Question

The business problem facing the director of broadcasting operations for a television station was the issue of standby hours​ (i.e. hours in which unionized graphic artists at the station are paid but are not actually involved in any​ activity) and what factors were related to standby hours. A study of standby hours was conducted for 26 weeks. The variables in the study are described below and the data from the study are shown in the accompanying table.

Standby_Hours_(Y)   Total_Staff_Present_(X1)   Remote_Hours_(X2)
245   338   414
177   333   598
271   358   656
211   372   631
196   339   528
135   289   409
195   334   382
118   293   399
116   325   343
147   311   338
154   304   353
146   312   289
115   283   388
161   307   402
274   322   151
245   335   228
201   350   271
183   339   440
237   327   475
175   328   347
152   319   449
188   325   336
188   322   267
197   317   235
261   315   164
232   331   270

Construct a​ 95% prediction interval for the standby hours for a single week in which the total staff present have 310​ people-days and the remote hours are 400.

The​ 95% prediction interval for the standby hours is.

Answer 1

Using R

standby = read.table("../Documents/Tutoring/Software/random data/standby_hours.txt",header=T)
model = lm(y~.,data = standby)
summary(model)
predict(model,data.frame(x1= 310,x2 = 400),interval="prediction",level=0.95)

95% prediction interval is (85.2013,236.4916)

Please give me a thumbs-up if this helps you out. Thank you! :)