Problem 4 (14 total points)

In this problem you will work with quarterly sales data of work T-shirts from a sample of 100 stores belonging to a large Retailer. The data is contained in problem4.xlsx, the first column is simply a store-id (STOREID), second column contains the quarterly sales in number of T-shirts sold (SALES), the third column gives you the quarter to which these sales belong (QUARTER) and finally the fourth column tells you whether the T-shirts were on promotion or not (PROM) [PROM = 1 implying that the T-shirts were on promotion].

(a) You need to run a regression with SALES as your dependent variable and QUARTER & PROM as your independent variables. Note that QUARTER is a categorical variable so you need to introduce appropriate dummy variables to represent it, choose the 4rth quarter as your reference when you introduce dummy variables. That is, estimate the following regression model

SALES = b₀ + b₁QTR1 + b₂QTR2 + b₃QTR3 + b₄PROM

where QTR1, QTR2, QTR3 are dummy variables for the first, second and third quarters respectively.

Report and interpret the estimated coefficient on QTR1

(b) Based on the estimated regression model in part (a) what is your estimate of the second quarter sales with and without promotions?

(c) What is the impact of promotions on sales?

STOREID SALES QUARTER PROM 2683 143 3 0 2069 62 3 0 2465 249 2 0 2288 161 1 0 2383 40 1 0 1794 281 1 1 1921 258 3 1 2374 415 4 1 2130 113 3 0 1730 226 2 0 2149 124 2 0 1820 225 1 1 1864 145 1 0 2374 466 2 0 2796 192 2 0 2279 85 2 0 2284 140 2 0 2412 59 1 0 2258 89 1 0 1810 170 1 0 2557 138 2 0 2056 87 1 0 2212 223 4 0 2043 95 1 0 1758 177 2 0 1924 565 2 1 1730 165 4 0 1921 298 4 0 2806 269 2 0 1750 259 1 1 2235 114 2 0 2143 124 2 0 2143 137 4 0 1780 176 1 0 1764 259 1 1 2225 56 1 0 2829 223 1 1 2026 98 1 0 2684 366 4 1 2231 206 2 0 2026 122 4 0 2235 73 1 0 2326 91 1 0 2635 101 3 0 2465 134 3 0 2644 286 2 0 1780 347 4 0 1863 142 3 0 2035 127 2 0 1863 116 1 0 2764 225 2 0 2048 85 3 0 2283 116 1 0 2052 83 4 0 2385 57 1 0 2808 95 4 0 1722 212 4 0 2048 129 2 0 1718 78 1 0 2714 99 3 0 1864 182 2 0 2056 98 2 0 1760 251 2 0 2664 395 4 1 2415 95 3 0 1998 163 4 0 2855 135 1 0 2829 137 3 0 2309 92 1 0 2480 65 4 0 2677 48 4 0 2764 106 1 0 2114 329 4 0 2020 81 4 0 1750 401 3 0 1758 164 1 0 2069 109 2 0 2077 163 2 0 2231 127 1 0 2064 435 4 1 1998 189 3 0 2283 210 3 1 2104 225 2 0 2064 243 3 0 1730 130 1 0 2473 142 4 0 2335 54 1 0 2415 185 4 0 2674 146 4 0 2331 116 3 0 1764 508 3 0 1760 235 4 1 2674 127 2 0 2825 74 1 0 2077 80 1 0 2305 233 2 0 2029 121 1 0 2764 197 4 0 2383 97 4 0 2453 184 2 0 2902 116 4 0 1750 429 2 1 1718 173 3 1 2077 70 3 0 2114 207 2 0 1750 424 4 1 1850 141 2 0 1824 433 2 1 2283 336 2 1 1924 408 4 1 1722 156 1 0 2279 92 4 0 2309 192 4 0 1780 272 2 0 1794 932 2 1 2043 87 3 0 2043 185 4 0 2855 168 4 0 2226 57 3 0 2684 143 1 0 2533 30 1 0 1998 233 2 0 1760 133 1 0 2684 148 3 0 1722 171 3 0 1824 323 3 1 2664 235 3 0 2694 317 2 1 2683 188 4 0 1773 187 2 0 2104 107 1 0 2196 94 2 0 2315 97 1 0 2683 98 1 0 2385 140 4 0 2714 71 1 0 1850 125 4 0 2825 174 4 0 2035 160 4 0 2374 372 3 1 2854 312 2 0 2677 73 3 0 2624 238 3 1 2130 144 4 0 2383 78 2 0 2829 221 2 0 2674 71 1 0 2760 114 3 0 2453 178 3 1 2820 163 2 0 2335 179 2 0 2331 149 4 0 2226 169 2 0 2279 124 3 0 2714 174 4 0 1820 360 2 1 2557 92 4 0 2412 104 4 0 1764 660 2 1 2644 295 4 0 2390 101 3 0 2052 45 1 0 2854 146 1 0 2760 90 1 0 1985 104 2 0 2284 146 4 0 2806 209 4 0 2624 324 4 0 1864 145 3 0 2933 301 1 1 2241 58 3 0 2677 40 1 0 2624 340 2 0 2389 236 2 0 2933 416 4 1 2335 120 3 0 2241 96 2 0 2335 134 4 0 2412 148 2 0 2677 125 2 0 2473 63 1 0 2382 117 4 0 2374 188 1 0 2654 373 2 1 1758 154 3 0 1794 802 3 1 2805 220 4 0 1985 166 4 0 2112 86 1 0 2664 363 2 1 2326 91 4 0 2104 236 4 0 2225 83 3 0 1978 247 4 0 2654 343 4 0 1921 141 1 0 2241 53 1 0 2683 212 2 0 2048 76 1 0 1773 72 1 0 2644 128 1 0 2279 59 1 0 2241 104 4 0 2064 385 2 0 2557 90 1 0 2130 145 2 0 2331 85 1 0 2212 204 2 0 2305 88 1 0 2331 191 2 0 2050 306 2 1 2808 114 2 0 2933 656 2 0 2284 110 3 0 2392 147 3 0 2415 145 2 0 2415 102 1 0 2043 168 2 0 1978 399 2 1 1978 337 3 0 1730 214 3 0 2796 214 4 0 2674 103 3 0 2149 151 3 0 1810 272 3 1 1824 186 1 0 2760 123 4 0 2465 143 1 0 1810 337 4 0 2288 199 3 0 2412 156 3 0 2035 73 1 0 2149 94 4 0 2026 128 3 0 1773 216 4 0 2064 184 1 0 1794 562 4 1 2052 96 2 0 2290 227 2 0 1894 339 2 0 2806 196 3 0 2840 75 1 0 2315 137 2 0 2385 90 3 0 2288 115 4 0 2806 138 1 0 2465 145 4 0 2114 101 1 0 2143 88 3 0 2226 107 4 0 2226 52 1 0 1760 211 3 0 2389 231 4 0 2820 141 3 0 2808 50 1 0 2533 74 3 0 2664 131 1 0 2796 151 3 0 2829 199 4 0 2283 217 4 0 2149 69 1 0 2315 107 3 0 2290 148 4 0 2326 82 3 0 2840 130 3 0 1924 284 1 1 2258 100 2 0 2820 66 1 0 2258 79 3 0 2390 283 4 0 1978 189 1 0 2694 175 3 0 2029 234 4 0 2382 84 1 0 1894 145 1 0 1998 161 1 0 1924 542 3 1 2533 90 2 0 2694 333 4 0 2112 204 4 0 1718 152 2 0 2902 194 2 0 2143 35 1 0 2533 148 4 0 2020 66 1 0 2635 163 2 0 1921 285 2 0 2624 152 1 0 2225 118 4 0 2933 452 3 1 2284 42 1 0 2290 110 3 0 2048 93 4 0 2288 238 2 0 2453 134 4 0 1863 275 4 0 2212 103 1 0 2069 74 4 0 1820 310 4 0 2840 128 2 0 2114 156 3 0 2050 295 4 0 2392 98 1 0 2383 59 3 0 2840 159 4 0 2069 36 1 0 2805 162 3 0 1722 198 2 0 2389 182 3 1 2392 180 4 0 2694 142 1 0 2020 38 3 0 2020 128 2 0 2480 124 2 0 2480 50 1 0 2235 170 4 0 2796 116 1 0 1985 64 1 0 2644 189 3 1 2231 107 4 0 2473 79 3 0 2902 96 3 0 2902 99 1 0 2309 253 2 0 2453 72 1 0 2196 65 3 0 2112 186 3 0 2473 95 2 0 2056 132 4 0 1758 195 4 0 2035 109 3 0 2854 262 4 0 2760 146 2 0 2480 68 3 0 2196 69 4 0 2684 280 2 0 2805 234 2 0 2029 220 2 0 2557 102 3 0 2855 157 3 0 1850 89 1 0 2385 135 2 0 2628 120 4 0 2714 103 2 0 2305 143 3 0 1850 119 3 0 2231 149 3 0 2290 76 1 0 2628 142 3 0 2805 139 1 0 1820 275 3 1 1824 447 4 1 2050 144 1 0 2258 100 4 0 2382 159 2 0 2050 202 3 0 2326 155 2 0 2104 168 3 1 2808 71 3 0 1718 128 4 0 2855 132 2 0 2130 79 1 0 2392 176 2 0 2635 49 1 0 2305 213 4 0 2390 227 2 0 1894 277 3 0 2052 83 3 0 2628 69 1 0 2029 201 3 1 2820 172 4 0 2309 229 3 1 2628 98 2 0 2315 137 4 0 1863 250 2 0 2077 123 4 0 2225 120 2 0 2825 198 2 0 2235 119 3 0 2112 209 2 0 2635 183 4 0 2390 78 1 0 2382 104 3 0 2654 243 3 0 1764 590 4 1 1780 281 3 1 1894 237 4 0 1864 169 4 0 2056 92 3 0 2212 188 3 0 2026 145 2 0 2654 180 1 0 2196 70 1 0 1985 77 3 0 1810 369 2 0 2825 95 3 0 1773 129 3 0 2854 148 3 0 2764 289 3 1 2389 124 1 0