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02/26/2012

Sample Correlational Analysis : IKHM


Correlation Analysis

As stated, this paper aimed to forecast the maintenance expenditure with respect to Home value but before we do such forecasting analysis, it is important to consider first the linear relationship of the variables.  This should be done using correlation statistics.

To determine the relationship between independent variables and dependent variables, the use of correlation statistics was employed. On the other hand, the strength of the linear association between two variables is quantified by the correlation coefficient (Guilford & Fruchter, 1973).

Given a set of observations (x1, y1), (x2,y2),...(xn,yn), the formula for computing the correlation coefficient is given by:

            Where:

= Correlation between X and Y

= Sum of Variable X

= Sum of Variable Y

= Sum of the product X and Y

N= Number of Cases

= Sum of squared X score

= Sum of squared Y score

 

Furthermore, the correlation coefficient always takes a value between -1 and 1, with 1 or -1 indicating perfect correlation (all points would lie along a straight line in this case). A positive correlation indicates a positive association between the variables (increasing values in one variable correspond to increasing values in the other variable), while a negative correlation indicates a negative association between the variables (increasing values in one variable correspond to decreasing values in the other variable). A correlation value close to 0 indicates no association between the variables.

Since the formula for calculating the correlation coefficient standardizes the variables, changes in scale or units of measurement will not affect its value. For this reason, the correlation coefficient is often more useful than a graphical depiction in determining the strength of the association between two variables.

In addition, if the correlation index of the computed rxy is not perfect, then it is suggested to use the following categorization (Guilford  & Fruchter, 1973):

                        rxy                                                  Indication

between ± 0.80 to ± 1.00    :           High Correlation

between ± 0.60 to ± 0.79    :           Moderately High Correlation

between ± 0.40 to ± 0.59    :           Moderate Correlation

between ± 0.20 to ± 0.39    :           Low Correlation

between ± 0.01 to ± 0.19    :           Negligible Correlation

 

 

To determine the relationship between maintenance expenditure (independent) and Home Value (dependent), the use of correlation statistics was employed. On the other hand, the strength of the linear association between two variables is quantified by the correlation coefficient (Guilford & Fruchter, 1973).

Basically correlation is a measure of relationship between two variables. Coefficient of correlation determines the validity, reliability and objectivity of an examination prepared.  It also indicates the amount of agreement or disagreement between group of scores, measurements, or individuals. Correlation ranges in value from -1.00 through 0.00 up to -1.00 (Guilford & Fruchter, 1973).

            From the data gathered, the following are results of SPSS correlation analysis:

Table 2. Correlations

 

 

The correlation table shows Pearson correlation coefficients, significance values, and the number of cases with non-missing values. Pearson correlation coefficients presuppose the data are in normal distribution. As stated, the Pearson correlation coefficient is a measure of linear association between two variables. Since the computed correlation value is close to 1 which is 0.943, and then we may say that home value and maintenance expenditure has significant relationship to each other.  In addition, the computed significance relationship (0.000) indicates that the degree of their relationship was very high. Meaning, the home value and maintenance expenditure based on the responses of the surveyed participants has positive and high relationship.

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