Question

Download the data set “Mine8” from the class D2L site. This data set can be used to test the impact of the 1952 Mine Safety Act on mining fatalities. One of the goals of the legislation was to cut down on the high accident rate in small mines. The authors of the original study hypothesized that mine fatalities were a function of the level of mine technology, average mine size, and mine safety regulation.

Consider the regression

Ft = β0+ β1Tt+ β2St+ β3Ot+ β4Rt+ β5Wt+ε

Where

F = fatal injuries per million man-hours worked in year t

T = percent of year t’s output that was mechanically loaded

S = the average number of workers per mine in year t

O = tons of coal produced per man-hour in year t

R = a regulation dummy = 1 for 1953-1965

(when the Mine Safety Act was in force) and = 0 otherwise

W = a war dummy = 1 in 1940-1944 and = 0 otherwise

a. What are the expected signs for each variable (note, the authors considered T and O, holding S constant, to be measures of mining technology).

b. Estimate the regression. Do coefficients have the expected signs? Are they significant?

c. Create a correlation matrix for the independent variables. Calculate VIFs for the independent variables in this data set. Based on this evidence, is multicollinearity a concern? (Explain).

d. How might you correct for multicollinearity in this regression? (You may mention more than one potential solution).

e. Re-estimate the regression without O. Do you prefer this model or the original? Why?

f. Extra Credit. Did the Mine Safety Act save lives? The data set also includes a variable (NF) which is the number of non-fatal injuries per million man-hours. Explore the impact of the regulation on non-fatal injuries (following what you did above for fatal injuries).

obs	F	NF	O	R	S	T	TI	W
1940	1.7	61.3	0.6	0	65.1	35.4	55.4	1
1941	1.36	59.3	0.6	0	66.4	40.7	59	1
1942	1.43	61	0.61	0	69.3	45.2	62.7	1
1943	1.41	58.8	0.61	0	68.3	48.9	65.3	1
1944	1.25	57.2	0.6	0	65	52.9	67.6	1
1945	1.17	57.9	0.62	0	65	56.1	70.9	0
1946	1.14	60.9	0.63	0	62.4	58.4	73	0
1947	1.28	59.2	0.67	0	49.9	60.7	76.6	0
1948	1.19	58.4	0.67	0	51	64.3	79.2	0
1949	0.98	53.9	0.69	0	53.4	67	82	0
1950	0.96	49.7	0.74	0	53.4	69.4	86.3	0
1951	1.22	49.1	0.78	0	43.3	73.1	91	0
1952	0.94	49.9	0.8	0	42.8	75.6	93.7	0
1953	0.94	47.2	0.88	1	39.2	79.6	100.6	0
1954	1.07	45.6	0.98	1	34.5	84	108.8	0
1955	1.02	45.5	1.05	1	29.1	84.6	112.8	0
1956	1.09	45.8	1.08	1	27.4	84	113.8	0
1957	1.27	46.6	1.13	1	27.8	84.8	117	0
1958	1.27	45.5	1.18	1	23.2	84.9	119.6	0
1959	1.02	42.7	1.27	1	21.8	86	125	0
1960	1.25	44.4	1.34	1	19.7	86.3	128.7	0
1961	1.35	46.6	1.42	1	18.9	86.3	132.8	0
1962	1.31	47.4	1.51	1	17.9	85.7	136.9	0
1963	1.22	46.8	1.6	1	16.9	85.8	141.6	0
1964	1.07	46	1.7	1	17.8	87.4	147.8	0
1965	1.23	47.5	1.76	1	18.2	89.2	152.1	0

Answer 1

a. Expected signs of the variables.
Considering S to be constant,
T(Mechanically load will have negative sign, with increase in the mechanical load fatal injuries will reduce.
O(coal produced per man hour) will have positive sign, increase in output would incrase fatal injuries.
R(Regulation) will have negative sign, with regulation the fatal injuries must reduce.
W(War) will have positive sign, since less workers and more work would be there, increasing the injuries.

b. Regression equation

The R code and explaination for each question is given in line with code, in the below given screenshots.