Regression Analysis of Assessed Value using Excel: A Report

This report presents a multiple regression analysis examining the relationship between assessed value (dependent variable) and heating area and age (independent variables). The regression equation is: Assessed Value = 163,775.1236 + 10.7252*Heating Area -284.2543*Age, with an R2 value of 0.8265. Hypothesis testing reveals a significant relationship between heating area and assessed value. The analysis also assesses the normality of the data, finding that assessed value is closest to being normally distributed, while age exhibits a strong positive skew. The report concludes that the normality condition is not fully satisfied for the regression model. Desklib provides students with access to similar solved assignments and past papers to aid in their studies.

BUSINESS RESEARCH METHODOLOGY
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A multiple regression model has been run taking into consideration assessed value as the
dependent variable while there are two independent variables in the form of age and heating
area. The requisite output obtained using Excel is indicated as follows.
The requisite regression equation is indicated as follows.
Accessed Value = 163,775.1236 + 10.7252*Heating Area -284.2543*Age
The intercept of the model is 163,777.1236 while the respective slopes of the two
independent variables are 10.7252 and -284.2543. The R2 value for the above regression
model is 0.8265 which implies that the jointly the variation in the independent variables can
offer explanation for 82.65% of the variation in the dependent variable. Hence, the given
model represents a good fit (Eriksson & Kovalainen, 2015).
In order to ascertain if there is a significant relationship between assessed value and heated
area of house, it needs to be ascertained if the above regression slope is significant or not
through the means of hypothesis testing.
The relevant hypotheses are as stated below.
Null Hypothesis: βHeatingArea = 0
Alternative Hypothesis: βHeatingArea ≠ 0
The level of significance is assumed as 5%.

For the slope coefficient of hearing area, the t statistic is 3.5581 with the corresponding p
value of 0.0039. Since the p value is lower than the level of significance, hence the available
evidence warrants null hypothesis rejection in favour of acceptance of alternative hypothesis
(Flick, 2015). Hence, it may be concluded that the slope is significance which implies that
there is a significant relationship between heating area and assessed value.
Further, one of the key assumptions with regards to linear regression is that the underlying
variables should be normally distributed. In order to ascertain the same, histograms of the
three data have been pasted below.
Assessed Value Histogram
Heating Area Histogram
1333.33337402344
1466.66667402344
1599.99997402344
1733.33327402344
1866.66657402344
0
2
4
6
Heating Area
Frequency
Age Histogram

5.33333349227905
10.6666664922791
15.9999994922791
21.3333324922791
26.6666654922791
0
3
6
9
Age
Frequency
Based on the above histograms it is apparent that dependent variable seems to have negligible
skew and therefore is closest to being normally distributed. With regards to resting area, there
is a slight negative skew as apparent from the histogram. However, for age, there is a very
strong positive skew owing to presence of outliers on the positive side. As a result, age is not
normally distributed (Hillier, 2016). As a result, the condition of normality of data does not
seem satisfied for the given regression model.

References
Eriksson, P. & Kovalainen, A. (2015) Quantitative methods in business research. 3rd ed.
London: Sage Publications.
Flick, U. (2015) Introducing research methodology: A beginner's guide to doing a research
project. 4th ed. New York: Sage Publications.
Hillier, F. (2016) Introduction to Operations Research. 6th ed. New York: McGraw Hill
Publications.