Question

Here is the data Stat7_prob3.txt :

"FATALS","CUTTING"
270,15692
183,16198
319,17235
103,18463
149,18959
124,19103
62,19618
298,20436
330,21229
486,18660
302,17551
373,17466
187,17388
347,15261
168,14731
234,14237
68,13216
162,12017
27,11845
40,11905
26,11881
41,11974
116,11892
84,11810
43,12076
292,12342
89,12608
148,13049
166,11656
32,13305
72,13390
27,13625
154,13865
44,14445
3,14424
3,14315
153,13761
11,12471
9,10960
17,9218
2,9054
5,9218
63,8817
41,7744
10,6907
3,6440
26,6021
52,5561
31,5309
3,5320
19,4784
10,4311
12,3663
88,3060
0,2779
41,2623
2,2058
5,1890
2,1535
0,1515
0,1595
23,1803
4,1495
0,1432

Here is the question :

Please Use R software/studio and provide all the R code and R output, please. Please answers all the questions (a & b). Pay attention to everything in Bold please. Show all work!

The file Stat7_prob3.txt contains data on the following two variables

• FATALS: the annual number of fatalities from gas and dust explosions in coal mines for years 1915 to 1978.

• CUTTING: the number of cutting machines in use

(a) Fit the regression model using FATALS as the dependent variable and CUTTING as the independent variable.

(b) Using appropriate residual plots and formal tests, investigate the violation of any assumptions. Do any assumptions of the linear regression model appear to be violated? If so, which one (or ones)? (Hint: Plot of residuals versus fitted values can be used for linearity, zero mean, and constant variance. Normal probability plot of the residuals can be used for normality. We also have formal tests for the constant variance and normality assumptions that you can do in R).

Answer 1