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
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