Regression Analysis finals

Regression Analysis
Student’s Name
Institutional Affiliation
Regression Analysis
Regression is a statistic concept for data analysis that shows the relationship among a set
of variables. It finds its application in various institutions that deal with numbers like in business,
research centers, finance, and engineering among others. The primary use of regression
technique is for prediction and establishing an inference from a given sample. Therefore, it is
vital to understand the interpretation of regression analysis results and the usefulness of
statistical model and coefficient estimates, which forms the focus of this essay.
Hand calculation accomplishes the regression analysis but is also done using statistical
software such as Excel, SPSS, and Stata, etc. Regression analysis utilizes equations that indicate
the relationship between dependent and independent variables (Ray, 2015). Expression of the
equation depends on the model in play. Some of the models include linear regression for one
single independent variable, multiple regression for more than one independent variable, and
logistic regression. The general regression equation is of the form Y = C
+ C
+ …. + A,
where Y stand for the dependent variable whose value is calculated from the equation. X
is the
individual independent variable, C the coefficients and A is a constant, i.e., the value of y when
all the independent variable are equated to zero. As an illustration, consider the SPSS model
results for estimating the outcome of job performance, the equation formulated by taking into
account the b-coefficient (column 1) establishes the relationship of the variables and hence
allowing estimation of the job performance of any worker.
Job performance = 18.13 + 0.265 x IQ-test + 0.308 x Motivation-test + 0.164 x social-support-
test …. (1)
Table 1. Show the output of an SPSS for job performance estimation. Sourced from
Another aspect of regression analysis is the significance level. It is of particular
importance in hypothesis testing and establishes rejection point of a null hypothesis. T-statistical
is obtained by dividing the coefficients by the standard error. Comparing the t statistic with the
student distribution gives the P value, which is the probability of rejection of a null hypothesis.
For instance, a significance level of 95% indicates the acceptance region of the calculated p-
value. In case of p-value 0.05, it shows significant evidence to drop the null hypothesis (Ray,
2015). P-value with a value more than 0.05 indicates considerable evidence to support the null
hypothesis. Column 3 in the table shows the beta coefficients that shows the strength of variables
compared to the rest. In this case, it has a ratio of 2:2:1 for IQ-test, motivation-test, and social-
support-test respectively.
The estimated coefficients are useful in regression analysis, and their interpretation
depends on the model. For example, in linear regression, the coefficient shows the response of a
change of independent predictor gives the predictor variables. Additionally, the sign of the
coefficient indicates the direction of the effect. The wrong direction suggests a problem in the
analysis known as multicollinearity (Long & Freese, 2014). In case of a single independent
variable, it extrapolates the expected rise (positive coefficient) or decline (negative coefficient)
for a unit change. In multiple regression models, on the other hand, it allows one to determine
change on dependent predictor for a unit change in independent predictors given other
independent variables are constant. However, other models such as logistic regression have no
direct interpretation of the coefficient effects.
In brief, regression analysis is a vital descriptive statistic that shows the relationship
between variables. The choice of a working model is essential and depends on the nature of data.
Interpretation of regression output are useful in prediction and drawing an inference of a sample.
Therefore, the right choice of model, dissemination of sample data, and correct interpretation of
output results form the cornerstone of regression analysis.
Long, J. S., & Freese, J. (2014). Regression models for categorical dependent variables using
Stata. Stata Press books. Retrieved from
Ray, S. (2015). 7 Types of Regression Techniques you should know. Analytics Vidhya. Retrieved
1 April 2018, from
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