Question

In: Statistics and Probability

It is rare that you will find a gas station these days that only sells gas....

It is rare that you will find a gas station these days that only sells gas. It has become more common to find a convenient store that also sells gas. The data named “Convenient Shopping data” the sales over time at a franchise outlet of the major US oil company. Each row summarize sales for one day. This particular station sells gas and has a convenient store and car awash. The column labeled Sales gives the dollar sales of the convenient store and the column Volume gives the number of gallons of gas sold.

Sales (Dollars) Volume (Gallons)
1756 2933
2203 3329
1848 3043
2016 3043
2346 3450
2410 3478
2050 3347
2097 3708
2311 3467
2419 4114
2523 3721
2061 3448
2247 3230
3479 3557
2135 3060
2102 3619
2536 3256
1227 1757
1966 2891
2219 3381
2226 2970
1969 3301
2044 3178
2360 3426
1907 3118
2156 3037
1816 3537
1897 3808
2051 3145
2079 3766
2328 2916
1841 3957
2104 3980
1973 3675
2089 3516
2266 4149
2327 3733
2032 3738
2137 4012
2186 4114
2369 3795
2087 3543
2273 3681
2113 3618
2181 4452
2776 4346
2652 4073
2250 4260
2548 4113
2678 3829
2878 4137
2220 4269
2303 3989
2718 4238
2317 3658
2338 4005
2143 3996
2402 4077
2401 3610
2051 3701
2468 3844
2398 3904
2106 3879
2461 3266
2466 3513
2745 4052
1994 4052
2020 2874
2241 3526
2648 3487
2022 3499
2524 3236
1919 2422
2164 2876
2074 2883
2310 2771
2062 2362
1807 2564
1976 2708
2171 2519
1745 2638
2108 3448
2057 1993
1679 2560
2014 2777
2109 3097
2274 2750
2640 3260
1664 2050
1913 2921
2331 2970
1920 2624
2074 3496
2272 3729
1651 2302
1996 2672
2093 3150
1995 2948
2337 3520
2433 3195
1731 2232
2183 2979
1795 3178
1689 2618
2040 3117
2076 2847
1483 2150
930 1528
1674 2309
1934 2805
2011 2721
2172 2812
1612 2173
1780 2767
2116 2544
1937 2805
1866 2131
2099 3292
2082 2221
1788 2816
2004 2686
1868 3207
2038 2925
2596 3603
1700 2165
1815 3338
1917 3107
2143 2906
2420 3448
2486 3433
1812 2104
2463 3283
2222 3750
2324 3494
2219 3154
2505 3465
2047 2216
2231 3236
2067 3425
2293 3667
2152 3618
1366 2257
2210 3606
2029 3460
2742 2336
2161 3113
2223 3058
2186 2429
2306 3501
1933 3183
2485 3337
2817 3566
2491 3398
1896 2519
2382 3716
2552 3856
2094 3488
2447 3457
2440 3831
2041 2280
2261 2411
2114 3208
2866 3539
2752 3719
2502 4150
1786 2927
2157 3044
2025 3390
2327 3840
2502 3697
2552 4104
2017 3749
2019 3511
2302 3972
2419 3413
2921 3882
2273 3950
2183 3292
2428 3979
2489 4668
2037 3832
2324 3930
2591 3853
2362 4014
3001 4759
1801 2661
1744 4165
2428 4139
2409 3664
2819 3851
1897 2522
1536 1208
2475 3844
2484 3766
2117 3535
2488 3900
2553 3900
2251 3814
2435 3387
2446 4009
2063 1951
2582 3779
1663 2368
2302 3379
2248 3549
2712 3807
2307 4009
2576 3759
1978 2378
2116 4090
2292 3241
2373 3874
2444 4142
2578 3645
1953 2419
2151 3289
2901 3872
2514 4136
2078 3626
2492 4240
1897 2415
2072 3028
2538 3731
2422 3851
2415 3818
2969 4268
1775 2514
2082 3708
2121 3367
2471 3685
2467 3415
2671 4226
1876 2061
1976 3805
2156 3427
2339 3670
2258 3939
2776 3798
2084 2668
2346 3945
2320 3787
2539 3854
2393 3598
2629 3717
2044 2536
2018 401
2350 2361
2452 4005
2041 2391
2038 3129
2181 3874
2516 4072
2181 3603
2427 4173
2111 3993
2182 3153
2794 3812

1) Draw a scatter plot for Sales on Volume where Sales is dependent on Volume of gas sold. Does there appear to be a linear pattern that relates to these two sequences?

2) Estimate the linear regression model using excel analysis tool I showed you in class. Write the linear model and interpret the slope (b1).

3) Interpret the R2 and tell if your linear model is a good fit or not.

4) Estimate the difference in sales at the convenient store (on average) between a day with 3,500 gallons sold and a day with 4,000 gallons sold.

5) With regard to inference statistics, formulate a hypothesis test for the slope (b1) and decide if it is statistically significant or not.

6) Construct a 95% confidence interval for the slope.

Solutions

Expert Solution

1)

Yes,it appears be a linear pattern that relates to these two sequences

2)

SUMMARY OUTPUT
Regression Statistics
Multiple R 0.6281
R Square 0.3945
Adjusted R Square 0.3921
Standard Error 249.5369
Observations 257
ANOVA
df SS MS F Significance F
Regression 1 10344773.5398 10344773.5398 166.1313 0.0000
Residual 255 15878506.9193 62268.6546
Total 256 26223280.4591
Coefficients Standard Error t Stat P-value Lower 95% Upper 95%
Intercept 1180.0870 81.6478 14.4534 0.0000 1019.2972 1340.8768
Volume (Gallons) 0.3095 0.0240 12.8892 0.0000 0.2622 0.3568

y^ = 1180.087 + 0.3095 x

slope - when volume increase by 1 gallons, on average sales increase 0.3095 dollars

3)

R^2 = 0.3945

which means 39.45% of variation is explained by this model

4)

difference = 0.3095 * 500 = 154.75

5)

p-value for b1 = 0.0000

p-value < alpha

hence we reject the null hypothesis

it is statistically significant

6) 95% confidence interval for slope

(0.2622 , 0.3568)

0.2622 0.3568

Please rate

orchestra answered 2 years ago
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