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HI6007 Statistics and Research Methods-The Estimated Regression

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. Find mean, median, mode, range, variance and standard deviation separately for every type
of business 
2. For every business type construct
a. frequency and relative frequency distributions starting from class 0 to 30
b. a relative frequency histogram 
3. Discuss the results obtained in parts 1 and 2 
4. Test if 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 the MS Excel output and write down the estimated regression equation 
2. How well the model fits the data
3. Test the hypothesis that there is no significant relationship between the dependent and any of the independent variables 
4. Interpret individual slope coefficients 
5. Construct a 95% confidence interval for the slope coefficients of individual variables 
6. Test the estimated slope coefficients for individual variables for significance
7. Remove all insignificant variables and re-estimate the model 
8. Using the 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 competitors. 

Answer:


ll; width: 100%;" width="100%">
The following data represent business startup costs (thousands of dollars) for shops.
X1 X2 X3 X4 X5
80 150 48 100 25
125 40 35 96 80
35 120 95 35 30
58 75 45 99 35
110 160 75 75 30
140 60 115 150 28
97 45 42 45 20
50 100 78 100 75
65 86 65 120 48
79 87 125 50 20
Source: https://college.cengage.com/mathematics/brase/understandable_statistics/7e/students/datasets/owan/frames/frame.html
X1 X2 X3 X4 X5
231 3 294 8.199999809 8.2
156 2.2 232 6.900000095 4.1
10 0.5 149 3 4.3
519 5.5 600 12 16.1
437 4.4 567 10.60000038 14.1
487 4.8 571 11.80000019 12.7
299 3.1 512 8.1 10.1
195 2.5 347 7.699999809 8.4
20 1.2 212 3.299999952 2.1
68 0.6 102 4.900000095 4.7
570 5.4 788 17.39999962 12.3
428 4.2 577 10.5 14
464 4.7 535 11.30000019 15
15 0.6 163 2.5 2.5
65 1.2 168 4.699999809 3.3
98 1.6 151 4.599999905 2.7
398 4.3 342 5.5 16
161 2.6 196 7.199999809 6.3
397 3.8 453 10.39999962 13.9
497 5.3 518 11.5 16.3
528 5.6 615 12.30000019 16
99 0.8 278 2.799999952 6.5
0.5 1.1 142 3.099999905 1.6
347 3.6 461 9.6 11.3
341 3.5 382 9.800000191 11.5
507 5.1 590 12 15.7
400 8.6 517 7 12
startup costs for pet stores MS F
Classes Frequency  Relative Frequency  190507.7883 611.5904
91 to 120 1 6.25 t Stat P-value
Total  16 100 -0.63 0.54

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