PROJECT REPORT INTRODUCTION TO STATISTICS

Project description
Calculate the pair-wise correlation coefficients between sales per square meter and
each of the other variables and test their statistical significance. Produce scatter
plots for each pair of variables. Provide a written interpretation for each of the
correlation coefficients and the related scatter plots
INTRODUCTION TO STATISTICS – (L1025)
PROJECT REPORT
The report should be 2,000 words in length and must be word-processed. Projects that exceed this word limit will be penalised.
The exercise should be treated as an exercise in report writing, not just a statistical exercise. You should pay a good deal of attention to structure and to ensuring that the main results from the exercise are clearly reported. A report that neglects the issues and just goes through statistical techniques in a mechanical manner will be penalised. You therefore need to think clearly about the issues that you are examining and layout your hypotheses and findings carefully.
Please note that you have to include in your report graphs and tables (they do not count for number of words). You have to clearly present tables and graphs, with appropriate labels and full explanations. Tables and Graphs should be numbered with self-explanatory headings. Rows and columns and graph axes must be labelled.
Marks will be lost for poor spelling and grammar, and for poorly presented work.
Collaboration and group work are NOT permitted on this project!
Deadline for Submission
4:00pm Thursday 9th April
There are penalties for late submission, which are set out in the Handbook for Candidates.
2
The dataset available on Study Direct contains annual sales data and other characteristics of 400 Dutch fashion stores in 1990. The following variables appear in the data set:
Variable
Description
sales
Sales per square metre
nfull
Number of full-timers
npart
Number of part-timers
hoursw
Total number of hours worked
ssize
Sales floor space of the store (in square metres)
1) Calculate the pair-wise correlation coefficients between sales per square meter and each of the other variables and test their statistical significance. Produce scatter plots for each pair of variables. Provide a written interpretation for each of the correlation coefficients and the related scatter plots.
[30 marks]
2) Write down an equation representing a linear regression model in which sales per square metre depend on a constant, the total number of hours worked and floor space of the store (in square metres). Estimate the equation, report the results, and comment on the overall goodness of the model.
[20 marks]
3) Interpret the estimated coefficients from an economic perspective and comment on their statistical significance.
[25 marks]
4) Does the inclusion of the number of full-timers and part-timers significantly improve the model?
[25 marks]

tsales sales nfull npart hoursw ssize
750000 4411.765 1 1 76 170
1926395 4280.878 2 3 192 450
1250000 4166.667 2 2.2222 114 300
694227 2670.104 1 1.2833 100 260
750000 15000 1.9556 1.2833 104 50
400000 4444.444 1.9556 1.2833 72 90
1300000 3250 1 3 161 400
495340 4953.4 1.9556 1.2833 80 100
1200000 2666.667 3 2.2222 158 450
495340 6604.533 1.9556 1.2833 87 75
911315 7594.292 1 1 156 120
231000 5775 1.9556 1 40 40
492033 5467.033 2.2656 1 96 90
1500000 13636.36 5 1 305 110
330000 8250 2.2656 2.0741 92 40
870000 4350 1 1.2833 80 200
694227 7713.633 1.9556 1 124 90
245228 3503.257 1.9556 1.2833 69 70
375000 3947.368 1.9556 1.2833 60 95
330000 4714.286 1.9556 1.2833 65 70
301133 2409.064 1.9556 1.2833 86 125
976817 5745.982 2 1.5946 116 170
1500000 6000 5 3 270 250
77369 1289.483 1.9556 1.2833 40 60
471000 4957.895 1.9556 1.2833 99 95
601000 3756.25 2 2.0741 124 160
976817 7235.682 1 1.2833 120 135
850000 15454.55 1.9556 1.2833 136 55
495340 4503.091 2.2656 2.0741 95 110
694227 5785.225 4.359 2 84 120
156168 3470.4 1.9556 1.2833 50 45
495340 4953.4 1.9231 1.5946 86 100
1000000 7142.857 3 1 190 140
694227 6311.155 1.9556 1.2833 80 110
976817 6302.045 1 2.0741 128 155
156168 3123.36 1.9556 1 48 50
400000 1818.182 1 1 98 220
179655 2530.352 1.9556 1.2833 43 71
876000 6257.143 1 2.2222 96 140
301133 2316.408 1.9556 1.2833 95 130
495340 11257.73 1.9556 1.2833 55 44
301133 3764.163 1.9231 1 64 80
853000 7049.587 1 1 118 121
976817 4884.085 1 1 141 200
1894931 5573.327 3 2 204 340
976817 6105.106 1 1 126 160
694227 4958.764 2.2656 1 144 140
495340 4307.304 1 1.2833 110 115
694227 1735.568 3 1 192 400
976817 10282.28 2.2656 1 80 95
976817 5141.142 3 1 183 190
815000 5821.429 1 2.0741 100 140
495340 6604.533 2.2656 2.0741 104 75
1718000 8590 4 1.2833 282 200
875000 14583.33 4.359 2.2222 86 60
790000 2633.333 2 2.0741 114 300
495340 3538.143 2.2656 2.0741 80 140
1850000 12333.33 5 1.2833 228 150
549000 4575 1 2.0741 88 120
745000 2660.714 2 2.0741 126 280
694227 7713.633 1.9231 1 62 90
156168 3904.2 1.9556 1.2833 43 40
976817 15027.95 1.9556 1 78 65
450000 5000 2 1.5946 117 90
156168 3904.2 1.9556 1.2833 70 40
700000 5833.333 1 1.2833 81 120
498000 2490 2.2656 2.0741 80 200
1421000 4736.667 2 1.5946 166 300
1600000 3200 5 2.2222 280 500
510000 3923.077 1.9556 1.2833 100 130
694227 4628.18 1.9231 1 110 150
700000 3111.111 1 1.2833 81 225
694227 3305.843 1.9231 1.5946 82 210
312107 2837.336 1.9231 1.5946 104 110
301133 8603.8 1.9556 1.2833 43 35
156168 1382.018 1.9556 1.2833 104 113
301133 3764.163 1.9556 1 66 80
301133 3011.33 1 1.2833 63 100
301133 3345.922 1.9556 1.2833 63 90
495340 3538.143 1.9231 1.5946 84 140
1926395 5206.473 5 3 296 370
1022300 10223 2 2 122 100
1343500 19192.86 3 2 154 70
1290500 18435.71 3 2 148 70
550000 4583.333 1.9231 1 152 120
2053200 14665.71 5 1 210 140
495340 12383.5 1.9556 1.2833 100 40
680000 7083.333 1.9556 1.2833 104 96
800000 9411.765 1 1.5946 130 85
235000 2350 1.9556 1.2833 43 100
976817 4884.085 1 1.2833 90 200
400000 8000 1.9231 1.5946 132 50
625000 6944.444 1.9556 1.2833 90 90
777362 5182.414 1.9556 1.2833 92 150
976817 4884.085 1.9556 2 104 200
301133 5018.883 1.9556 1.2833 65 60
800000 8000 1.9556 1.2833 88 100
495340 4953.4 1.9556 1 74 100
553809 6153.433 2.2656 2.0741 61 90
976817 6977.264 2 2 162 140
425000 2361.111 2.2656 2.0741 80 180
495340 1981.36 2.2656 2.0741 120 250
495340 4503.091 2.2656 2.0741 72 110
301133 3764.163 1.9556 1 52 80
876845 5480.281 1 1 126 160
420000 14000 1 2.0741 80 30
694227 5833.84 2.2656 1 108 119
156168 1952.1 1.9556 1 71 80
495340 8255.667 1.9556 1 62 60
694227 4338.919 1.9556 2 125 160
1033543 4306.429 1 2 188 240
200005 2500.063 1.9556 1.2833 52 80
1158200 8516.177 2 2.2222 128 136
393000 2079.365 2.2656 2.0741 63 189
77369 4835.563 1.9556 1.2833 62 16
156168 1952.1 1.9556 1.2833 32 80
1926395 3210.658 5 2.0741 271 600
976817 9768.17 1 1.2833 72 100
694227 3305.843 1 1 118 210
301133 3345.922 1.9556 1.2833 42 90
687800 7642.222 1 2.0741 87 90
949840 2713.829 2 1.2833 122 350
694227 5553.816 1 3 114 125
976817 2790.906 1 2.2222 117 350
400000 2857.143 1.9556 1.2833 100 140
495340 3002.061 1.9556 1.2833 72 165
301133 2007.553 1.9556 1.2833 100 150
3543400 9842.777 5 1.2833 244 360
495340 3538.143 1.9556 1.2833 51 140
1283500 8556.667 1 2 142 150
976817 5745.982 2.2656 2.0741 151 170
767905 5485.036 2.2656 2.0741 102 140
832000 4622.222 1.9231 1.5946 75 180
495340 4953.4 2.2656 2.0741 70 100
1300000 11304.35 2 1.2833 160 115
976817 13954.53 1 2.2222 92 70
976817 12210.21 1.9231 1 120 80
630000 4500 1 1.5946 104 140
694227 5340.208 2.2656 2.0741 124 130
976817 5280.092 2.2656 2 100 185
1378586 7877.634 2 2 175 175
145000 2900 1.9556 1.2833 62 50
1943500 24293.75 2.2656 2.0741 318 80
301133 6022.66 1.9556 1.2833 80 50
1000000 5000 2 2.2222 180 200
775000 12916.67 1.9556 1.2833 120 60
1223975 7649.844 1 1 132 160
694227 4083.688 1.9556 1 72 170
976817 9768.17 1.9556 1.2833 120 100
1350000 6192.661 2 2.0741 116 218
390000 5571.429 1.9231 1.5946 86 70
535000 4458.333 1.9556 1.2833 80 120
2500000 10416.67 4 1 199 240
1926395 17512.68 4 1.2833 240 110
524000 6550 1.9556 1.2833 62 80
729353 9116.912 2.2656 1 114 80
620000 2254.545 1 1.5946 103 275
1223000 11759.62 1 1.2833 91 104
625000 8333.333 1 1 65 75
538055 4483.792 1 2 96 120
250000 4545.455 1.9556 1.2833 51 55
301133 9410.406 1.9556 1.2833 51 32
77369 1487.865 1.9556 1.2833 40 52
1378586 13785.86 2 2 147 100
495340 6191.75 1.9556 1.2833 85 80
333000 2081.25 1.9231 1.5946 75 160
1378586 6892.93 1 2.0741 111 200
301133 2007.553 1.9556 1.2833 82 150
340000 4250 1.9556 1.2833 71 80
976817 5426.761 2.2656 1 98 180
1926395 7269.415 2 2 184 265
1001500 3576.786 2 1 174 280
301133 6022.66 1.9556 1.2833 71 50
750000 3750 1 2.0741 131 200
694227 3085.453 1 2.0741 128 225
495340 4953.4 1 1.2833 120 100
750000 7500 1 1.2833 98 100
694227 5340.208 1.9556 1.2833 78 130
750000 7653.061 1.9556 1.2833 104 98
400000 3333.333 2.2656 2.0741 59 120
1200000 6000 3 1.5946 192 200
694227 2169.459 1 1 94 320
250000 2272.727 1.9556 1.2833 63 110
976817 4884.085 3 1 196 200
845000 4225 1 2 144 200
1926395 12842.63 5 4 297 150
976817 2382.48 4 3 313 410
600000 5454.545 1 1.2833 90 110
694227 9917.528 4.359 2.2222 150 70
760000 5066.667 1.9231 1.5946 86 150
976817 9768.17 4 1.2833 191 100
156168 6246.72 1.9556 1.2833 104 25
495340 6191.75 1 1.2833 120 80
1378586 5143.978 3 1 212 268
1164149 12934.99 1 1 128 90
1200000 8000 1.9556 1.2833 97 150
976817 12210.21 1.9556 2 93 80
694227 9256.36 2 1.2833 80 75
694227 3305.843 1 3 102 210
694227 4958.764 1 3 102 140
694227 4958.764 1 2 92 140
1926395 4815.987 2 1 297 400
301133 3764.163 1.9556 1.2833 90 80
1340000 8375 1 2 179 160
785000 4361.111 1 2 74 180
1400000 4117.647 3 2 142 340
2700000 27000 3 1.2833 160 100
1926395 8756.341 4 1 236 220
694227 6428.028 1.9556 1.2833 80 108
600000 6000 1 1.5946 81 100
976817 8880.154 3 1.2833 170 110
694227 5785.225 1 2 120 120
694227 4338.919 1 1 116 160
495340 4127.833 1.9231 1 114 120
495340 3669.185 1.9231 1.5946 70 135
350000 2916.667 1 1.2833 90 120
77369 910.2235 1.9556 1.2833 45 85
976817 5141.142 2 1 190 190
1475000 4402.985 2 2 170 335
795655 1768.122 2 1.5946 160 450
570000 5700 1.9556 1 63 100
976817 6977.264 1 1 135 140
711661 6469.646 1 1.2833 139 110
156168 6246.72 1.9556 1.2833 60 25
960000 7680 2.2656 2.0741 100 125
860000 3822.222 1 2 145 225
694227 8677.838 1.9556 1 68 80
777102 5180.68 2 1.5946 146 150
976817 3256.057 1 1 142 300
770200 2026.842 2.2656 2 126 380
560000 7000 1.9556 1.2833 86 80
495340 3810.308 1.9231 1 88 130
1182183 1688.833 5 1.2833 240 700
694227 12622.31 1.9556 1 116 55
716000 7955.556 2 2.0741 108 90
976817 4341.409 3 2.2222 122 225
495340 2896.725 1.9556 1.2833 87 171
820000 6833.333 1 1.2833 80 120
1040000 11555.56 2 1.2833 101 90
3545901 23639.34 4 1 228 150
900000 3600 2 1 244 250
436000 7266.667 1.9556 1 79 60
800000 8000 2 1.2833 87 100
301133 7528.325 1.9556 1 56 40
495340 7620.615 1.9556 1.2833 82 65
1400000 7777.778 1.9556 3 160 180
640000 3878.788 1 1.2833 158 165
301133 6022.66 1.9556 1.2833 40 50
495340 1905.154 1 2.0741 90 260
156168 3904.2 1.9556 1 55 40
971500 3736.539 1 2 171 260
812397 9026.634 1.9231 1 67 90
1054268 10542.68 1 1.2833 132 100
750000 8823.529 1 1.2833 84 85
77369 1547.38 1.9556 1.2833 43 50
126179 3154.475 1.9556 1.2833 52 40
1378586 12883.98 2 1.2833 88 107
694227 10680.42 4.359 1 86 65
1378586 14360.27 2 4 154 96
976817 2790.906 2 1 165 350
490000 8166.667 2 1 102 60
301133 4182.403 1.9556 1.2833 62 72
694227 4958.764 2 1.2833 126 140
1130000 13294.12 2 1.2833 132 85
156168 4338 1.9556 1.2833 62 36
976817 13954.53 2.2656 2.0741 116 70
1000000 8333.333 2 1.2833 100 120
1926395 19263.95 4 2.2222 582 100
243517 4427.582 1.9556 1.2833 72 55
301133 3764.163 1.9556 1.2833 55 80
4000000 9302.325 7 1 359 430
750000 3750 1 1 173 200
301133 3011.33 1.9556 1.2833 87 100
850000 7727.273 1 2 143 110
301133 2737.573 1.9556 1 90 110
229000 2726.19 1.9556 1.2833 60 84
400000 5000 2.2656 2.0741 80 80
976817 15027.95 1.9556 1 110 65
976817 12210.21 1.9556 1.2833 100 80
1926395 7705.58 3 2 213 250
1378586 5105.874 1 4 178 270
2737701 7822.003 6 2 294 350
694227 4958.764 2 2.2222 84 140
800000 5333.333 1 1 192 150
890700 7125.6 2 2 134 125
1891500 5404.286 4 1 250 350
60000 300 1.9556 1.2833 50 200
976817 6105.106 1 2 107 160
976817 3907.268 1 2.2222 86 250
976817 3907.268 1 2.2222 86 250
1076500 5053.991 2 3 186 213
1378586 6352.931 4 1.5946 191 217
409167 5114.587 1.9556 1.2833 67 80
694227 15427.27 2 1.2833 80 45
900000 5000 1 2 137 180
1926395 5503.986 5 3 284 350
976817 4884.085 1 1 58 200
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1300000 8666.667 1 1.2833 177 150
156168 3549.273 1.9556 1.2833 63 44
1000000 10638.3 2 1 184 94
528000 6600 2.2656 2.0741 120 80
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694227 6942.27 1.9231 1.5946 65 100
475000 11309.52 1.9556 1.2833 60 42
800000 5555.556 3 2.0741 240 144
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77369 859.6556 2.2656 2.0741 90 90
976817 4884.085 1 3 133 200
495340 6191.75 1 1 131 80
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301133 5018.883 1 1.2833 40 60
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694227 6942.27 2.2656 2.0741 104 100
694227 4958.764 1.9231 1.5946 72 140
525000 10937.5 1.9556 1.2833 60 48
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300000 5000 1.9556 1.2833 69 60
301133 5018.883 1.9556 1.2833 45 60
694227 7713.633 1.9556 1.2833 50 90
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650000 7647.059 1.9556 1.2833 100 85
950000 5277.778 1.9231 2 198 180
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199286 3321.433 1.9231 1.5946 65 60
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502000 5020 2.2656 2.0741 110 100
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580000 1933.333 3 2 176 300
1000000 4545.455 4.359 1 120 220
671755 6106.864 2.2656 1 140 110
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445000 11125 1.9556 1.2833 70 40
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420000 5600 1.9556 1.2833 82 75
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846000 6042.857 1 2.2222 150 140
500000 8333.333 1.9556 1.2833 110 60
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695000 3861.111 1 1 151 180
407400 2314.773 1.9231 1.5946 106 176
1800000 3964.758 2.2656 3 221 454
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500000 5000 1.9231 1 104 100
5000000 16666.67 8 9 120 300
517381 5173.81 1 1.5946 92 100
1252320 3339.52 2 1.5946 170 375
600000 8571.429 1.9556 1.2833 74 70

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