Question

In: Statistics and Probability

For the data​ below, the regression model Yi=−401.3488+1.9721X1i−0.0993X2i uses total staff present and remote hours to...

For the data​ below, the regression model Yi=−401.3488+1.9721X1i−0.0993X2i uses total staff present and remote hours to predict standby hours. Develop a regression model to predict standby hours that includes total staff​ present, remote​ hours, and the interaction of total staff present and remote hours.

Standby

Total Staff

Remote

287

312

381

271

358

656

188

325

336

188

322

267

197

317

235

261

315

164

118

293

399

116

325

343

147

311

338

177

333

598

A. At the 0.10 level of​ significance, is there evidence that the interaction term makes a significant contribution to the​ model?

B. Which regression model is more​ appropriate, the model with the interaction term used in​ (a) or the original​model?

Solutions

Expert Solution

A)

SUMMARY OUTPUT
Regression Statistics
Multiple R 0.600807
R Square 0.360969
Adjusted R Square 0.041453
Standard Error 59.72854
Observations 10
ANOVA
df SS MS F Significance F
Regression 3 12091.01 4030.336 1.129737 0.409191
Residual 6 21404.99 3567.498
Total 9 33496
Coefficients Standard Error t Stat P-value Lower 95% Upper 95%
Intercept 2133.193 2069.986 1.030535 0.342498 -2931.88 7198.267
TOTAL STAFF -5.86834 6.42947 -0.91273 0.396579 -21.6007 9.864004
REMOTE -5.22811 4.094418 -1.27689 0.24883 -15.2468 4.790574
INTERACTION 0.015645 0.012479 1.253656 0.256601 -0.01489 0.046181

FROM ABOVE TABLE ,

P VALUE FOR INTERACTION COEFFICIENT = 0.2566

P VALUE > 0.1 , NOT SIGNIFICANT

there IS NOT SUFFICIENT evidence that the interaction term makes a significant contribution to the​ model

................

B)

SUMMARY OUTPUT
Regression Statistics
Multiple R 0.439977
R Square 0.193579
Adjusted R Square -0.03683
Standard Error 62.11955
Observations 10
ANOVA
df SS MS F Significance F
Regression 2 6484.134 3242.067 0.840167 0.47094
Residual 7 27011.87 3858.838
Total 9 33496
Coefficients Standard Error t Stat P-value Lower 95% Upper 95%
Intercept -401.349 462.1929 -0.86836 0.413976 -1494.26 691.5638
TOTAL STAFF 1.972145 1.551138 1.271418 0.244193 -1.69571 5.640003
REMOTE -0.09929 0.171813 -0.57791 0.581431 -0.50556 0.30698

MODAL WITH INTERACTION TERM IS MORE USEFUL AS MULTIPLE R AN R SQUARE ARE GOOD IN INTERACTION MODAL

..................

Please let me know in case of any doubt.

Thanks in advance!


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orchestra answered 2 years ago
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