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A supermarket chain analyzed data on sales of a particular brand of snack cracker at 104...

A supermarket chain analyzed data on sales of a particular brand of snack cracker

at 104 stores for a certain one week period. The analyst decided to build a regresion model to predict the sales of the snack cracker based on the total sales of all brands in the snack cracker category.

f. Produce a 90% confidence prediction interval for the sales of the cracker

   in a store where the category sales is 1005. Also produce the90 %

   confidence prediction interval in a store where category sales is 900.

  Can you with 90% confidence claim which store has higher cracker sales?

CategorySales Sales
1348 394
1110 388
1096 357
1208 385
1063 346
1097 326
1277 358
1275 359
1328 360
1281 374
1127 362
1339 406
1055 354
1263 368
1158 391
1286 370
1401 372
1085 381
1178 371
1248 353
1241 372
1320 375
1353 369
1173 353
1208 364
1280 371
1214 391
1213 381
1291 371
1230 335
1095 338
1149 320
1305 370
1134 351
1127 328
1053 295
1107 318
1054 296
1141 327
1190 313
1071 346
1147 361
1127 350
1204 367
1301 411
1184 390
1214 367
1132 341
1213 380
1173 347
1226 365
1261 352
1118 341
1096 321
1211 329
1033 336
1228 361
1241 386
1381 408
1332 359
1253 375
1043 330
1456 341
1099 340
1044 336
1230 341
1143 371
1238 378
1357 371
1150 378
1218 386
1215 357
1238 376
1196 349
1193 364
1282 361
1317 365
1157 346
1294 356
1198 343
1436 358
1278 368
1124 312
1116 315
1109 338
1285 327
1189 309
1197 330
1091 345
1251 344
1124 355
1130 346
1067 328
1150 352
1238 375
1409 370
1264 377
1151 340
1206 350
1297 375
1164 364
1108 370
1187 365
1459 396

Solutions

Expert Solution

I used Excel for fitting regression line.

Output:

CategorySales (x) Sales (x- xbar)^2
1348 394 20380.418
1110 388 9070.6576 SUMMARY OUTPUT
1096 357 11933.378
1208 385 7.6176 Regression Statistics
1063 346 20232.218 Multiple R 0.517059
1097 326 11715.898 R Square 0.26735
1277 358 5149.4976 Adjusted R Square 0.260167
1275 359 4866.4576 Standard Error 20.27043
1328 360 15070.018 Observations 104
1281 374 5739.5776
1127 362 6121.4976 ANOVA
1339 406 17891.738 df SS MS F Significance F
1055 354 22572.058 Regression 1 15293.63 15293.63 37.2207 1.91E-08
1263 368 3336.2176 Residual 102 41910.83 410.8905
1158 391 2231.6176 Total 103 57204.46
1286 370 6522.1776
1401 372 38321.978 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%
1085 381 14457.658 Intercept 205.7064 24.84049 8.281091 5E-13 156.4354 254.9774 156.4354 254.9774
1178 371 742.0176 X Variable 1 0.125338 0.020544 6.100877 1.91E-08 0.084589 0.166088 0.084589 0.166088
1248 353 1828.4176
1241 372 1278.7776
1320 375 13169.858 x bar = 1205.24
1353 369 21833.018 sxx 973515
1173 353 1039.4176
1208 364 7.6176

milcah answered 2 years ago
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