Question

In: Statistics and Probability

"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...

"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

The le hmw7 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 tted 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).

the data is separated into fatals and cutting and the two data points are separated by a comma

Solutions

Expert Solution

Sol:

RCODE:

fatalaties <- read.csv("C:/Users/M1045151/Downloads/fatalaties.txt", comment.char="#")
View(fatalaties)

reg <- lm(fatalaties$FATALS~fatalaties$CUTTING)
coefficients(reg)
summary(reg)

Output:

(Intercept) fatalaties$CUTTING
-47.70922903 0.01343187

Regression eq is

FATALS= -47.70922903 + 0.01343187 *CUTTING

Solutionb:

par(mfrow=c(2,2))
plot(reg)

From Residuals vs Fitted: non random pattern is not observed.constant variance assumption is violated

Residuals are normally distributed since residuals points follow the straight dashed line.

From residuals v leverageplot we see outliers that influence the regression.

Homogenity of variance assumption is violated.

orchestra answered 1 year ago

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