

Jul-93 741 17.90

Aug-93 797 18.00

Sep-93 848 17.50

Oct-93 860 18.15

Nov-93 868 16.75

Dec-93 857 15.55

Jan-94 789 15.00

Feb-94 754 14.75

Mar-94 735 14.65

Apr-94 723 16.30

May-94 716 17.85

Jun-94 756 19.05

Jul-94 771 19.65

Aug-94 766 18.35

Sep-94 809 17.45

Oct-94 822 17.65

Nov-94 835 18.10

Dec-94 816 17.16

Jan-95 748 17.99

Feb-95 713 18.53

Mar-95 665 18.54

Apr-95 678 19.87

May-95 679 19.64

Jun-95 674 18.50

Jul-95 723 17.42

Aug-95 745 17.96

Sep-95 765 18.03

Oct-95 761 17.33

Nov-95 772 17.79

Dec-95 763 18.83

Jan-96 709 18.89

Feb-96 700 19.07

Mar-96 714 21.16

Apr-96 741 23.20

May-96 764 21.08

Jun-96 774 20.27

Jul-96 784 21.36

Aug-96 811 21.97

Sep-96 811 23.92

Oct-96 836 24.94

Nov-96 848 23.66

Dec-96 852 25.32

Jan-97 822 24.93

Feb-97 849 21.83

Mar-97 897 20.69

Apr-97 901 19.40

May-97 924 20.50

Jun-97 976 18.87

Jul-97 969 19.30

Aug-97 993 19.62

Sep-97 1009 19.59

Oct-97 996 21.21

Nov-97 983 19.88

Dec-97 1013 18.09

Jan-98 993 16.51

Feb-98 974 15.81

Mar-98 932 14.76

Apr-98 886 15.32

May-98 855 14.90

Jun-98 854 13.71

Jul-98 816 14.11

Aug-98 792 13.40

Sep-98 774 14.98

Oct-98 734 14.42

Nov-98 688 12.96

Dec-98 647 11.31

Jan-99 587 12.49

Feb-99 542 12.01

Mar-99 526 14.66

Apr-99 496 17.34

May-99 516 17.75

Jun-99 558 17.89

Jul-99 588 20.07

Aug-99 639 21.25

Sep-99 696 23.86

Oct-99 741 22.64

Nov-99 782 24.85

Dec-99 798 26.08

Jan-00 775 27.27

Feb-00 763 29.28

Mar-00 773 29.92

Apr-00 805 25.84

May-00 844 28.83

Jun-00 878 31.86

Jul-00 936 29.97

Aug-00 987 31.31

Sep-00 1011 33.89

Oct-00 1055 33.05

Nov-00 1067 34.37

Dec-00 1097 28.40

Jan-01 1118 29.55

Feb-01 1136 29.57

Mar-01 1163 27.24

Apr-01 1206 27.42

May-01 1234 28.61

Jun-01 1270 27.56

Jul-01 1278 26.44

Aug-01 1252 27.45

Sep-01 1193 26.12

Oct-01 1111 22.18

Nov-01 1000 19.59

Dec-01 901 19.31

Jan-02 867 19.69

Feb-02 825 20.72

Mar-02 763 24.38

Apr-02 750 26.24

May-02 826 27.04

Jun-02 842 25.51

Jul-02 851 26.92

Aug-02 848 28.37

Sep-02 860 29.67

Oct-02 851 28.85

Nov-02 834 26.28

Dec-02 856 29.44

Jan-03 854 32.95

Feb-03 907 35.80

Mar-03 941 33.32

Apr-03 983 28.22

May-03 1034 28.13

Jun-03 1067 30.71

Jul-03 1081 30.75

Aug-03 1090 31.58

Sep-03 1093 28.28

Oct-03 1105 30.32

Nov-03 1111 31.09

Dec-03 1114 32.12

Jan-04 1101 34.24

Feb-04 1119 34.73

Mar-04 1135 36.73

Apr-04 1151 36.71

May-04 1164 40.29

Jun-04 1176 38.03

Jul-04 1213 40.82

Aug-04 1234 44.92

Sep-04 1240 45.93

Oct-04 1240 53.25

Nov-04 1262 48.45

Dec-04 1246 43.23

Jan-05 1255 46.82

Feb-05 1276 47.96

Mar-05 1306 54.17

Apr-05 1334 52.96

May-05 1320 49.81

Jun-05 1355 56.39

Jul-05 1398 58.67

Aug-05 1436 64.96

Sep-05 1452 65.54

Oct-05 1479 62.36

Nov-05 1486 58.28

Dec-05 1470 59.41

Jan-06 1473 65.48

Feb-06 1533 61.62

Mar-06 1551 62.89

Apr-06 1597 69.41

May-06 1635 70.93

Jun-06 1665 70.93

Jul-06 1681 74.40

Aug-06 1738 73.04

Sep-06 1739 63.82

Oct-06 1734 58.85

Nov-06 1706 59.13

Dec-06 1718 62.00

Jan-07 1714 54.24

Feb-07 1736 59.25

Mar-07 1749 60.60

Apr-07 1750 63.94

May-07 1748 63.45

Jun-07 1771 67.49

Jul-07 1777 74.14

Aug-07 1804 72.38

Sep-07 1783 79.91

Oct-07 1762 85.90

Nov-07 1798 94.76

Dec-07 1811 91.36

Jan-08 1749 92.98

Feb-08 1765 95.38

Mar-08 1797 105.47

Apr-08 1829 112.62

May-08 1863 125.01

Jun-08 1902 133.93

Jul-08 1932 133.38

Aug-08 1987 116.64

Sep-08 2014 103.94

Oct-08 1976 76.61

Nov-08 1935 57.29

Dec-08 1782 41.44

Jan-09 1553 41.74

Feb-09 1320 39.15

Mar-09 1105 47.52

Apr-09 995 49.81

May-09 918 59.13

Jun-09 895 69.62

Jul-09 931 64.12

Aug-09 980 71.06

Sep-09 1009 69.44

Oct-09 1044 75.77

Nov-09 1107 78.00

Dec-09 1172 74.49

Jan-10 1267 78.36

Feb-10 1350 76.41

Mar-10 1419 81.25

Apr-10 1479 84.48

May-10 1513 73.73

Jun-10 1531 75.35

Jul-10 1573 76.35

Aug-10 1638 76.60

Sep-10 1655 75.29

Oct-10 1668 81.90

Nov-10 1683 84.24

Dec-10 1711 89.15

Jan-11 1711 89.41

Feb-11 1718 89.53

Mar-11 1720 102.92

Apr-11 1790 109.96

May-11 1836 101.28

Jun-11 1863 96.25

Jul-11 1900 97.31

Aug-11 1957 86.32

Sep-11 1978 85.58

Oct-11 2017 86.41

Nov-11 2011 97.12

Dec-11 2003 98.56

Jan-12 2003 100.29

Feb-12 1990 102.21

Mar-12 1979 106.15

Apr-12 1962 103.28

May-12 1977 94.68

Jun-12 1972 82.36

Jul-12 1944 87.90

Aug-12 1913 94.11

Sep-12 1859 94.51

Oct-12 1834 89.52

Nov-12 1809 86.68

Dec-12 1784 88.22

Jan-13 1756 94.74

Feb-13 1762 95.30

Mar-13 1756 92.91

Apr-13 1755 92.02

May-13 1767 94.76

Jun-13 1761 95.79

Jul-13 1766 104.70

Aug-13 1781 106.55

Sep-13 1760 106.25

Oct-13 1744 100.50

Nov-13 1756 93.95

Dec-13 1771 97.85

Jan-14 1769 94.86

Feb-14 1769 100.73

Mar-14 1803 100.57

Apr-14 1835 102.08

May-14 1859 101.86

Jun-14 1861 105.24

Jul-14 1876 102.94

Aug-14 1904 96.38

Sep-14 1930 93.22

Oct-14 1925 84.40

Nov-14 1925 75.81

Dec-14 1882 59.26

Jan-15 1683 47.27

Feb-15 1348 50.61

Mar-15 1109 47.78

Apr-15 976 54.44

May-15 889 59.27

Jun-15 861 59.80

Jul-15 866 50.90

Aug-15 883 42.86

Sep-15 848 45.45

Oct-15 791 46.20

Nov-15 760 42.70

Dec-15 711 37.23

Jan-16 643 31.54

Feb-16 532 30.39

Mar-16 477 37.77

Apr-16 437 40.96

May-16 407 46.73

Jun-16 417 48.75

Jul-16 449 44.69

Aug-16 481 44.75

Sep-16 509 45.20

Oct-16 543 49.89

Nov-16 580 45.57

Dec-16 634 52.01

Jan-17 683 52.51

Feb-17 744 53.40

Mar-17 789 49.58

Apr-17 853 51.06

May-17 893 48.50

Jun-17 931 45.17

Jul-17 953 46.65

Aug-17 947 48.03

Sep-17 940 49.83

Oct-17 922 51.56

Nov-17 911 56.65

Dec-17 930 57.94

Jan-18 937 63.67

Feb-18 969 62.17

Mar-18 989 62.76

Apr-18 1011 66.32

May-18 1046 69.98

Jun-18 1056 67.52

Jul-18 1050 70.84

Aug-18 1050 67.99

Sep-18 1053 70.21

Oct-18 1063 70.75

Nov-18 1077 56.67

Dec-18 1077 48.95