0 Data for Sales Over Time The accompanying data describe sales over time at a franchise outlet of a major U.S. oil company. Each row summarizes sales for one day. This particular stati dollar sales of the convenience store. The explanatory variable Volume gives the number of gallons of gasoline sold, and Washes gives the number of car wash E Click the icon to view the table of data for sales over time. Full data set e Sales Volume Washes Sales Volume Washes B. Car washes because the slope for Washes is larger than the slope for Volume and the daily number of car washes is more than the volume of gallons se c. Gasoline sales because the slope for Volume is larger than the slope for Washes and the daily volume of gallons sold is more than the number of car wa D. Car washes because one car wash costs more than a tank of gas. (Dollars) (Gallons) 3478 3721 3619 2970 3808 3675 3516 3795 (Dollars) (Gallons) 2184 3283 2258 3606 3501 2234 127 95 148 2210 2286 149 222 118 2261 2112 2306 2274 2237 2304 2411 2271 2314 2363 1986 2051 2113 2154 306 294 106 62 2285 1982 2236 2187 2354 2271 2327 1876 2306 2321 2289 2204 1971 2258 2019 2357 2145 3716 2411 3511 3292 271 193 92 256 Do the slopes of these variables in the multiple regression provide the full answer? O A. The slopes do not provide any part of the answer. The answer depends on the p-value corresponding to each explanatory variable. 358 324 279 4014 260 4260 3658 3844 3664 99 OB. The slopes provide the full answer. The larger the (positive) slope, the more that variable contributes to the model. OC. The slopes only provide part of the answer. The volume of gallons of gasoline and the number of car washes per day is also important. 165 169 246 251 316 302 182 3900 177 1952 3807 3872 3731 3367 4052 403 307 168 327 (c) Find the variance inflation factor. 2422 2709 2970 3150 3178 2767 2816 3338 VIF(Volume) = VIF(Washes) = (Round to two decimal places as needed.) 278 2361 Interpret the variance inflation factor. Choose the correct answer below. 2160 2065 2076 2196 271 211 181 3603 2567 4028 3115 240 319 324 185 O A. Collinearity has a significant effect on the standard errors. 38 OB. The two variables Volume and Washes are perfectly collinear. One of the variables should be dropped from the model (the one with the lower p-value). c. Collinearity has litle effect on the standard errors. OD. Collinearity has no effect on the standard errors. Print Done (d) One of the explanatory variables is just barely statistically significant. Assuming the same estimated value, would a complete lack of collinearity have made this explanatory variable noticeably more statistically significant?

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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- X
Data for Sales Over Time
The accompanying data describe sales over time
dollar sales of the convenience store. The explanatory variable Volume gives the number of gallons of gasoline sold, and Washes gives the number of car wash
a franchise outlet of a major U.S. oil company. Each row summarizes sales for one day. This particular static
je
Click the icon to view the table of data for sales over time.
Full data set A
Sales
Volume Washes
Sales
Volume Washes
B. Car washes because the slope for Washes is larger than the slope for Volume and the daily number of car washes is more than the volume of gallons sc
(Dollars) (Gallons)
2210
2286
(Dollars) (Gallons)
3478
149
2184
3283
127
O C. Gasoline sales because the slope for Volume is larger than the slope for Washes and the daily volume of gallons sold is more than the number of car wa
3721
222
2258
3606
95
O D. Car washes because one car wash costs more than a tank of gas.
2261
3619
118
2234
3501
148
2112
2970
306
2285
3716
271
Do the slopes of these variables in the multiple regression provide the full answer?
2306
3808
294
1982
2411
193
2274
3675
106
2236
3511
92
3292
4014
2237
3516
62
2187
O A. The slopes do not provide any part of the answer. The answer depends on the p-value corresponding to each explanatory variable.
256
260
2304
3795
358
2354
O B. The slopes provide the full answer. The larger the (positive) slope, the more that variable contributes to the model.
2411
4260
324
2271
3664
99
2327
1876
2271
3658
279
3900
165
O C. The slopes only provide part of the answer. The volume of gallons of gasoline and the number of car washes per day is also important.
2314
2363
1986
2051
3844
177
1952
169
4052
403
2306
3807
246
(c) Find the variance inflation factor.
2422
2709
251
316
307
2321
3872
3731
3367
168
2289
VIF(Volume) = VIF(Washes) = (Round to two decimal places as needed.)
2113
2154
2160
2065
2076
327
278
2204
1971
2258
2019
302
182
2970
3150
2361
Interpret the variance inflation factor. Choose the correct answer below.
3178
2767
3603
2567
4028
240
319
271
211
181
2357
2145
2816
324
A. Collinearity has a significant effect on the standard errors.
2196
3338
38
3115
185
O B. The two variables Volume and Washes are perfectly collinear. One of the variables should be dropped from the model (the one with the lower p-value).
OC. Collinearity has little effect on the standard errors.
Print
Done
O D. Collinearity has no effect on the standard errors.
(d) One of the explanatory variables is just barely statistically significant. Assuming the same estimated value, would a complete lack of collinearity have made this explanatory variable noticeably more statistically significant?
O A. No, collinearity does not effect the p-values for explanatory variables.
O B. Yes, because the variance inflation factor is not 1.
O C. Yes, because collinearity has a significant impact on the standard errors of the explanatory variables in this problem.
O D. No, there is almost no collinearity.
Transcribed Image Text:- X Data for Sales Over Time The accompanying data describe sales over time dollar sales of the convenience store. The explanatory variable Volume gives the number of gallons of gasoline sold, and Washes gives the number of car wash a franchise outlet of a major U.S. oil company. Each row summarizes sales for one day. This particular static je Click the icon to view the table of data for sales over time. Full data set A Sales Volume Washes Sales Volume Washes B. Car washes because the slope for Washes is larger than the slope for Volume and the daily number of car washes is more than the volume of gallons sc (Dollars) (Gallons) 2210 2286 (Dollars) (Gallons) 3478 149 2184 3283 127 O C. Gasoline sales because the slope for Volume is larger than the slope for Washes and the daily volume of gallons sold is more than the number of car wa 3721 222 2258 3606 95 O D. Car washes because one car wash costs more than a tank of gas. 2261 3619 118 2234 3501 148 2112 2970 306 2285 3716 271 Do the slopes of these variables in the multiple regression provide the full answer? 2306 3808 294 1982 2411 193 2274 3675 106 2236 3511 92 3292 4014 2237 3516 62 2187 O A. The slopes do not provide any part of the answer. The answer depends on the p-value corresponding to each explanatory variable. 256 260 2304 3795 358 2354 O B. The slopes provide the full answer. The larger the (positive) slope, the more that variable contributes to the model. 2411 4260 324 2271 3664 99 2327 1876 2271 3658 279 3900 165 O C. The slopes only provide part of the answer. The volume of gallons of gasoline and the number of car washes per day is also important. 2314 2363 1986 2051 3844 177 1952 169 4052 403 2306 3807 246 (c) Find the variance inflation factor. 2422 2709 251 316 307 2321 3872 3731 3367 168 2289 VIF(Volume) = VIF(Washes) = (Round to two decimal places as needed.) 2113 2154 2160 2065 2076 327 278 2204 1971 2258 2019 302 182 2970 3150 2361 Interpret the variance inflation factor. Choose the correct answer below. 3178 2767 3603 2567 4028 240 319 271 211 181 2357 2145 2816 324 A. Collinearity has a significant effect on the standard errors. 2196 3338 38 3115 185 O B. The two variables Volume and Washes are perfectly collinear. One of the variables should be dropped from the model (the one with the lower p-value). OC. Collinearity has little effect on the standard errors. Print Done O D. Collinearity has no effect on the standard errors. (d) One of the explanatory variables is just barely statistically significant. Assuming the same estimated value, would a complete lack of collinearity have made this explanatory variable noticeably more statistically significant? O A. No, collinearity does not effect the p-values for explanatory variables. O B. Yes, because the variance inflation factor is not 1. O C. Yes, because collinearity has a significant impact on the standard errors of the explanatory variables in this problem. O D. No, there is almost no collinearity.
The accompanying data describe sales over time at a franchise outlet of a major U.S. oil company. Each row summarizes sales for one day. This particular station sells gas, and it also has a convenience store and a car wash. The response Sales gives the
dollar sales of the convenience store. The explanatory variable Volume gives the number of gallons of gasoline sold, and Washes gives the number of car washes sold at the station. Complete parts a through d below.
Click the icon to view the table of data for sales over time.
Data for Sales Over Time
(a) Fit the multiple regression of Sales on Volume and Washes. Do both explanatory variables improve the fit of the model? Use a = 0.05.
O A. Both explanatory variables improve the fit
the model, though the variable Volume just barely improves the model.
O B. Both explanatory variables improve the fit of the model, though the variable Washes just barely improves the model.
Full data set O
Sales
Volume Washes
Sales
Volume
Washes
O C. Only the variable Washes improves the fit of the model, though just barely.
(Dollars) (Gallons)
2210
2286
2261
(Dollars) (Gallons)
2184
2258
2234
2285
149
222
O D. Only the variable Volume improves the fit of the model, though just barely.
3478
3283
127
3721
3606
95
(b) Which explanatory variable is more important to the success of sales at the convenience store: gasoline sales or car washes?
3619
118
3501
148
2112
2970
306
3716
271
2306
2274
3808
294
1982
2411
193
O A. Gasoline sales because more gallons of gasoline are sold each day than the number of car washes.
3675
106
2236
3511
92
Car washes because the slope for Washes is larger than
slope for Volume and the daily number of car washes is more than the volume of gallons
2237
3516
62
2187
3292
256
2304
3795
358
2354
4014
260
O C. Gasoline sales because the slope for Volume is larger than the slope for Washes and the daily volume of gallons sold is more than the number of car washes.
2411
2271
4260
324
2271
3664
99
3658
279
2327
3900
165
O D. Car washes because one car wash costs more than a tank of gas.
2314
3844
177
1876
1952
169
4052
2363
1986
2051
2113
2154
2160
2065
403
2306
3807
246
Do the slopes of these variables in the multiple regression provide the full answer?
2422
307
2321
3872
251
2709
168
2289
3731
316
O A. The slopes do not provide any part of the answer. The answer depends on the p-value corresponding to each explanatory variable.
2970
327
2204
3367
302
3150
278
1971
2361
182
O B. The slopes provide the full answer. The larger the (positive) slope, the more that variable contributes to the model.
3178
271
2258
3603
240
OC. The slopes only provide part of the answer. The volume of gallons of gasoline and the number of car washes per day is also important.
2767
211
2019
2567
319
2076
2816
181
2357
4028
324
(c) Find the variance inflation factor.
2196
3338
38
2145
3115
185
VIF(Volume) = VIF(Washes) = (Round to two decimal places as needed.)
Print
Done
Interpret the variance inflation factor. Choose the correct answer below.
O A. Collinearity has a significant effect on the standard errors.
O B. The two variables Volume and Washes are perfectly collinear. One of the variables should be dropped from the model (the one with the lower p-value).
Transcribed Image Text:The accompanying data describe sales over time at a franchise outlet of a major U.S. oil company. Each row summarizes sales for one day. This particular station sells gas, and it also has a convenience store and a car wash. The response Sales gives the dollar sales of the convenience store. The explanatory variable Volume gives the number of gallons of gasoline sold, and Washes gives the number of car washes sold at the station. Complete parts a through d below. Click the icon to view the table of data for sales over time. Data for Sales Over Time (a) Fit the multiple regression of Sales on Volume and Washes. Do both explanatory variables improve the fit of the model? Use a = 0.05. O A. Both explanatory variables improve the fit the model, though the variable Volume just barely improves the model. O B. Both explanatory variables improve the fit of the model, though the variable Washes just barely improves the model. Full data set O Sales Volume Washes Sales Volume Washes O C. Only the variable Washes improves the fit of the model, though just barely. (Dollars) (Gallons) 2210 2286 2261 (Dollars) (Gallons) 2184 2258 2234 2285 149 222 O D. Only the variable Volume improves the fit of the model, though just barely. 3478 3283 127 3721 3606 95 (b) Which explanatory variable is more important to the success of sales at the convenience store: gasoline sales or car washes? 3619 118 3501 148 2112 2970 306 3716 271 2306 2274 3808 294 1982 2411 193 O A. Gasoline sales because more gallons of gasoline are sold each day than the number of car washes. 3675 106 2236 3511 92 Car washes because the slope for Washes is larger than slope for Volume and the daily number of car washes is more than the volume of gallons 2237 3516 62 2187 3292 256 2304 3795 358 2354 4014 260 O C. Gasoline sales because the slope for Volume is larger than the slope for Washes and the daily volume of gallons sold is more than the number of car washes. 2411 2271 4260 324 2271 3664 99 3658 279 2327 3900 165 O D. Car washes because one car wash costs more than a tank of gas. 2314 3844 177 1876 1952 169 4052 2363 1986 2051 2113 2154 2160 2065 403 2306 3807 246 Do the slopes of these variables in the multiple regression provide the full answer? 2422 307 2321 3872 251 2709 168 2289 3731 316 O A. The slopes do not provide any part of the answer. The answer depends on the p-value corresponding to each explanatory variable. 2970 327 2204 3367 302 3150 278 1971 2361 182 O B. The slopes provide the full answer. The larger the (positive) slope, the more that variable contributes to the model. 3178 271 2258 3603 240 OC. The slopes only provide part of the answer. The volume of gallons of gasoline and the number of car washes per day is also important. 2767 211 2019 2567 319 2076 2816 181 2357 4028 324 (c) Find the variance inflation factor. 2196 3338 38 2145 3115 185 VIF(Volume) = VIF(Washes) = (Round to two decimal places as needed.) Print Done Interpret the variance inflation factor. Choose the correct answer below. O A. Collinearity has a significant effect on the standard errors. O B. The two variables Volume and Washes are perfectly collinear. One of the variables should be dropped from the model (the one with the lower p-value).
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