QUESTION
ID number | Customer |
City |
Produce | Quantity (sold/day) |
Price $/kg |
% of Produce Damage |
49 |
1 |
2 |
1 |
334.34 |
1.08 |
0.00 |
38 |
1 |
1 |
1 |
350.90 |
1.52 |
0.00 |
77 |
1 |
2 |
1 |
483.57 |
0.96 |
0.11 |
8 |
1 |
1 |
1 |
61.10 |
2.99 |
0.35 |
15 |
1 |
2 |
1 |
354.89 |
1.47 |
0.65 |
80 |
1 |
2 |
1 |
529.41 |
0.36 |
0.77 |
6 |
1 |
1 |
1 |
42.14 |
3.16 |
0.92 |
46 |
1 |
2 |
1 |
43.14 |
2.69 |
0.95 |
83 |
1 |
1 |
1 |
398.26 |
1.01 |
1.01 |
62 |
1 |
1 |
1 |
409.62 |
1.41 |
1.06 |
93 |
1 |
2 |
1 |
96.42 |
2.02 |
1.10 |
29 |
1 |
1 |
1 |
158.48 |
2.54 |
1.13 |
64 |
1 |
1 |
1 |
371.90 |
0.51 |
1.13 |
68 |
1 |
1 |
1 |
321.88 |
1.25 |
1.15 |
26 |
1 |
1 |
1 |
154.44 |
2.58 |
1.43 |
36 |
1 |
1 |
1 |
383.62 |
1.09 |
1.51 |
42 |
1 |
2 |
1 |
11.10 |
2.99 |
1.64 |
24 |
1 |
1 |
1 |
81.88 |
3.25 |
1.72 |
74 |
1 |
2 |
1 |
396.38 |
0.81 |
1.82 |
57 |
1 |
1 |
1 |
356.38 |
2.04 |
1.82 |
73 |
1 |
2 |
1 |
328.90 |
1.51 |
1.85 |
84 |
1 |
1 |
1 |
498.50 |
1.19 |
1.87 |
20 |
1 |
2 |
1 |
188.77 |
2.23 |
1.90 |
27 |
1 |
1 |
1 |
104.48 |
3.05 |
2.03 |
61 |
1 |
1 |
1 |
358.20 |
2.02 |
2.23 |
63 |
1 |
1 |
1 |
337.18 |
1.04 |
2.36 |
54 |
1 |
2 |
1 |
275.88 |
1.82 |
2.45 |
76 |
1 |
2 |
1 |
528.76 |
0.37 |
2.48 |
89 |
1 |
2 |
1 |
231.71 |
1.70 |
2.51 |
86 |
1 |
1 |
1 |
95.95 |
2.88 |
2.62 |
47 |
1 |
2 |
1 |
81.14 |
2.31 |
2.63 |
65 |
1 |
1 |
1 |
370.08 |
0.54 |
2.66 |
11 |
1 |
2 |
1 |
315.36 |
1.94 |
2.68 |
14 |
1 |
2 |
1 |
284.97 |
2.27 |
2.71 |
67 |
1 |
1 |
1 |
313.50 |
1.36 |
2.71 |
34 |
1 |
1 |
1 |
358.05 |
1.43 |
2.74 |
69 |
1 |
2 |
1 |
393.05 |
0.85 |
2.80 |
92 |
1 |
2 |
1 |
443.89 |
1.27 |
2.81 |
51 |
1 |
2 |
1 |
322.62 |
1.24 |
2.85 |
3 |
1 |
1 |
1 |
235.31 |
1.88 |
3.04 |
31 |
1 |
1 |
1 |
314.48 |
1.95 |
3.07 |
44 |
1 |
2 |
1 |
29.48 |
2.82 |
3.07 |
10 |
1 |
1 |
1 |
48.90 |
3.10 |
3.10 |
43 |
1 |
2 |
1 |
59.49 |
2.53 |
3.13 |
7 |
1 |
1 |
2 |
91.06 |
2.71 |
3.17 |
32 |
1 |
1 |
2 |
343.58 |
1.61 |
3.19 |
91 |
1 |
2 |
2 |
417.01 |
0.84 |
3.22 |
39 |
1 |
2 |
2 |
11.10 |
2.99 |
3.23 |
28 |
1 |
1 |
2 |
103.36 |
3.06 |
3.26 |
71 |
1 |
2 |
2 |
327.79 |
1.52 |
3.29 |
94 |
1 |
2 |
2 |
67.39 |
1.70 |
3.38 |
56 |
1 |
2 |
2 |
301.70 |
1.51 |
3.41 |
1 |
1 |
1 |
2 |
218.70 |
2.01 |
3.44 |
79 |
1 |
2 |
2 |
528.11 |
0.38 |
3.67 |
19 |
1 |
2 |
2 |
97.78 |
3.11 |
3.70 |
82 |
1 |
1 |
2 |
312.38 |
1.57 |
3.82 |
52 |
1 |
2 |
2 |
291.10 |
1.64 |
3.85 |
214 |
2 |
2 |
2 |
116.51 |
2.19 |
3.86 |
163 |
2 |
1 |
2 |
338.60 |
1.02 |
3.92 |
178 |
2 |
2 |
2 |
502.84 |
0.73 |
3.96 |
99 |
2 |
1 |
2 |
258.38 |
1.69 |
4.13 |
126 |
2 |
2 |
2 |
142.10 |
2.70 |
4.15 |
106 |
2 |
1 |
2 |
77.34 |
2.84 |
4.16 |
135 |
2 |
1 |
2 |
121.98 |
2.89 |
4.16 |
169 |
2 |
2 |
2 |
308.38 |
1.69 |
4.16 |
132 |
2 |
1 |
2 |
135.82 |
2.76 |
4.18 |
156 |
2 |
1 |
2 |
343.48 |
0.95 |
4.19 |
164 |
2 |
2 |
2 |
390.51 |
0.88 |
4.25 |
153 |
2 |
1 |
2 |
396.04 |
1.58 |
4.25 |
208 |
2 |
2 |
2 |
14.00 |
2.35 |
4.27 |
110 |
2 |
1 |
2 |
75.20 |
2.86 |
4.30 |
193 |
2 |
1 |
2 |
90.43 |
2.85 |
4.31 |
107 |
2 |
1 |
2 |
93.14 |
2.69 |
4.34 |
176 |
2 |
2 |
2 |
528.76 |
0.37 |
4.37 |
120 |
2 |
2 |
2 |
305.48 |
2.05 |
4.42 |
123 |
2 |
2 |
2 |
293.48 |
2.18 |
4.43 |
177 |
2 |
2 |
2 |
525.47 |
0.42 |
4.46 |
144 |
2 |
2 |
2 |
344.85 |
0.93 |
4.46 |
175 |
2 |
2 |
2 |
520.70 |
0.49 |
4.49 |
111 |
2 |
1 |
2 |
16.76 |
3.38 |
4.51 |
212 |
2 |
2 |
2 |
23.49 |
1.96 |
4.54 |
139 |
2 |
1 |
2 |
322.40 |
1.86 |
4.54 |
150 |
2 |
1 |
2 |
352.74 |
2.08 |
4.58 |
170 |
2 |
2 |
2 |
394.72 |
0.83 |
4.58 |
211 |
2 |
2 |
2 |
85.31 |
2.34 |
4.66 |
114 |
2 |
1 |
2 |
78.41 |
2.83 |
4.69 |
137 |
2 |
1 |
2 |
374.12 |
1.22 |
4.76 |
190 |
2 |
1 |
2 |
18.00 |
2.82 |
4.79 |
134 |
2 |
1 |
2 |
64.40 |
3.40 |
4.79 |
100 |
2 |
1 |
2 |
276.68 |
1.53 |
4.79 |
206 |
2 |
2 |
2 |
359.55 |
1.79 |
4.83 |
194 |
2 |
1 |
2 |
5.00 |
2.28 |
4.85 |
141 |
2 |
2 |
3 |
104.56 |
2.06 |
4.92 |
136 |
2 |
1 |
3 |
364.28 |
1.35 |
4.94 |
147 |
2 |
2 |
3 |
290.28 |
1.65 |
4.94 |
115 |
2 |
2 |
3 |
297.20 |
2.14 |
4.95 |
203 |
2 |
2 |
3 |
404.24 |
1.08 |
4.97 |
165 |
2 |
2 |
3 |
342.91 |
1.38 |
4.97 |
142 |
2 |
2 |
3 |
64.50 |
2.48 |
5.04 |
121 |
2 |
2 |
3 |
290.66 |
2.21 |
5.05 |
180 |
2 |
1 |
3 |
433.90 |
1.38 |
5.08 |
185 |
2 |
1 |
3 |
379.22 |
1.14 |
5.12 |
168 |
2 |
2 |
3 |
388.80 |
0.90 |
5.13 |
189 |
2 |
1 |
3 |
91.82 |
2.93 |
5.17 |
158 |
2 |
1 |
3 |
344.16 |
0.94 |
5.18 |
202 |
2 |
2 |
3 |
367.66 |
1.27 |
5.19 |
116 |
2 |
2 |
3 |
350.09 |
1.53 |
5.24 |
108 |
2 |
1 |
3 |
91.06 |
2.71 |
5.25 |
128 |
2 |
2 |
3 |
145.21 |
2.67 |
5.25 |
140 |
2 |
2 |
3 |
35.82 |
2.76 |
5.27 |
200 |
2 |
2 |
3 |
356.02 |
1.05 |
5.28 |
199 |
2 |
2 |
3 |
411.20 |
1.71 |
5.31 |
125 |
2 |
2 |
3 |
146.24 |
2.66 |
5.36 |
171 |
2 |
2 |
3 |
304.83 |
1.72 |
5.36 |
159 |
2 |
1 |
3 |
323.37 |
1.23 |
5.44 |
113 |
2 |
1 |
3 |
81.60 |
2.80 |
5.47 |
191 |
2 |
1 |
3 |
5.00 |
2.54 |
5.60 |
160 |
2 |
1 |
3 |
356.88 |
0.75 |
5.62 |
195 |
2 |
1 |
3 |
82.03 |
2.17 |
5.62 |
109 |
2 |
1 |
3 |
90.02 |
2.72 |
5.66 |
127 |
2 |
2 |
3 |
162.50 |
2.50 |
5.71 |
122 |
2 |
2 |
3 |
352.50 |
1.50 |
5.73 |
133 |
2 |
1 |
3 |
72.61 |
3.33 |
5.80 |
97 |
2 |
1 |
3 |
230.27 |
1.92 |
5.88 |
204 |
2 |
2 |
3 |
422.67 |
1.24 |
5.93 |
157 |
2 |
1 |
3 |
318.86 |
1.29 |
5.94 |
102 |
2 |
1 |
3 |
217.39 |
2.02 |
5.94 |
172 |
2 |
2 |
3 |
516.45 |
0.55 |
5.95 |
174 |
2 |
2 |
3 |
493.05 |
0.85 |
6.03 |
130 |
2 |
2 |
3 |
167.48 |
2.45 |
6.12 |
104 |
2 |
1 |
3 |
182.03 |
2.28 |
6.15 |
179 |
2 |
2 |
3 |
457.25 |
1.24 |
6.17 |
161 |
2 |
1 |
3 |
371.90 |
0.51 |
6.18 |
166 |
2 |
2 |
3 |
296.42 |
1.79 |
6.21 |
154 |
2 |
1 |
3 |
396.85 |
1.57 |
6.23 |
282 |
3 |
1 |
3 |
381.88 |
1.75 |
6.26 |
310 |
3 |
1 |
3 |
428.18 |
1.65 |
6.27 |
250 |
3 |
1 |
3 |
93.28 |
3.15 |
6.28 |
314 |
3 |
1 |
3 |
113.45 |
2.27 |
6.33 |
283 |
3 |
1 |
3 |
363.28 |
0.65 |
6.34 |
328 |
3 |
2 |
3 |
118.80 |
1.60 |
6.41 |
330 |
3 |
2 |
3 |
30.62 |
2.51 |
6.41 |
324 |
3 |
2 |
3 |
447.20 |
0.91 |
6.45 |
245 |
3 |
1 |
3 |
106.69 |
3.03 |
6.50 |
322 |
3 |
2 |
3 |
445.55 |
1.59 |
6.59 |
259 |
3 |
1 |
3 |
318.90 |
1.90 |
6.64 |
277 |
3 |
1 |
3 |
387.78 |
1.68 |
6.73 |
327 |
3 |
2 |
3 |
360.72 |
1.53 |
6.75 |
298 |
3 |
2 |
3 |
530.05 |
0.35 |
6.76 |
318 |
3 |
1 |
3 |
42.45 |
2.45 |
6.80 |
300 |
3 |
2 |
3 |
480.90 |
0.99 |
6.80 |
242 |
3 |
2 |
3 |
181.14 |
2.31 |
6.81 |
238 |
3 |
2 |
3 |
128.41 |
2.83 |
6.86 |
251 |
3 |
1 |
4 |
63.22 |
3.41 |
6.86 |
219 |
3 |
1 |
4 |
267.66 |
1.61 |
6.88 |
313 |
3 |
1 |
4 |
82.03 |
2.05 |
6.95 |
311 |
3 |
1 |
4 |
381.38 |
1.39 |
7.01 |
269 |
3 |
2 |
4 |
342.78 |
0.96 |
7.05 |
244 |
3 |
1 |
4 |
110.00 |
3.00 |
7.07 |
227 |
3 |
1 |
4 |
111.50 |
2.51 |
7.12 |
280 |
3 |
1 |
4 |
418.10 |
1.30 |
7.20 |
289 |
3 |
1 |
4 |
377.24 |
0.42 |
7.21 |
272 |
3 |
2 |
4 |
331.46 |
1.12 |
7.24 |
292 |
3 |
2 |
4 |
310.72 |
1.67 |
7.35 |
261 |
3 |
2 |
4 |
83.06 |
2.29 |
7.38 |
306 |
3 |
1 |
4 |
420.42 |
1.24 |
7.41 |
217 |
3 |
1 |
4 |
182.03 |
2.28 |
7.47 |
302 |
3 |
2 |
4 |
456.25 |
1.25 |
7.47 |
230 |
3 |
2 |
4 |
360.40 |
1.40 |
7.53 |
236 |
3 |
2 |
4 |
361.96 |
1.38 |
7.63 |
335 |
3 |
2 |
4 |
60.80 |
1.87 |
7.65 |
303 |
3 |
2 |
4 |
523.45 |
0.45 |
7.65 |
299 |
3 |
2 |
4 |
517.88 |
0.53 |
7.74 |
225 |
3 |
1 |
4 |
34.17 |
3.23 |
7.74 |
265 |
3 |
2 |
4 |
88.77 |
2.23 |
7.86 |
285 |
3 |
1 |
4 |
375.48 |
0.45 |
7.87 |
253 |
3 |
1 |
4 |
329.32 |
1.78 |
7.89 |
286 |
3 |
1 |
4 |
344.85 |
0.93 |
7.89 |
333 |
3 |
2 |
4 |
63.45 |
1.88 |
7.90 |
294 |
3 |
2 |
4 |
303.64 |
1.73 |
7.92 |
249 |
3 |
1 |
4 |
136.88 |
2.75 |
7.95 |
260 |
3 |
2 |
4 |
69.45 |
2.43 |
8.05 |
264 |
3 |
2 |
4 |
84.97 |
2.27 |
8.23 |
247 |
3 |
1 |
4 |
97.78 |
3.11 |
8.29 |
297 |
3 |
2 |
4 |
489.66 |
0.89 |
8.41 |
284 |
3 |
1 |
4 |
314.28 |
1.35 |
8.62 |
281 |
3 |
1 |
4 |
379.32 |
1.78 |
8.83 |
312 |
3 |
1 |
4 |
89.04 |
2.28 |
8.86 |
319 |
3 |
1 |
4 |
57.45 |
2.21 |
9.19 |
291 |
3 |
2 |
4 |
301.25 |
1.75 |
9.19 |
305 |
3 |
1 |
4 |
398.26 |
1.46 |
9.28 |
331 |
3 |
2 |
4 |
1.50 |
2.00 |
9.28 |
317 |
3 |
1 |
4 |
33.26 |
2.55 |
9.43 |
271 |
3 |
2 |
4 |
280.17 |
1.77 |
9.58 |
228 |
3 |
1 |
4 |
20.28 |
3.35 |
9.76 |
288 |
3 |
1 |
4 |
366.40 |
0.60 |
9.85 |
332 |
3 |
2 |
4 |
70.00 |
2.05 |
9.97 |
276 |
3 |
1 |
4 |
419.62 |
1.28 |
10.27 |
295 |
3 |
2 |
4 |
372.67 |
1.08 |
10.48 |
321 |
3 |
2 |
4 |
369.94 |
0.82 |
10.54 |
SOLUTION
1. Introduction and Variable List
This report seeks to analyze data from a fruits and vegetable market supplying fresh produce to supermarkets in NSW and Victoria states. The data being examined pertains to customers in Sydney and Melbourne. The raw data consists of various variables such as: the customer, the type of produce, quantity sold per day, the price per Kg of produce and the percentage of produce that is damaged.
2. Data
Please refer sheet “Random Sample” in attached excel sheet.
3. Pivot Table
Please refer sheet “Pivot Table 1”. The Pivot table has been constructed taking the variable “Quantity” as the value of comparison. It is evident from the pivot table that Coles only sells Apples and Oranges while Safeway only sells Potatoes and Tomatoes.
4. Pivot Table
Please refer sheet “Pivot Table 2”.
a) Coles has the highest average price/kg for apples. Private customers have the highest average price/kg for oranges.
b) Safeway has the highest average % of produce damaged for tomatoes. Coles has the highest average % of produce damaged for apples.
5. T-Test
a) Please refer sheet “T Test” for these values.
b) Null Hypothesis: H0: Average % of produce damaged at Coles stores in Sydney and Melbourne is < 5%
Alternative Hypothesis: H1: Average % of produce damaged at Coles stores in Sydney and Melbourne is > 5%
Assume Alpha = 0.05
Number of Coles customers n = 57
Degrees of Freedom = n – 1 = 56
This is a two-tailed test. If “t” is less than -1.673 or greater than +1.673, reject the null hypothesis.
Calculate t =
Sample mean x = 2.231578947
Population mean = 5
Sample Std. dev. s = 1.052595075
Sample size n = 57
t = -0.348364091
Result: Accept Null Hypothesis.
6. Scatterplot
Please refer sheet “Scatterplot”.
7. Relationship
Most of the damaged produce seems to be concentrated in the 4-8% zone irrespective of the price/Kg of the produce.
8. Regression Analysis
a)
b) Regression Equation is
Price/Kg = 1.864 – 0.0092*(% of produce damaged)
c) The R-squared of the regression is the fraction of the variation in the dependent variable that is accounted for (or predicted by) the independent variables. It measures the fit of the model. In this case the R-square value of 0.0000748 is very low. The Standard error is 0.8. This is the standard deviation of the sample independent variables around the fitted value.
d) The gradient of the regression line is -0.0092. This shows a negative slope indicating that, as the % of produce damaged increases the price/kg decreases. This is understood as wastage will be less in higher value items.
e) Yes, the values of the constant and intercept are significant in this case. They show a negative co-relation between the dependent and independent variables. The sample data collected is also in-line with this.
f) The R-square value is very less to justify this model to be a good fit regression model. Increasing the number of observations could help to increase the R-square and achieve a good fit.
9. Conclusion
Although the Regression analysis could not get a good fit due to the low value of the R-square, it does show how the consumer behavior is shaped depending on the value of the product. In cases where the value of the product is high, wastage is low. This is true for all customers and all produce categories.
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