Statistics_Computer assessment Essay Example

AFE135 Business Data Analysis

QUESTION 1

1. The survey method is using questionnaire. This is the most appropriate due to large population and various question which will be asked. The questionnaire will consist of both close ended and open ended questionnaire.

2. Simple random sampling is the most appropriate method of sampling technique to be used in this study. This is because it is simple and very much objective in dealing with large population

3. Two main variables is expenditure verses income

4. Reliability of the information which are being provided by the respondent may be in doubt since there is no way the researcher can authenticate the information.

QUESTION TWO

1. The recommended graphical comparison of each weekly take-home pay category should be histograms since they are more clearly giving the level of each frequency at every weekly take-home category. This is shown in the diagram below:-

From the graph, it can be seen that group three has the highest frequency of 35 followed by group six with frequency of 30. This is followed closely by group four and two with 26 and 25 respectively group five is the second lowest with 19 frequency and the lowest is group one with 15.

2. Pie chart is the most appropriate in this case as it shows frequency and even the percentage of the proportion. This is shown in the figure below:-

From the figure above, group 3 is having the highest propotion of 20% folloed closely by group 2 with 19%, group 4 having 18% while group five having 17%. Group 6 and group 1 are having 13% each and are the lowest.

Question three

1. To determine the number of classes, the following formula is most appropriate

To create grouping for characteristics with equal amplitude you just divide the range (max value -min value) by the amplitude. if you have age between 10 and 90 yrs, if you want classes of 10 yrs amplitude (deciles) then the number of classes is : range/10=(90-10)/10=8 classes.

2. Class width

The number of classes is what you want like in this case it is eight. From the data we have

Weekly take home pay

Highest = 1090

Lowest = 105

Class you need = 8

= (1090-105)/8

Highest = 375

Lowest = 44

Class you need = 8

= (373-44)/8

3. Histograms

From the two graphs, take home pay is not normally distributed but it tends to move to left, that is , it is left handed distributed while weekly expenditure is normally distributed to the center.

Question four

1. descriptive statistics

Take-home pay	Weekly food expenditure
	501.5866667		197.991266
Standard Error	19.40476241	Standard Error	6.756779581
			190.87045
Standard Deviation	237.6588324	Standard Deviation	82.75331139
Sample Variance	56481.72063	Sample Variance	6848.110547
Kurtosis	-0.777016935	Kurtosis	-0.909166653
Skewness	0.32628762	Skewness	0.088943042
			329.1642
			373.4779
			29698.6899
Largest(1)		Largest(1)	373.4779
Smallest(1)		Smallest(1)
Confidence Level (95.0%)	38.34406623	Confidence Level (95.0%)	13.35148549

2. Correlation coefficient

	Take-home pay	Weekly food expenditure
Take-home pay
Weekly food expenditure	0.994480486

The correlation coefficient is positively correlated and is new 1 or 1 hence there are perfectly positive correlation

Question five

1. From the analysis, food expenditure depends on weekly pay hence food expenditure is the dependent variable while weekly pay is the independent variable in this case

2. Line graph

3. Regression output

Regression Statistics
Multiple R	0.994480486
	0.988991437
Adjusted R Square	0.988917054
Standard Error	8.711902022
Observations
					Significance F
Regression		1009135.68	1009135.68	13296.08	8.1E-147
Residual		11232.79105	75.89723684
		1020368.471
	Coefficients	Standard Error			Lower 95%
Intercept	24.30172358	1.665810737	14.5885262	1.94E-30	21.00988
Take-home pay	0.346280222	0.003003073	115.3086263	8.1E-147	0.340346

From the coefficient table above, the linear equation will be given by

y = 0.3463x + 24.302

The coefficient indicates that it is positively related and a unit increase in weekly pay increases food expenditure by 0.3463 while the intercept where even if there is no monthly income food expenditure will still be 24.302.

4. Correlation coefficient (R²)

From the table, the correlation coefficient is given as 0.988 indicating that 98.8% of the dependent variables is explained by independent variables in the model.