Hi6007 Statistics And Research Methods-The Assessment Answers
The data for Task 1 in the data file for Assignment represents the starting costs in thousands of dollars) for different kind of business.
- 1. Findmean, median, mode, range, variance and standard deviation separately for every type of business
- 2. For everybusiness type construct
- frequencyandrelative frequency distributions starting from class 0 to 30
- b. arelative frequency histogram
- 3. Discussthe results obtained in parts 1 and 2
- 4. Testif there significant difference in the starting costs for these types of business.
The data for Task 2 in the data file for Assignment represents the following variables for franchisees of All Greens Pty Ltd: annual sales ($’000), the floor area (sq.ft.’000), inventory ($’000), advertising expenditure ($’000), the size of the area where the business operates (number of families, ‘000) and the number of competitors in the area.
- 1. Present theMS Excel output and write down the estimated regression equation
- 2. Howwell the model fits the data
- 3. Testthe hypothesis that there is no significant relationship between the dependent and any of the independent variables
- 4. Interpretindividual slope coefficients
- 5. Constructa 95% confidence interval for the slope coefficients of individual variables
- 6. Testthe estimated slope coefficients for individual variables for significance
- 7. Removeall insignificant variables and re-estimate the model
- 8. Usingthe model from part (g), predict annual sales for a franchisee with 1,000 sq ft floor area, $150,000 inventory, $5,000 spent on advertising, 5,000 families in the area of operation and 2 competiton.
Answer:
X1 | X4 | X5 | Summary Statistics: Starting Costs in $'000 | Type of Business | |
125 | 96 | 80 | Mean | 83 | 92.09 |
35 | 35 | 30 | Median | 80 | 87 |
58 | 99 | 35 | Mode | 35 | #N/A |
110 | 75 | 30 | Standard Deviation | 34.13 | 38.89 |
140 | 150 | 28 | Sample Variance | 1165.17 | 1512.69 |
97 | 45 | 20 | Range | 105 | 120 |
Variable X1: Pizza Shops | X2 | X3 | X4 | X5 | X6 |
Starting Costs (in $000) | 3 | 294 | 8.2 | 8.2 | 11 |
0 to 30 | 2.2 | 232 | 6.9 | 4.1 | 12 |
31 to 60 | 0.5 | 149 | 3 | 4.3 | 15 |
61 to 90 | 5.5 | 600 | 12 | 16.1 | 1 |
91 to 120 | 4.4 | 567 | 10.6 | 14.1 | 5 |
121 to 150 | 4.8 | 571 | 11.8 | 12.7 | 4 |
Total | 3.1 | 512 | 8.1 | 10.1 | 10 |
Variable X2: Baker or Donuts Shops | 0.6 | 102 | 4.9 | 4.7 | 8 |
Starting Costs (in $000) | 5.4 | 788 | 17.4 | 12.3 | 1 |
0 to 30 | 4.2 | 577 | 10.5 | 14 | 7 |
31 to 60 | 4.7 | 535 | 11.3 | 15 | 3 |
61 to 90 | 0.6 | 163 | 2.5 | 2.5 | 14 |
91 to 120 | 1.2 | 168 | 4.7 | 3.3 | 11 |
121 to 150 | 1.6 | 151 | 4.6 | 2.7 | 10 |
151 to 180 | 4.3 | 342 | 5.5 | 16 | 4 |
Total | 2.6 | 196 | 7.2 | 6.3 | 13 |
Variable X3: Shoe Store | 5.6 | 615 | 12.3 | 16 | 0 |
Starting Costs (in $000) | 0.8 | 278 | 2.8 | 6.5 | 14 |
0 to 30 | 1.1 | 142 | 3.1 | 1.6 | 12 |
31 to 60 | 3.6 | 461 | 9.6 | 11.3 | 6 |
61 to 90 | 3.5 | 382 | 9.8 | 11.5 | 5 |
91 to 120 | 5.1 | 590 | 12 | 15.7 | 0 |
121 to 150 | 8.6 | 517 | 7 | 12 | 8 |
121 to 150 | Regression | 5 | 952538.9 | 190507.8 | 611.590 |
Starting Costs (in $000) | Intercept | -18.86 | 30.15 | -0.626 | 0.5384 |
0 to 30 | X2 | 16.20 | 3.54 | 4.571 | 0.0002 |
31 to 60 | X3 | 0.17 | 0.06 | 3.032 | 0.0063 |
61 to 90 | X4 | 11.53 | 2.53 | 4.552 | 0.0002 |
91 to 120 | X5 | 13.58 | 1.77 | 7.671 | 0.0000 |
121 to 150 | X6 | -5.31 | 1.71 | -3.114 | 0.0052 |
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