The business problem facing the director of broadcasting operations for a televi

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. Complete parts a through g below.

Standby Remote Total Staff Hours (Y)Present (X1 Hours (X2 338 414 596 656 631 528 399 382 399 343 338 353 289 388 402 151 228 271 440 475 347 449 336 267 235 164 270 245 270 211 196 135 195 118 116 147 154 146 115 161 274 245 201 183 237 175 152 188 188 197 261 232 358 372 341 289 334 293 325 311 304 312 283 307 322 335 350 339 327 328 319 325 322 317 315 331

Explanation / Answer

We use minitab to solve your question,

Regression Analysis: y versus x1, x2

Analysis of Variance

Source DF Adj SS Adj MS F-Value P-Value
Regression 2 27659 13830 11.11 0.000
x1 1 27164 27164 21.81 0.000
x2 1 7177 7177 5.76 0.025
Error 23 28643 1245
Total 25 56302

Model Summary

S R-sq R-sq(adj) R-sq(pred)
35.2892 49.13% 44.70% 32.04%

Coefficients

Term Coef SE Coef T-Value P-Value VIF
Constant -331 116 -2.85 0.009
x1 1.767 0.378 4.67 0.000 1.18
x2 -0.1416 0.0590 -2.40 0.025 1.18

Regression Equation

y = -331 + 1.767 x1 - 0.1416 x2

Prediction for y

Regression Equation

y = -331 + 1.767 x1 - 0.1416 x2

Variable Setting
x1 310
x2 400

Fit SE Fit 95% CI 95% PI
160.509 9.23248 (141.410, 179.608) (85.0505, 235.967)

___________________________________________________________________________________________

a)
Yi^ = -330.7 + 1.8 *X1i -0.1 *X2i
b)
For a given number of remote hours, each each increase of one unit of total staff present is estimated to result in a mean increase in a stand by hours of b1 units.for a given number of total staff present, each increase of one unit in remote hours is estimated to result in a mean decreases in a standby hours of the absolute value of b2 units.
c)
regression coefficient bo has no pratical meaning in the context of this problem because,
it estimate the standby hours when there are no staff present and no remote hours.
d)
Yi^ = -330.7 + 1.8 *X1i -0.1 *X2i
At x1 = 310, x2 = 400
Yi^ = -330.7 + 1.8 * 310 -0.1 * 400
Yi^ = 273.781
There would be 273.78 standby hours predicted for the week.
e)
95% confidence interval estimate for the mean stand by hours At x1 = 310, x2 = 400
141.41 < My|x < 179.61
f)
95% prediction interval estimate for the mean stand by hours At x1 = 310, x2 = 400
85.05 < My|x < 235.97
g)
The model uses both the number of staff present and the remote hours to predict the number of stand by hours.This produces a better model than if only one variable were included.

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