Question

The director of the Canadian Interagency Forest Fire Centre (CIFFC-22) coordinates resources across provincial boundaries and wants to study the issue of “reserve hours”, which represent hours in which staff are paid to maintain equipment and be on-call but are not actually involved in fire fighting. The variables to be considered are:

Reserve – the total reserve hours; 1000s of hours per month

Total staff – the total number of people per month

Remote – the total hours per month worked remotely on forest fires; 1000s of hours per month

The data for 26 months are given below.

[2 marks] Develop a model to predict the Reserve Hours using Total Staff and Remote as predictor variables. From your results, state the estimated multiple regression equation.

[2 marks] Interpret the meaning of the slopes in this problem, using the context of the question.

[2 marks] Predict the average reserve hours for a month in which the total staff is 3100 people per month and the remote hours are 400 (thousands of hours) . Include a statement in context.

[4 marks] State and test the assumptions of the regression model. Support your claims.

[4 marks] Conduct an appropriate test of autocorrelation (there are 3 possibilities). Substantiate your choice of test.

[3 marks] Are there any influential observations? Substantiate your claim.

[3 marks] Another field of data that was not included consists of the Fire Weather Index (FWI). The levels are Low, Moderate, High, and Extreme and the values entered in the data set are Lo, Mo, Hi, and Ex, respectively. If you were to extend your multiple regression model to include the FWI, how would you go about doing this? Explain.

Month   Reserve   Total Staff   Remote
1   245   3718   415
2   177   3663   599
3   271   3938   657
4   211   4092   632
5   196   3729   529
6   135   3179   410
7   195   3674   383
8   118   3223   400
9   116   3575   344
10   147   3421   339
11   154   3344   354
12   146   3432   290
13   115   3113   389
14   161   3377   403
15   274   3542   152
16   245   3685   229
17   201   3850   272
18   183   3729   441
19   237   3597   476
20   175   3608   348
21   152   3509   450
22   188   3575   337
23   188   3542   268
24   197   3487   236
25   261   3465   165
26   232   3641   271

Answer 1

> data
Month Reserve Total_staff Remote_hrs
1 1 245 3718 415
2 2 177 3663 599
3 3 271 3938 657
4 4 211 4092 632
5 5 196 3729 529
6 6 135 3179 410
7 7 195 3674 383
8 8 118 3223 400
9 9 116 3575 344
10 10 147 3421 339
11 11 154 3344 354
12 12 146 3432 290
13 13 115 3113 389
14 14 161 3377 403
15 15 274 3542 152
16 16 245 3685 229
17 17 201 3850 272
18 18 183 3729 441
19 19 237 3597 476
20 20 175 3608 348
21 21 152 3509 450
22 22 188 3575 337
23 23 188 3542 268
24 24 197 3487 236
25 25 261 3465 165
26 26 232 3641 271

[2 marks] Develop a model to predict the Reserve Hours using Total Staff and Remote as predictor variables. From your results, state the estimated multiple regression equation.

> model = lm(Reserve~Total_staff+Remote_hrs,data=data)
> summary(model)

Call:
lm(formula = Reserve ~ Total_staff + Remote_hrs, data = data)

Residuals:
Min 1Q Median 3Q Max
-79.241 -22.082 -1.326 15.136 61.016

Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -330.53587 116.46779 -2.838 0.00932 **
Total_staff 0.16044 0.03446 4.656 0.00011 ***
Remote_hrs -0.13897 0.05880 -2.363 0.02693 *
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 35.39 on 23 degrees of freedom
Multiple R-squared: 0.4899,   Adjusted R-squared: 0.4456
F-statistic: 11.05 on 2 and 23 DF, p-value: 0.0004345

Equation : Reserve = -330.54 + 0.16*Total_staff - 0.14*Remote_hrs

[2 marks] Interpret the meaning of the slopes in this problem, using the context of the question.

Interpretation:

Total_staff: For 1 increase in Total_staff, Reserves increase by 0.16 units

Remote_hrs: For 1 unit fo increase in Remote_hrs, Reserves decrease by -0.14 units

[2 marks] Predict the average reserve hours for a month in which the total staff is 3100 people per month and the remote hours are 400 (thousands of hours) . Include a statement in context.

Reserve = -330.54 + 0.16*Total_staff - 0.14*Remote_hrs

= -330.54 + 0.16*3100 - 0.14*400 = 109.46 hrs

[4 marks] State and test the assumptions of the regression model. Support your claims.

Assumptions:

• Linear relationship : The variables independent and dependent must be linearly related

The model is linear and hence this holds true.

• No heteroscedasticity : The variances are constant

The pattern is random and hence there is no heteroscedasticity

• Normality of dependent variable or error terms

Data is normal (straight line on Q-Q plot shows so)

• No multicollinearlity

Remote hours and Total staff show some pattern

> cor(data$Total_staff,data$Remote_hrs)
[1] 0.3804372 (low)

• No autocorrelation

[4 marks] Conduct an appropriate test of autocorrelation (there are 3 possibilities). Substantiate your choice of test.

you can use dwtest() in R under library(car), mine is throwing errors so couldnt proceed

Please rate my answer and comment for doubt