Correlation Analysis of Annual Income and Expenditure in New York Suburb

The objective of the given task is to analyse the underlying relationship between annual income of household and the underlying expenditure. In this regards, data has been collected from 30 households randomly selected across a suburb in New York. The face to face survey method has been used to collect the required data. The scatter plot for annual income as the independent variable and annual expenditure as the dependent variable is indicated. The linear regression equation is indicated. It may be concluded that moderate strength positive correlation exists between annual income and annual expenditure. Further, the slope of the regression line obtained is significant but more independent variables are required to be inserted for enhancing the fit of the model.

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Introduction
The objective of the given task is to analyse the underlying relationship between annual
income of household and the underlying expenditure. In this regards, data has been collected
from 30 households randomly selected across a suburb in New York. The face to face survey
method has been used to collect the required data. Considering the nature of information and
the fact that certain clarification may be required, face to face survey was preferred. Also, the
sample size 30 was chosen as it is least number of samples required in order to assume the
underlying distribution is normal.
Correlation and Regression Analysis
The scatter plot for annual income as the independent variable and annual expenditure as the
dependent variable is indicated as follows.
It is apparent from above that there is a positive correlation between income and expenditure
which is evident from the positive sloping best fit line. However, the magnitude of correlation
is 0.5879 which is only moderate and not high. This highlights that while income may be a
significant variable impacting the expenditure of households, there are other variables that
may be driving the same (Flick, 2015).
The output of the regression analysis is as highlighted below.

The linear regression equation is indicated as follows.
Annual expenditure = 5037.07 + 0.0537* Annual Income
The intercept value is $5,037.07 which is the annual expenditure when there is no income.
Further, the slope of the regression equation is 0.0537 which implies that as the annual
income increases by $ 1, the annual expenditure would increase by 0.0537. Further, the
coefficient of determination is 0.3456 which implies that income as an independent variable
can account for only 34.56% of the changes witnessed in dependent variable expenditure
(Hillier, 2016).
The slope coefficient is significant as is apparent from the p value of the slope which is lower
than 0.05 (assumed significance level). Also, the regression model is significant as
determined from the ANOVA output. The significance F value is 0.0006 which is lower than
the assumed significance level of 0.05 thus indicating the slope canoe be assumed as zero.
However, it is imperative that other additional independent variables need to be introduced in
order to enhance the predictive power of the model (Eriksson & Kovalainen, 2015).
Conclusion
It may be concluded that moderate strength positive correlation exists between annual income
and annual expenditure. Further, the slope of the regression line obtained is significant but
more independent variables are required to be inserted for enhancing the fit of the model.

References
Eriksson, P. & Kovalainen, A. (2015). Quantitative methods in business research London:
Sage Publications.
Flick, U. (2015). Introducing research methodology: A beginner's guide to doing a research
project New York: Sage Publications.
Hillier, F. (2016). Introduction to Operations Research.New York: McGraw Hill Publications