Any Statistical Study Of Mass Social Phenomena Includes 3 Main Stages: Term Paper Example

Business Statistics 2

Introduction

Statistical observation is a formed primary statistical data, or initial statistical information, which is the basis of statistical research. If the collection of primary statistical data, or material mistake turned out to be bad quality, it will affect the accuracy and reliability of both theoretical and practical conclusions;
Summary and grouping of data - at this stage of the totality of shares on the basis of differences and combined on the basis of similarity calculated totals in groups and as a whole. Using the method of the phenomena groups depending from the essential features are divided into types, groups, and subgroups. Method allows you to restrict groups qualitatively similar materially aggregate that is a prerequisite for the definition and application of general indicators;
Processing and analysis of data, identification of patterns. At this stage, with the help of general indicators are calculated relative and average values, given a summary assessment of variation of features that characterize the dynamics of phenomena, applied indexes, the balance of construction, calculated indicators describing the closeness of the relationship in changing signs. For the purpose of the most rational and intuitive presentation of digital material, it appears in the form of tables and graphs.

In this study we demonstrate basic statistical tools of hypothesis testing.

Data Description
We are given with a data set of Buena School District Bus. There are 80 observations in this data set: each bus is characterized by 7 factors (variables):

X1, bus number

X2, maintenance
X3, age of the bus
X4, mileage of the bus
X5, type of engine
X6, bus manufacturer
X7, the amount of passenger seats in the bus
We begin with descriptive statistics of this data. It helps us to visualize the data and gives us an idea which hypothesis to test.

Descriptive Statistics: Maintenance; Age; Miles

Results for Type = Diesel; Bus-Mfg = Bluebird

Variable Passenger N N* Mean SE Mean StDev Minimum Q1

Maintenance 14 Passenger 1 0 458,00 * * 458,00 *
42 Passenger 4 0 458,8 15,6 31,2 432,0 432,3
55 Passenger 25 0 439,5 10,6 53,1 329,0 392,0
6 Passenger 2 0 403,5 46,5 65,8 357,0 *

Age 14 Passenger 1 0 4,0000 * * 4,0000 *

42 Passenger 4 0 7,500 0,866 1,732 6,000 6,250
55 Passenger 25 0 6,640 0,550 2,752 1,000 4,500
6 Passenger 2 0 7,00 1,00 1,41 6,00 *

Miles 14 Passenger 1 0 817,00 * * 817,00 *

42 Passenger 4 0 819,50 2,63 5,26 815,00 815,50
55 Passenger 25 0 834,3 10,1 50,3 741,0 807,0
6 Passenger 2 0 808,0 48,0 67,9 760,0 *

Variable Passenger Median Q3 Maximum

Maintenance 14 Passenger 458,00 * 458,00
42 Passenger 454,5 489,5 494,0
55 Passenger 441,0 490,5 505,0
6 Passenger 403,5 * 450,0

Age 14 Passenger 4,0000 * 4,0000

42 Passenger 7,000 9,250 10,000
55 Passenger 7,000 9,000 10,000
6 Passenger 7,00 * 8,00

Miles 14 Passenger 817,00 * 817,00

42 Passenger 818,00 825,00 827,00
55 Passenger 835,0 855,0 1008,0
6 Passenger 808,0 * 856,0
Results for Type = Diesel; Bus-Mfg = Keiser

Variable Passenger N N* Mean SE Mean StDev Minimum Q1

Maintenance 14 Passenger 3 0 475,7 20,9 36,1 444,0 444,0
42 Passenger 5 0 455,4 16,3 36,5 403,0 425,5
55 Passenger 7 0 461,3 19,9 52,5 380,0 428,0

Age 14 Passenger 3 0 6,67 3,71 6,43 2,00 2,00

42 Passenger 5 0 8,00 1,05 2,35 4,00 6,00
55 Passenger 7 0 7,286 0,522 1,380 6,000 6,000

Miles 14 Passenger 3 0 817,3 40,8 70,6 757,0 757,0

42 Passenger 5 0 825,0 15,9 35,7 790,0 798,0
55 Passenger 7 0 824,14 9,55 25,27 799,00 803,00

Variable Passenger Median Q3 Maximum

Maintenance 14 Passenger 468,0 515,0 515,0
42 Passenger 452,0 487,0 503,0
55 Passenger 462,0 493,0 546,0

Age 14 Passenger 4,00 14,00 14,00

42 Passenger 9,00 9,50 10,00
55 Passenger 7,000 9,000 9,000

Miles 14 Passenger 800,0 895,0 895,0

42 Passenger 815,0 857,0 883,0
55 Passenger 816,00 842,00 870,00
Results for Type = Diesel; Bus-Mfg = Thompson

Variable Passenger N N* Mean SE Mean StDev Minimum Q1

Maintenance 14 Passenger 1 0 570,00 * * 570,00 *
55 Passenger 4 0 513,5 23,2 46,4 457,0 466,8
6 Passenger 1 0 459,00 * * 459,00 *

Age 14 Passenger 1 0 9,0000 * * 9,0000 *

55 Passenger 4 0 8,25 2,25 4,50 2,00 3,50
6 Passenger 1 0 11,000 * * 11,000 *

Miles 14 Passenger 1 0 844,00 * * 844,00 *

55 Passenger 4 0 834,75 6,88 13,77 815,00 820,75
6 Passenger 1 0 859,00 * * 859,00 *
Variable Passenger Median Q3 Maximum

Maintenance 14 Passenger 570,00 * 570,00

55 Passenger 518,0 555,8 561,0
6 Passenger 459,00 * 459,00

Age 14 Passenger 9,0000 * 9,0000

55 Passenger 9,50 11,75 12,00
6 Passenger 11,000 * 11,000

Miles 14 Passenger 844,00 * 844,00

55 Passenger 838,50 845,00 847,00
6 Passenger 859,00 * 859,00
Results for Type = Gasoline; Bus-Mfg = Bluebird

Variable Passenger N N* Mean SE Mean StDev Minimum Q1

Maintenance 55 Passenger 15 0 445,2 16,8 65,0 337,0 396,0
Age 55 Passenger 15 0 7,267 0,746 2,890 2,000 5,000
Miles 55 Passenger 15 0 842,5 12,6 48,6 784,0 806,0
Variable Passenger Median Q3 Maximum

Maintenance 55 Passenger 439,0 497,0 558,0

Age 55 Passenger 8,000 10,000 11,000
Miles 55 Passenger 842,0 865,0 980,0
Results for Type = Gasoline; Bus-Mfg = Keiser

Variable Passenger N N* Mean SE Mean StDev Minimum Q1

Maintenance 14 Passenger 2 0 429,50 2,50 3,54 427,00 *
55 Passenger 7 0 432,9 15,8 41,8 359,0 406,0
6 Passenger 1 0 382,00 * * 382,00 *

Age 14 Passenger 2 0 5,500 0,500 0,707 5,000 *

55 Passenger 7 0 6,286 0,969 2,563 3,000 4,000
6 Passenger 1 0 3,0000 * * 3,0000 *

Miles 14 Passenger 2 0 808,5 28,5 40,3 780,0 *

55 Passenger 7 0 812,6 15,6 41,3 751,0 775,0
6 Passenger 1 0 818,00 * * 818,00 *

Variable Passenger Median Q3 Maximum

Maintenance 14 Passenger 429,50 * 432,00
55 Passenger 449,0 469,0 474,0
6 Passenger 382,00 * 382,00

Age 14 Passenger 5,500 * 6,000

55 Passenger 7,000 9,000 9,000
6 Passenger 3,0000 * 3,0000

Miles 14 Passenger 808,5 * 837,0

55 Passenger 817,0 857,0 864,0
6 Passenger 818,00 * 818,00
Results for Type = Gasoline; Bus-Mfg = Thompson

Variable Passenger N N* Mean SE Mean StDev Minimum Q1 Median

Maintenance 55 Passenger 2 0 485,5 18,5 26,2 467,0 * 485,5
Age 55 Passenger 2 0 7,500 0,500 0,707 7,000 * 7,500
Miles 55 Passenger 2 0 846,5 19,5 27,6 827,0 * 846,5
Variable Passenger Q3 Maximum
Maintenance 55 Passenger * 504,0
Age 55 Passenger * 8,000
Miles 55 Passenger * 866,0
Statistical Hypotheses
According to the descriptive statistics stored above we want to test if there any association between mileage of the bus and its age. It’s natural to assume that there is a positive association between these two factors.

Construct a scatterplot of Miles and Age:

It seems that there is some positive association between the variables. Let’s perform correlation analysis:
Null hypothesis: there is no linear association between the variables
Alternative hypothesis: there is a significant linear association between the variables:
H0: ρ=0Ha: ρ≠0
Set level of significance alpha = 0.05

Correlations: Age; Miles

Pearson correlation of Age and Miles = 0,522
P-Value = 0,000
Since p-value of the test is lesser than 0.05 we can reject the null hypothesis and say that there is a significant linear association between the variables (at 5% level of significance).
The coefficient of correlation is 0.522 which is an evidence of moderate positive linear association between the variables. Now we can perform regression analysis to predict the possible age of bus with given mileage.

We test the following regression equation:

y=β0+β1x

Where y is Age, x is Miles, betas 0 and 1 are the coefficients of linear regression

H0: β0=β1=0Ha: β0,β1≠0
Set level of significance alpha = 0.05

Perform regression testing:

Regression Analysis: Age versus Miles
The regression equation is
Age = - 21,3 + 0,0340 Miles

Predictor Coef SE Coef T P

Constant -21,261 5,235 -4,06 0,000
Miles 0,034045 0,006298 5,41 0,000
S = 2,36162 R-Sq = 27,3% R-Sq(adj) = 26,3%

Analysis of Variance

Source DF SS MS F P
Regression 1 162,97 162,97 29,22 0,000
Residual Error 78 435,03 5,58
Total 79 598,00
According to the analysis of variance results, we have F value of 29.22 which is significant (p-value is less than 0.001). Also, all coefficients of the regression equation are also significant.
That’s why our regression equation is significant. However, coefficient of determination R-squared is only 0.273, which means that only 27.3% of response variable’s variation is explained by this model. This is a weak indicator. However, the regression may be improved if we add some new variables or test more observations.

The regression equation is:

Age = - 21.3 + 0,0340 Miles

Works Cited

Lindley, D.V. (1987). "Regression and correlation analysis," New Palgrave: A Dictionary of Economics, v. 4, pp. 120–23.