Question

Problem # 1 (sheet # 1). In 1974 W. Andrews and C. Christenson published a pioneering study of underground coal mine safety in which a major purpose was to figure out the impact of the 1952 Mine Safety Act on mine fatalities. One of the goals of the legislation was to cut down on the high accident rate in small mines. The authors hypothesized that mine fatalities were a function of the level of mine technology, average mine size, and mine safety regulation. Using the data set in the spreadsheet, estimate the following model and answer the following questions: (10) F= Bo + B.*T+ B2*S4 + B3*Qx+ Bu*R: +Bs*W: The variables are defined as follows: F fatal injuries per million man-hours worked in yeart T- percent of year t's output that was mechanically loaded Si= the average number of workers per mine in yeart Os = tons of coal produced per man-hour in yeart Re - a regulation dummy equal to 1 for 1953-1965 (when the Mine Safety Act was in force and o otherwise W = a war dummy equal to 1 in 1940-1944 and 0 otherwise A. Which variables are significant at a critical value of +/- 1.96. B. How much of the variation in fatal injuries is explained by this model? C. Interpret the coefficient estimate on Qt. D. Interpret the coefficient estimate on Wt. E. What are the mean values of the following variables: T1, S, and 0.2 To get the mean values. you need to run the descriptive statistics from the drop-down menu with the regression tool. F. What is your conclusion: Did the 1952 Mine Safety Act save lives? Explain.

Answer 1

The regression results are shown below.

A. A critical value of +/- 1.96 means 5% level of significance. As per the rule of thumb, a t value of 2 means significant at 5% level of significance. As per the above result, the t-value of the coefficients of S and T including the intercept are more than 2. Hence, these two variables S and T including the intercept are statistically significant at a critical value of +/-1.96. This is also confirmed by the p-value. The p-value for these variables are less than 0.05 or 5%.

B. Since R2 = 0.7320, the variation explained by this model = 73.2%.

C. Since the coefficient of Ot is not significant (i.e., the coefficient is statistically equal to zero), we may conclude that this variable does not have any influence on fatal injuries. i.e., Tonnes of coal produced per man-hour does not influence fatal injuries.

D. Since the coefficient of Wt is not significant (i.e., the coefficient is statistically equal to zero), we may conclude that this variable does not have any influence on fatal injuries. i.e., there is no difference in fatal injuries between the war time and non-war time.

E. The mean values of Tt, St and Ot are respectively 77.6, 41 and 0.84 as shown in the table below with all the descriptive statistics.

0 R ST W 0.19 0.08 0 Mean Standard Error Median Mode Standard Deviation Sample Variance Kurtosis Skewness Range Minimum 1.20 0.03 1.22 1.25 0.18 0.03 1.08 0.66 0.76 0.94 0.40 0.16 0.98 0.5 0.07 0.1 0.84 0.5 0.6 0 0.38 0.509902 0.15 0.26 -0.81 -2.17391 0.71 -2.9E-17 1.16 1 0.6 0 1.76 1 25.52 1 3 26 26 41.07 3.77 41 65 19.21 368.95 -1.59 0.15 52.4 16.9 69.3 1067.7 26 71.40 3.27 77.6 84 16.67 277.92 -0.73 -0.76 53.8 35.4 89.2 1856.3 26 0.81 1.7 Maximum Sum Count 31.14

F. Since the coefficient of Rt is not statistically significant, we may conclude that 1952 Mine Safety Act did not have significant impact on fatal injuries or it did not save life.