1. Find a subject area of interest where you can gather sample data. (Note: Make sure the...

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1. Find a subject area of interest where you can gather sample data. (Note: Make sure the "population" for your area of interest is large enough that it is reasonable to gather data from a "sample" rather than doing a complete census.) o The project should not involve research on human subjects because such research requires approval of EIU's Institutional Review Board (IRB) and there is not enough time to obtain such approval before the end of the semester. However, there are still a lot of possibilities for projects where the data is about humans as long as the data is already publicly available. An example is in the area of sports where large quantities of data are generally available, both about physical characteristics of the athletes and about their performance. Doing a project involving such publicly available data would not require IRB approval. 2. Identify a few variables for which you can collect sample data. 3. Include both categorical and quantitative data. 4. Include some variables you believe are interrelated. 5. Develop descriptive statistics (graphical and numerical) to describe the sample data you collected (including correlation and other measures for interrelated variables). 6. Make inferences about the broader population from which your sample data was drawn: o Confidence intervals about population parameters. o Hypothesis tests about population parameters. o Regression between interrelated variables. These optional projects will be assessed based on the report you write including your data analysis. You should submit both a written report (in Microsoft Word .doc or .docx format, or .rtf or .pdf format) and one or more Microsoft Excel files. The written report should describe your subject area, your questions of interest, any hypotheses you made, how you defined your variables, how you collected your data, summaries of the data (including interrelationships where appropriate), how you analyzed the data, and summaries of your analyses and results (including inferences about the broader population parameters). The Microsoft Excel files should contain your sample data, your descriptive statistics (including their calculation), and your analysis of your sample data (including inferences about the population).

Rajeswari · Accepted Answer

48414 Assignment
The subject of interest was the market prices of houses in Sydney of late.  I took interest to study about the real estate and hence how the market prices of built houses is influenced by some factors.  
Here I have taken a sample of 400 prices of houses in cities around Sydney.  I collected these data from internet sources and grouped according to my convenience. The variables I included were Market price, Sydney price index, total number of square metres and age of the house.
According to common sense we know that a house price is determined by its location, access to nearby schools, markets. Age of the house is inversely associated with price in the sense when age of the house increases the price decreases.
So we can make age of the house as qualitative variable with 0 – 5 years very new, with value attached as 5, >5 – 10 years as new with value attached as 4, >10-15 years with value 3, >15-20 with value 2, >20 -30 with value 1 and above 30 years with value 0.5.  This is segregating the house according to age categorically and assigning values.
Now mean, median, mode and other descriptive values are found out using the excel tools. 
We got 
	 
	Market Price ($000)
	 
	Sydney price Index
	 
	Total number of square meters
	 
	Age of house (years)
	 
	
	
	
	
	
	
	
	
	
	200.5
	Mean
	777.0375
	Mean
	106.0568
	Mean
	209.4885
	Mean
	17.755
	5.780715
	Standard Error
	3.969241
	Standard Error
	1.480512
	Standard Error
	2.267691
	Standard Error
	0.574074
	200.5
	Median
	777.5
	Median
	105.9
	Median
	211
	Median
	16.5
	#N/A
	Mode
	748
	Mode
	120.9
	Mode
	234.4
	Mode
	12
	115.6143
	Standard Deviation
	79.38483
	Standard Deviation
	29.61024
	Standard Deviation
	45.35382
	Standard Deviation
	11.48149
	13366.67
	Sample Variance
	6301.951
	Sample Variance
	876.7663
	Sample Variance
	2056.969
	Sample Variance
	131.8245
	-1.2
	Kurtosis
	-0.03229
	Kurtosis
	0.001878
	Kurtosis
	0.163011
	Kurtosis
	-0.2305
	2.24E-17
	Skewness
	-0.1442
	Skewness
	0.050154
	Skewness
	-0.00848
	Skewness
	0.553923
	399
	Range
	430
	Range
	177.3
	Range
	263.5
	Range
	54
	1
	Minimum
	541
	Minimum
	19.8
	Minimum
	84.7
	Minimum
	0
	400
	Maximum
	971
	Maximum
	197.1
	Maximum
	348.2
	Maximum
	54
	80200
	Sum
	310815
	Sum
	42422.7
	Sum
	83795.4
	Sum
	7102
	400
	Count
	400
	Count
	400
	Count
	400
	Count
	400
	11.36447
	Confidence Level(95.0%)
	7.80324
	Confidence Level(95.0%)
	2.910579
	Confidence Level(95.0%)
	4.458115
	Confidence Level(95.0%)
	1.128588
We find that maximum age of years is 54 and minimum is 0.  We made it as categorical variable with very new, new….old, very old etc and assigned weights assuming that old houses have low prices.
The mean represents the average value of the variable, Median the middle value and mode the highest repeated value.
Range is the value giving the difference between maximum and minimum.
Variance is a measure of dispersion showing how the values are deviated from the mean.  The higher the variance the more variable is the data.
The standard deviation is the square root of variance.
Confidence intervals here represents the margin of error.
Margin of error for 95%= 1.96 * std error 
Std error = std dev/sqrt n
The interpretation of margin of error is for large samples randomly drawn we expect the average to be within this value from either side of mean  with 95% confidence.
Once we completed these descriptive statistics, we find that mean, median are almost equal thus representing the symmetric distribution of data. 
Now let us check correlation i.e. measure of association between the variables.  Here price of house is dependent variable while Sydney price index, area of house in sqm and age are independent variables.
i) Price vs Sydney price index
We find regression equation as Price = 0.02 (Sydney price index)+90.51322
i.e. slope is very low showing low impact of this variable on price.  Also correlation coefficient is 0.05 nearly 0 showing very weak association.  
Hypothesis test for slope =0 is done and results show a p value of 0.28 which makes us accept that slope is almost 0.
i.e. Sydnes price index does not influence price so we can leave this as independent variable. The scatter plot also confirms that there cannot be a linear relation between these two.
ii)   Price Vs square metres.
Here the scatter plot shows a trend of a line very perfectly.  Let us confirm this using statistical tools
	SUMMARY OUTPUT
	
	
	
	
	
	
	
	
	
	
	
	
	
	
	
	
	Regression Statistics
	
	
	
	
	
	
	
	Multiple R
	0.996855
	
	
	
	
	
	
	
	R Square
	0.993719
	
	
	
	
	
	
	
	Adjusted R Square
	0.993703
	
	
	
	
	
	
	
	Standard Error
	6.299283
	
	
	
	
	
	
	
	Observations
	400
	
	
	
	
	
	
	
	
	
	
	
	
	
	
	
	
	ANOVA
	
	
	
	
	
	
	
	
	 
	df
	SS
	MS
	F
	Significance F
	
	
	
	Regression
	1
	2498685
	2498685
	62969.38
	0
	
	
	
	Residual
	398
	15793.02
	39.68096
	
	
	
	
	
	Total
	399
	2514478
	 
	 
	 
	
	
	
	
	
	
	
	
	
	
	
	
	 
	Coefficients
	Standard Error
	t Stat
	P-value
	Lower 95%
	Upper 95%
	Lower 95.0%
	Upper 95.0%
	Intercept
	411.5137
	1.490299
	276.1284
	0
	408.5838607
	414.4435
	408.5839
	414.4435
	Total number of square meters
	1.744839
	0.006953
	250.937
	0
	1.731169666
	1.758509
	1.73117
	1.758509
The r is 0.99 almost near to 1.  Hence perfect linear positive relationship
Slope is 1.7448 and intercept is 411.5137
i.e. Price of house = 1.7448(area in square metres)+411.5137
The hypothesis test for slope =0 shows a p value =0 stating that the slope is almost 100% perfect.
Thus price of house is predicted from area in square metres with almost 100% accuracy.

1. Find a subject area of interest where you can gather sample data. (Note: Make sure the "population" for your area of interest is large enough that it is reasonable to gather data from a "sample"...

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