An Australian manufacturing company which is a market leader in the sanitary product sector
in the Australasian market with operating headquarters in Sydney is keen to develop new
products so that company can expand into Australian and Asian markets. Research and
Development (R&D) department of the company has prepared a proposal to work on new
product line of fragrance.
Assume you work as an Analyst for this company and you have been asked to study the
market for fragrances. You have been asked to study the characteristics of currently available
fragrances so the company will be in a better position to price its proposed new product. You
have collected data for 95 products on the market. The data is on an excel file named
“FRAGRANCE”.
First Column: PRICE (that is Price of the product in Australian dollars for 100 ml of a
fragrance).
Second Column: GENDER (1 for Female product and 2 for Male product).
Third Column: TYPE (Type of fragrance: 1 for perfume and 2 for cologne).
Forth Column: MADE (the country in which the fragrance is produced: 1 made in France, 2
made in USA, 3 made in other countries).
Fifth Column: INTEN (Intensity or strength of the product: 1 for strong, 2 for medium and 3
for mild).
See next pages for more information. Questions:
Part 1) Provide a description of the data (for all the 95 products together) and show what
Mean, Standard Deviation, Coefficient of Variation mean in this context.
Part 2) Calculate the Mean, Median, Mode, Standard Deviation, Coefficient of Variation,
95% confidence interval for means for:
o Prices for gender - male and female.
o Prices for fragrance - perfume and cologne.
o Prices for intensity - strong, medium and mild.
o Prices for different countries – France, USA and other.
What conclusions can you draw from these analyses? Also comment on the shape of
distributions.
Part 3) You are also required to answer the following questions (For one-sided tests, use the
question of interest as the alternative hypothesis):
1. Determine if average prices for female products exceed average prices for male
products.
2. Determine if there is evidence to suggest that the variance of prices for male products
is equal to those of female products.
3. Determine if average prices for perfume exceeds the average price of cologne.
4. Determine if there is evidence to suggest that the variance of prices for perfume and
cologne are equals.
5. Determine if there is a difference in the prices for intensity.
6. Determine if there is a difference for the prices for different countries.
Give conclusions for each of the analysis plus an overall conclusion which combine all of the
above (parts 1 and 2). Be clear in the conclusion that you draw from your analysis, and
provide some useful suggestions to the company’s manager.
Notes:
v You must follow the hypothesis testing steps to test the above hypotheses. v You must clearly specify all hypotheses and the chosen test procedures.
v Use 0.05 level of significance in your analyses and assume that we have normal
distributions and also “equal variances” of populations.
v Each part requires an output from any statistical computer package (Excel, SPSS, R etc.).
The statistical output must be provided.
v Use and interpret appropriate output from statistical computer packages such as
SPSS/Minitab/Excel/PHStat to conduct hypothesis testing.
v Prepare and produce a business report based on the information provided in the
“Presentation of the assignment”.
v You report can be maximum 3000 words, penalties will be applied if the report is longer
than this.
v Submit the business report as indicated in the “Presentation of the assignment” BEFORE
4pm, 17 April 2014 at the Business Central.
v No assignment will be accepted after 4pm, 17 April 2014.
v Take your assignment to the Business Central to be scanned and submitted
v Please ensure that you have signed the plagiarism declaration before submitting your
assignment for scanning at Business Central.
Executive summary
In this business report the analyst analyze the market about the fragrances. To analyze the market the analyst have taken different kind of variable such as the price of the product, type of the fragrance, the effective gender, the country where the product made and the intensity and the strength of the product.
The analyst use different kind of statistical tools to analyze the market of fragrances. The important statistical tools are mean, median, mode, standard deviation and correlation coefficient.
As per the analysis, the analyzer observes that the value of mean of price is 29 and the value of median of price of the fragrance is 124. The value of the mode of the product is 69 and the value of the standard deviation is 79.64.
IMPORTANT:
It is compulsory for all students to submit their assignments (only final version) into
the Turnitin system BEFORE submitting the hard copy to the Business Central. Then
an 'originality report' will automatically be sent to the Lecturer (Dr Amir Arjomandi).
Otherwise your assignment will not be marked and therefore you will be awarded a 0
for this assessment task.
• You must submit your assignment to Turnitin before the due date (4pm, 15 April
2014). No assignment will be accepted by Turnitin after 4pm, 15 April 2014.
• The first time a UOW student uses the Turnitin system, they must register using a
functioning UOW email address as their user name and adhere to the following
guidelines:
1. Use one sign in name only
2. Use one document name only for each assignment that includes your UOW student
number 3. Any resubmissions must use the same document name as the original submission
4. References must be included in your Turnitin submission
5. Do not include the assignment topic question at the beginning of your submission.
• Failure to comply with these requirements may result in penalties being applied.
-------------------------------------------------------------
Introduction
An Australian manufacturing company which is a market leader in the sanitary sector in the Australian market with operating headquarters in the Sydney which is keen to develop new products so that company can expand into the Australian and Asian markets. Research and development of this company is going to prepare a proposal to work a new product line in the fragrance. In this project the analyst study the market for fragrance. In this project, the analyst has collected data for 95 products on the market. The analyst has to study the characteristics of the currently available fragrance so the company will be in a better position to price its proposed new product.
The terms of mean median mode and the range that describes properties of the statistical distribution. In the method of statistics, a distribution is one set of possible values which represent defined the events (Atkinson, 2008). Random variable can be expressed as a variable. There are two major type of statistical distribution. The effective type has a discrete random variable. It express hat every term is precise and isolated numerical value (Dimarco, 2008). One of the distributions of discrete random variables is that a set of result for the test taken by the class. Another major type of distribution is a continuous random variable (Comaniciu and Meer, 2002). In that situation, a term has to acquire any within an unbroken interval. This is one of the functions which can be used by a computer in an attempt which forecast the path of a weather system (Lee et al. 2011).
Mean
One of the most common expressions for the mean of statistical distribution with the discrete random variable is the mathematical average of every term. When the analyst calculates the mean then they have to add the values of all the terms and they have to divide the number of terms (Evanovich, 2007). This method can be called the arithmetic mean. On the other hand, there are other expressions for the mean that a finite set of terms but in mathematics these form are rarely used in the statistical calculation (Comaniciu et al. 2000). The proper mean of the statistical distribution with a following random variables and this can also called the expected value that can be obtained by the integrating the product of the variable with its probability as defined by the effective distribution. The value of mean can be representing by the lower case Greek letter mu (Hughes and Jagannathan, 2009).
Median
Median is another method of dispersion with the discrete random variables which depends on whether the number of the term as per the distribution. When the number of term is odd, then the median is the value of the term in the middle (American Mathematical Society, 2014). When the term of this variable is even then the median is the average of the two terms in the middle which that the numbers of terms have the value greater than or equal to as it is the same as the number of term has the value less than or equal to it (Lenn and Stefano, 2012). On the other hand, the median of the distribution as a continuous random variables is one of the value m such that the probability is at least 50 per cent that a random chosen point on the function that will be less than or equal to the m and on the other aspect the probability is at least ½ that of the random chosen in the point on the function that will be greater than or equal to the m (Arxiv.org, 2014).
Mode
Mode is another aspect of dispersion. As per the mode it is common for a distribution with the discrete random variable that has to be more than one mode, in this case there are not many terms (Fagam et al. 2008). This kind of incident happens at the time when two or more terms occur with the equal frequency. A distribution of the two modes can be known as bimodal. On the other hand, a distribution of three modes can be called as tri modal (Schwarz and Yenmez, 2009). The mode of the distribution as per the continuous random variables is the maximum value of the function (Math.berkeley.edu, 2014). There may more than one mode with discrete distribution.
Standard deviation
Standard deviation is the measure of dispersion of the set of data for the mean. When the data is more spread the there is a chance of higher deviation. This method is calculated as the square root of the variance (Weissman, 2007). As per the part in finance, standard deviations have to be applied to the annual rate of return of an investment which measures the volatility of the investment (Pagel and Hudetz, 2011). The standard deviation can be known as the historical volatility and which is used by the investors as per the gauge for the amount of expected volatility. When the analyst have to look at the peoples typical daily consumption then number of people typical consumption have to turn out to be normally distributed. The consumption will be close to the mean. The x axis is the value of question which calories consumed, dollars earned or the crimes committed. On the other hand, y axis is the number of data points for every value of x axis.
Standard deviation can be defined as the mean of the mean. This helps the analyst to find the story behind the data. This helps to understand the concept of normal distribution. A normal distribution of the certain data means that the most of the in the set of data which is close to the average, on the other hand, relatively few example tend to one extreme (Lee et al. 2008).
Coefficient of Variation
The correlation coefficient of the two variables in the data sample can be defined as the covariance divided by the product of the individual’s standard of the variation. This can be known as normalized measurement of how they are linearly related. A correlation coefficient is one of the statistical measures of the certain degree of which change to the value of one variable can predict the change to the other variable (Lazaridis, 2005). The negatively correlated value defines that when the value of one variable increase then the value of other variable decrease. The value of r can be defined as the liner correlation coefficient that helps to determine the strength and the direction of the liner relationship between the different variables. The linear correlation can be defined as the Pearson product moment correlation coefficient (Math.mit.edu, 2014). The effective value of r can be -1, +1 or 0 which is used for positive liner correlation and negative liner correlation respectively.
Positive correlation
Positive correlation can be representing by the value of +1. The value of the positive 1 can indicates the perfect positive fit. This value also indicates the relationship between x and y variable. In this case, when the value of x increases then the value of y also increases (Siddiqui and Siddiqui, 2006).
Negative correlation
Negative correlation indicates that the value of -1. The value of negative 1 represent the perfect negative fit. The negative value indicates the negative relationship such that when the value of x increase then the value of y decrease (Madura, 2011).
No correlation
No correlation indicates the weak linear correlation. In this case the value of r is close to 0. A value of zero means that there is no relation between two variables. That indicates that if the value of x increase then the value of y may not change (Math.umn.edu, 2014).
Calculation
Mean
Mean
|
Median
|
Mode
|
Standard deviation
| |
Price
| ||||
29
|
124
|
69
|
79.64251
| |
Price and gender
SUMMARY OUTPUT
| ||||||||
Regression Statistics
| ||||||||
Multiple R
|
0.138716
| |||||||
R Square
|
0.019242
| |||||||
Adjusted R Square
|
0.008582
| |||||||
Standard Error
|
78.53473
| |||||||
Observations
|
94
| |||||||
ANOVA
| ||||||||
Df
|
SS
|
MS
|
F
|
Significance F
| ||||
Regression
|
1
|
11132.73
|
11132.73
|
1.805004
|
0.182413192
| |||
Residual
|
92
|
567428.7
|
6167.703
| |||||
Total
|
93
|
578561.4
| ||||||
Coefficients
|
Standard Error
|
t Stat
|
P-value
|
Lower 95%
|
Upper 95%
|
Lower 95.0%
|
Upper 95.0%
| |
Intercept
|
164.2359
|
24.37366
|
6.738255
|
1.37E-09
|
115.8277393
|
212.6441
|
115.8277
|
212.6441
|
1
|
-23.7965
|
17.71229
|
-1.3435
|
0.182413
|
-58.97466951
|
11.3816
|
-58.9747
|
11.3816
|
The residual output of above calculation will be given below
RESIDUAL OUTPUT
| ||
Observation
|
Predicted 267
|
Residuals
|
1
|
140.4394
|
76.56061
|
2
|
140.4394
|
106.5606
|
3
|
140.4394
|
106.5606
|
4
|
140.4394
|
138.5606
|
5
|
140.4394
|
116.5606
|
6
|
140.4394
|
136.5606
|
7
|
140.4394
|
126.5606
|
8
|
140.4394
|
164.5606
|
9
|
140.4394
|
136.5606
|
10
|
140.4394
|
106.5606
|
11
|
140.4394
|
146.5606
|
12
|
140.4394
|
166.5606
|
13
|
140.4394
|
66.56061
|
14
|
140.4394
|
66.56061
|
15
|
140.4394
|
66.56061
|
16
|
140.4394
|
124.5606
|
17
|
116.6429
|
68.35714
|
18
|
116.6429
|
68.35714
|
19
|
116.6429
|
66.35714
|
20
|
140.4394
|
58.56061
|
21
|
140.4394
|
102.5606
|
22
|
140.4394
|
22.56061
|
23
|
140.4394
|
111.5606
|
24
|
140.4394
|
82.56061
|
25
|
140.4394
|
72.56061
|
26
|
140.4394
|
42.56061
|
27
|
140.4394
|
32.56061
|
28
|
140.4394
|
2.560606
|
29
|
116.6429
|
76.35714
|
30
|
116.6429
|
66.35714
|
31
|
140.4394
|
-1.43939
|
32
|
140.4394
|
2.560606
|
33
|
140.4394
|
22.56061
|
34
|
116.6429
|
16.35714
|
35
|
116.6429
|
6.357143
|
36
|
140.4394
|
-7.43939
|
37
|
140.4394
|
-67.4394
|
38
|
140.4394
|
-57.4394
|
39
|
140.4394
|
18.56061
|
40
|
140.4394
|
47.56061
|
41
|
116.6429
|
0.357143
|
42
|
116.6429
|
-5.64286
|
43
|
116.6429
|
60.35714
|
44
|
140.4394
|
-1.43939
|
45
|
140.4394
|
-51.4394
|
46
|
116.6429
|
-19.6429
|
47
|
116.6429
|
-47.6429
|
48
|
116.6429
|
-59.6429
|
49
|
116.6429
|
18.35714
|
50
|
116.6429
|
40.35714
|
51
|
116.6429
|
42.35714
|
52
|
116.6429
|
2.357143
|
53
|
140.4394
|
-101.439
|
54
|
140.4394
|
-21.4394
|
55
|
116.6429
|
-47.6429
|
56
|
140.4394
|
-71.4394
|
57
|
116.6429
|
-87.6429
|
58
|
116.6429
|
-47.6429
|
59
|
140.4394
|
-75.4394
|
60
|
140.4394
|
-36.4394
|
61
|
140.4394
|
-89.4394
|
62
|
140.4394
|
-89.4394
|
63
|
140.4394
|
-97.4394
|
64
|
116.6429
|
-87.6429
|
65
|
140.4394
|
-65.4394
|
66
|
140.4394
|
-71.4394
|
67
|
140.4394
|
-85.4394
|
68
|
140.4394
|
-85.4394
|
69
|
140.4394
|
-85.4394
|
70
|
140.4394
|
-99.4394
|
71
|
140.4394
|
-91.4394
|
72
|
140.4394
|
-89.4394
|
73
|
140.4394
|
-95.4394
|
74
|
140.4394
|
-75.4394
|
75
|
140.4394
|
-75.4394
|
76
|
140.4394
|
-97.4394
|
77
|
140.4394
|
-97.4394
|
78
|
116.6429
|
-51.6429
|
79
|
116.6429
|
-80.6429
|
80
|
116.6429
|
-0.64286
|
81
|
116.6429
|
-42.6429
|
82
|
140.4394
|
-94.4394
|
83
|
140.4394
|
-14.4394
|
84
|
140.4394
|
-74.4394
|
85
|
140.4394
|
-92.4394
|
86
|
140.4394
|
-102.439
|
87
|
140.4394
|
-106.439
|
88
|
140.4394
|
-104.439
|
89
|
116.6429
|
-50.6429
|
90
|
116.6429
|
58.35714
|
91
|
116.6429
|
38.35714
|
92
|
140.4394
|
-28.4394
|
93
|
140.4394
|
45.56061
|
94
|
140.4394
|
-16.4394
|
Price and type
SUMMARY OUTPUT
| ||||||||
Regression Statistics
| ||||||||
Multiple R
|
0.63254
| |||||||
R Square
|
0.400107
| |||||||
Adjusted R Square
|
0.393586
| |||||||
Standard Error
|
61.42111
| |||||||
Observations
|
94
| |||||||
ANOVA
| ||||||||
Df
|
SS
|
MS
|
F
|
Significance F
| ||||
Regression
|
1
|
231486.5
|
231486.5
|
61.3607
|
7.98903E-12
| |||
Residual
|
92
|
347074.9
|
3772.553
| |||||
Total
|
93
|
578561.4
| ||||||
Coefficients
|
Standard Error
|
t Stat
|
P-value
|
Lower 95%
|
Upper 95%
|
Lower 95.0%
|
Upper 95.0%
| |
Intercept
|
287.0064
|
20.61327
|
13.92338
|
2.25E-24
|
246.0666549
|
327.9461
|
246.0667
|
327.9461
|
1
|
-99.611
|
12.71635
|
-7.83331
|
7.99E-12
|
-124.8667935
|
-74.3553
|
-124.867
|
-74.3553
|
The residual output of above calculation will be given below
RESIDUAL OUTPUT
| ||
Observation
|
Predicted 267
|
Residuals
|
1
|
187.3953
|
29.60465
|
2
|
187.3953
|
59.60465
|
3
|
187.3953
|
59.60465
|
4
|
187.3953
|
91.60465
|
5
|
187.3953
|
69.60465
|
6
|
187.3953
|
89.60465
|
7
|
187.3953
|
79.60465
|
8
|
187.3953
|
117.6047
|
9
|
187.3953
|
89.60465
|
10
|
187.3953
|
59.60465
|
11
|
187.3953
|
99.60465
|
12
|
187.3953
|
119.6047
|
13
|
187.3953
|
19.60465
|
14
|
187.3953
|
19.60465
|
15
|
187.3953
|
19.60465
|
16
|
187.3953
|
77.60465
|
17
|
187.3953
|
-2.39535
|
18
|
87.78431
|
97.21569
|
19
|
87.78431
|
95.21569
|
20
|
187.3953
|
11.60465
|
21
|
187.3953
|
55.60465
|
22
|
187.3953
|
-24.3953
|
23
|
187.3953
|
64.60465
|
24
|
187.3953
|
35.60465
|
25
|
187.3953
|
25.60465
|
26
|
187.3953
|
-4.39535
|
27
|
187.3953
|
-14.3953
|
28
|
187.3953
|
-44.3953
|
29
|
87.78431
|
105.2157
|
30
|
87.78431
|
95.21569
|
31
|
187.3953
|
-48.3953
|
32
|
187.3953
|
-44.3953
|
33
|
87.78431
|
75.21569
|
34
|
87.78431
|
45.21569
|
35
|
87.78431
|
35.21569
|
36
|
187.3953
|
-54.3953
|
37
|
187.3953
|
-114.395
|
38
|
187.3953
|
-104.395
|
39
|
187.3953
|
-28.3953
|
40
|
187.3953
|
0.604651
|
41
|
187.3953
|
-70.3953
|
42
|
187.3953
|
-76.3953
|
43
|
187.3953
|
-10.3953
|
44
|
87.78431
|
51.21569
|
45
|
87.78431
|
1.215686
|
46
|
87.78431
|
9.215686
|
47
|
87.78431
|
-18.7843
|
48
|
87.78431
|
-30.7843
|
49
|
87.78431
|
47.21569
|
50
|
87.78431
|
69.21569
|
51
|
87.78431
|
71.21569
|
52
|
187.3953
|
-68.3953
|
53
|
87.78431
|
-48.7843
|
54
|
87.78431
|
31.21569
|
55
|
87.78431
|
-18.7843
|
56
|
187.3953
|
-118.395
|
57
|
187.3953
|
-158.395
|
58
|
187.3953
|
-118.395
|
59
|
87.78431
|
-22.7843
|
60
|
87.78431
|
16.21569
|
61
|
87.78431
|
-36.7843
|
62
|
87.78431
|
-36.7843
|
63
|
87.78431
|
-44.7843
|
64
|
87.78431
|
-58.7843
|
65
|
87.78431
|
-12.7843
|
66
|
87.78431
|
-18.7843
|
67
|
87.78431
|
-32.7843
|
68
|
87.78431
|
-32.7843
|
69
|
87.78431
|
-32.7843
|
70
|
87.78431
|
-46.7843
|
71
|
87.78431
|
-38.7843
|
72
|
87.78431
|
-36.7843
|
73
|
87.78431
|
-42.7843
|
74
|
87.78431
|
-22.7843
|
75
|
87.78431
|
-22.7843
|
76
|
87.78431
|
-44.7843
|
77
|
87.78431
|
-44.7843
|
78
|
87.78431
|
-22.7843
|
79
|
87.78431
|
-51.7843
|
80
|
87.78431
|
28.21569
|
81
|
187.3953
|
-113.395
|
82
|
87.78431
|
-41.7843
|
83
|
87.78431
|
38.21569
|
84
|
87.78431
|
-21.7843
|
85
|
87.78431
|
-39.7843
|
86
|
87.78431
|
-49.7843
|
87
|
87.78431
|
-53.7843
|
88
|
87.78431
|
-51.7843
|
89
|
87.78431
|
-21.7843
|
90
|
87.78431
|
87.21569
|
91
|
87.78431
|
67.21569
|
92
|
187.3953
|
-75.3953
|
93
|
187.3953
|
-1.39535
|
94
|
87.78431
|
36.21569
|
Price and country
SUMMARY OUTPUT
| ||||||||
Regression Statistics
| ||||||||
Multiple R
|
0.058164
| |||||||
R Square
|
0.003383
| |||||||
Adjusted R Square
|
-0.00745
| |||||||
Standard Error
|
79.16714
| |||||||
Observations
|
94
| |||||||
ANOVA
| ||||||||
Df
|
SS
|
MS
|
F
|
Significance F
| ||||
Regression
|
1
|
1957.318
|
1957.318
|
0.3123
|
0.57763
| |||
Residual
|
92
|
576604.1
|
6267.436
| |||||
Total
|
93
|
578561.4
| ||||||
Coefficients
|
Standard Error
|
t Stat
|
P-value
|
Lower 95%
|
Upper 95%
|
Lower 95.0%
|
Upper 95.0%
| |
Intercept
|
146.003
|
24.06721
|
6.066469
|
2.87E-08
|
98.20342
|
193.8025
|
98.20342
|
193.8025
|
1
|
-6.25937
|
11.20069
|
-0.55884
|
0.57763
|
-28.5049
|
15.98617
|
-28.5049
|
15.98617
|
The residual output of above calculation will be given below
RESIDUAL OUTPUT
| ||
Observation
|
Predicted 267
|
Residuals
|
1
|
139.7436
|
77.25639
|
2
|
139.7436
|
107.2564
|
3
|
139.7436
|
107.2564
|
4
|
139.7436
|
139.2564
|
5
|
139.7436
|
117.2564
|
6
|
139.7436
|
137.2564
|
7
|
139.7436
|
127.2564
|
8
|
133.4842
|
171.5158
|
9
|
133.4842
|
143.5158
|
10
|
133.4842
|
113.5158
|
11
|
133.4842
|
153.5158
|
12
|
133.4842
|
173.5158
|
13
|
133.4842
|
73.51576
|
14
|
133.4842
|
73.51576
|
15
|
133.4842
|
73.51576
|
16
|
133.4842
|
131.5158
|
17
|
133.4842
|
51.51576
|
18
|
133.4842
|
51.51576
|
19
|
133.4842
|
49.51576
|
20
|
127.2249
|
71.77513
|
21
|
127.2249
|
115.7751
|
22
|
127.2249
|
35.77513
|
23
|
127.2249
|
124.7751
|
24
|
127.2249
|
95.77513
|
25
|
127.2249
|
85.77513
|
26
|
127.2249
|
55.77513
|
27
|
127.2249
|
45.77513
|
28
|
127.2249
|
15.77513
|
29
|
127.2249
|
65.77513
|
30
|
127.2249
|
55.77513
|
31
|
139.7436
|
-0.74361
|
32
|
139.7436
|
3.256388
|
33
|
139.7436
|
23.25639
|
34
|
139.7436
|
-6.74361
|
35
|
139.7436
|
-16.7436
|
36
|
133.4842
|
-0.48424
|
37
|
133.4842
|
-60.4842
|
38
|
133.4842
|
-50.4842
|
39
|
133.4842
|
25.51576
|
40
|
133.4842
|
54.51576
|
41
|
133.4842
|
-16.4842
|
42
|
133.4842
|
-22.4842
|
43
|
133.4842
|
43.51576
|
44
|
133.4842
|
5.515758
|
45
|
133.4842
|
-44.4842
|
46
|
133.4842
|
-36.4842
|
47
|
133.4842
|
-64.4842
|
48
|
133.4842
|
-76.4842
|
49
|
133.4842
|
1.515758
|
50
|
133.4842
|
23.51576
|
51
|
133.4842
|
25.51576
|
52
|
127.2249
|
-8.22487
|
53
|
127.2249
|
-88.2249
|
54
|
127.2249
|
-8.22487
|
55
|
127.2249
|
-58.2249
|
56
|
139.7436
|
-70.7436
|
57
|
139.7436
|
-110.744
|
58
|
139.7436
|
-70.7436
|
59
|
139.7436
|
-74.7436
|
60
|
139.7436
|
-35.7436
|
61
|
139.7436
|
-88.7436
|
62
|
139.7436
|
-88.7436
|
63
|
139.7436
|
-96.7436
|
64
|
139.7436
|
-110.744
|
65
|
133.4842
|
-58.4842
|
66
|
133.4842
|
-64.4842
|
67
|
133.4842
|
-78.4842
|
68
|
133.4842
|
-78.4842
|
69
|
133.4842
|
-78.4842
|
70
|
133.4842
|
-92.4842
|
71
|
133.4842
|
-84.4842
|
72
|
133.4842
|
-82.4842
|
73
|
133.4842
|
-88.4842
|
74
|
133.4842
|
-68.4842
|
75
|
133.4842
|
-68.4842
|
76
|
133.4842
|
-90.4842
|
77
|
133.4842
|
-90.4842
|
78
|
133.4842
|
-68.4842
|
79
|
133.4842
|
-97.4842
|
80
|
133.4842
|
-17.4842
|
81
|
127.2249
|
-53.2249
|
82
|
127.2249
|
-81.2249
|
83
|
127.2249
|
-1.22487
|
84
|
127.2249
|
-61.2249
|
85
|
127.2249
|
-79.2249
|
86
|
127.2249
|
-89.2249
|
87
|
127.2249
|
-93.2249
|
88
|
127.2249
|
-91.2249
|
89
|
127.2249
|
-61.2249
|
90
|
127.2249
|
47.77513
|
91
|
127.2249
|
27.77513
|
92
|
139.7436
|
-27.7436
|
93
|
139.7436
|
46.25639
|
94
|
139.7436
|
-15.7436
|
Price and intensity
SUMMARY OUTPUT
| ||||||||
Regression Statistics
| ||||||||
Multiple R
|
0.881551
| |||||||
R Square
|
0.777131
| |||||||
Adjusted R Square
|
0.774709
| |||||||
Standard Error
|
37.43736
| |||||||
Observations
|
94
| |||||||
ANOVA
| ||||||||
Df
|
SS
|
MS
|
F
|
Significance F
| ||||
Regression
|
1
|
449618.2
|
449618.2
|
320.7993
|
9.61E-32
| |||
Residual
|
92
|
128943.2
|
1401.556
| |||||
Total
|
93
|
578561.4
| ||||||
Coefficients
|
Standard Error
|
t Stat
|
P-value
|
Lower 95%
|
Upper 95%
|
Lower 95.0%
|
Upper 95.0%
| |
Intercept
|
300.2355
|
10.08592
|
29.76777
|
5.2E-49
|
280.204
|
320.267
|
280.204
|
320.267
|
1
|
-82.5639
|
4.609707
|
-17.9109
|
9.61E-32
|
-91.7191
|
-73.4086
|
-91.7191
|
-73.4086
|
The residual output of above calculation will be given below
RESIDUAL OUTPUT
| ||
Observation
|
Predicted 267
|
Residuals
|
1
|
217.6716
|
-0.67161
|
2
|
217.6716
|
29.32839
|
3
|
217.6716
|
29.32839
|
4
|
217.6716
|
61.32839
|
5
|
217.6716
|
39.32839
|
6
|
217.6716
|
59.32839
|
7
|
217.6716
|
49.32839
|
8
|
217.6716
|
87.32839
|
9
|
217.6716
|
59.32839
|
10
|
217.6716
|
29.32839
|
11
|
217.6716
|
69.32839
|
12
|
217.6716
|
89.32839
|
13
|
217.6716
|
-10.6716
|
14
|
217.6716
|
-10.6716
|
15
|
217.6716
|
-10.6716
|
16
|
217.6716
|
47.32839
|
17
|
217.6716
|
-32.6716
|
18
|
217.6716
|
-32.6716
|
19
|
217.6716
|
-34.6716
|
20
|
217.6716
|
-18.6716
|
21
|
217.6716
|
25.32839
|
22
|
217.6716
|
-54.6716
|
23
|
217.6716
|
34.32839
|
24
|
217.6716
|
5.328387
|
25
|
217.6716
|
-4.67161
|
26
|
217.6716
|
-34.6716
|
27
|
217.6716
|
-44.6716
|
28
|
217.6716
|
-74.6716
|
29
|
217.6716
|
-24.6716
|
30
|
217.6716
|
-34.6716
|
31
|
135.1077
|
3.892258
|
32
|
135.1077
|
7.892258
|
33
|
135.1077
|
27.89226
|
34
|
135.1077
|
-2.10774
|
35
|
135.1077
|
-12.1077
|
36
|
135.1077
|
-2.10774
|
37
|
135.1077
|
-62.1077
|
38
|
135.1077
|
-52.1077
|
39
|
135.1077
|
23.89226
|
40
|
135.1077
|
52.89226
|
41
|
135.1077
|
-18.1077
|
42
|
135.1077
|
-24.1077
|
43
|
135.1077
|
41.89226
|
44
|
135.1077
|
3.892258
|
45
|
135.1077
|
-46.1077
|
46
|
135.1077
|
-38.1077
|
47
|
135.1077
|
-66.1077
|
48
|
135.1077
|
-78.1077
|
49
|
135.1077
|
-0.10774
|
50
|
135.1077
|
21.89226
|
51
|
135.1077
|
23.89226
|
52
|
135.1077
|
-16.1077
|
53
|
135.1077
|
-96.1077
|
54
|
135.1077
|
-16.1077
|
55
|
135.1077
|
-66.1077
|
56
|
52.54387
|
16.45613
|
57
|
52.54387
|
-23.5439
|
58
|
52.54387
|
16.45613
|
59
|
52.54387
|
12.45613
|
60
|
52.54387
|
51.45613
|
61
|
52.54387
|
-1.54387
|
62
|
52.54387
|
-1.54387
|
63
|
52.54387
|
-9.54387
|
64
|
52.54387
|
-23.5439
|
65
|
52.54387
|
22.45613
|
66
|
52.54387
|
16.45613
|
67
|
52.54387
|
2.456129
|
68
|
52.54387
|
2.456129
|
69
|
52.54387
|
2.456129
|
70
|
52.54387
|
-11.5439
|
71
|
52.54387
|
-3.54387
|
72
|
52.54387
|
-1.54387
|
73
|
52.54387
|
-7.54387
|
74
|
52.54387
|
12.45613
|
75
|
52.54387
|
12.45613
|
76
|
52.54387
|
-9.54387
|
77
|
52.54387
|
-9.54387
|
78
|
52.54387
|
12.45613
|
79
|
52.54387
|
-16.5439
|
80
|
52.54387
|
63.45613
|
81
|
52.54387
|
21.45613
|
82
|
52.54387
|
-6.54387
|
83
|
52.54387
|
73.45613
|
84
|
52.54387
|
13.45613
|
85
|
52.54387
|
-4.54387
|
86
|
52.54387
|
-14.5439
|
87
|
52.54387
|
-18.5439
|
88
|
52.54387
|
-16.5439
|
89
|
52.54387
|
13.45613
|
90
|
217.6716
|
-42.6716
|
91
|
217.6716
|
-62.6716
|
92
|
135.1077
|
-23.1077
|
93
|
135.1077
|
50.89226
|
94
|
135.1077
|
-11.1077
|
Conclusion
From the calculation it is observed that the value of mean will be 29 and the value of the median will be 124. On the other hand, it is observed that the value of the mode will be 69 and the value of the standard deviation will be 79.64251.
Price and gender
From the above calculation it is observe that the value of R square is .0192 which is not good fit. 1 per cent of the variation in price is explained by the gender. Here the significance F is .1824. Here, the regression line is in negative slope.
Price and type
From the calculation it is observed that, the value of R square will be .400. It indicates that there is good fit between price of the products and products type. Here, the value of significance F is 7.989.
Price and country
From the calculation it is observed that the value of R square will be .0033 which indicates there is no good fit. Here, the value of significance F will be .57763. The price of the product may not dependent by the area where it is produced.
Price and intensity
From the above calculation, it is observed that the value of the R square will be .777 which is the good fit. It indicates 77 per cent of variation in price is explained by the variables of intensity. Here, the significance F is 9.61.
