Question

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.

c. The difference in category sales between two stores is 150. What is the

    predicted differnece of the cracker sales between these stores?

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

Answer 1

I have fitted the regression in R. Please ask if you have any doubts. I have saved the data in data2.csv and then read it through the command. data2.csv has to be in same working directory.

data2<- read.csv("data2.csv")
model1<- lm(Sales ~ CategorySales, data = data2)
summary(model1)

# Call:
# lm(formula = Sales ~ CategorySales, data = data2)
#
# Residuals:
# Min 1Q Median 3Q Max
# -47.199 -11.521 1.099 12.283 43.168
#
# Coefficients:
# Estimate Std. Error t value Pr(>|t|)
# (Intercept) 205.70638 24.84049 8.281 5.00e-13 ***
# CategorySales 0.12534 0.02054 6.101 1.91e-08 ***
# ---
# Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#
# Residual standard error: 20.27 on 102 degrees of freedom
# Multiple R-squared: 0.2674,   Adjusted R-squared: 0.2602
# F-statistic: 37.22 on 1 and 102 DF, p-value: 1.914e-08

Since the coefficient of the CategorySales is 0.12534. If there is 150 difference in CategorySales, there will be 150*0.12534 change in the predicted value of Sales since we have fit linear regression.

Hence difference in predicted value of Sales is 18.801

Please ask in the comments below if you have any doubts. Thumbs up if you like.