The document discusses using linear regression to analyze the relationship between the duration of studying before an exam (independent variable) and exam performance (dependent variable). It provides an overview of linear regression, noting it describes how a dependent variable relates to one or more independent variables. It also discusses key assumptions that must be met for linear regression, such as having continuous and linearly related variables, independence of observations, and normally distributed residuals. Checking tools like histograms and normal P-P plots are recommended to validate meeting the assumptions.

1. Presented By:
Dr. Nur Tasmia Taharat
Dr. Anika Naziat Mazumdar
Dr. Aktar Jahan Priya
How to select the appropriate
method for our study of Interest?
Assigned By:
Azaz Bin Sharif
Assistant Professor, Full Time Faculty
North South University

2. EXAMPLE SCENARIO
A student of North South University wants
to determine whether there is a relationship
between the duration of studying in the
night before the exam and the exam
performance. As such, the individual's "the
duration of studying" is the independent
variable and the "the exam performance" is
the dependent variable.

3. What kind of method we will
use for this Scenario?
LINEAR REGRESSION?

4. Linear regression
• Linear Regression was made in the field of statistics,
• The linear regression model describes how the
dependent variable is related to the independent
variable(s) and the error term
• Used as a model for understanding the association
between the independent and dependent variables
• These models are utilized to foresee the connection
between two quantitative variables where the
predictor variables are known as an independent
variable and the variable which is being predicted is
called a dependent variable.
• A linear relationship is a term used to describe a
straight-line relationship between two variables.
• When we have a single independent variable then we
call it Linear Regression and when there are more
than 2 independent variables we call it Multiple
Linear Regression simple as that.
.

5. What kind of relationship can a Linear Regression
show?
• Positive Relationship - The regression line between the two variables moves in the same direction
with an upward slope.
• Negative Relationship - The regression line between the two variables moves in the same direction
with a downward slope.
• No Relationship - The best fit line is flat (not sloped)
.

6. how do we know what kind of
relationship these variables have?
By using
• Correlation - tells us the direction of the relationship between X and Y but it doesn’t tell us how
positive or negative the relationship is.
• Covariance - tells us the direction of the relationship as well as the strength of the relationship
.

7. Least Square Method
In layman’s terms, the Least square method is the process of fitting the best curve for a set of data
points by reducing the distance between the actual value and predicted value (Sum of Squared
Residuals). The distance between the actual and the predicted value is often known as Error or
Variation or Variance.
The distance between the actual and the predicted value is often known as Error or Variation or
Variance.
The equation of the best fit line for Linear Regression it becomes:
β0 = β1 + X1
Where β0 is the Y-intercept of the regression line
β1 Is the slope of the regression line
Xi Is the explanatory variable

9. Your two variables
should be continuous
variables (i.e., they are
either be interval or
ratio variables)

10. There needs to be a linear relationship
between the two variables.

11. There should be no significant outliers

12. Should have independence of observations
Data needs to show homoscedasticity

13. check that the residuals (errors) of the regression
line are approximately normally distributed
Two common methods to check this assumption include:
• Histogram (with a superimposed normal curve)
• Normal P-P Plot.
If assumptions are not met
• We may be able to ignore "outliers" if we can justify their inclusion.
• We may be able to "transform data" when it is not "normal"
• There may be alternative statistical tests that you can run that don't require the same
assumptions to be met.

14. References
:
• https://statistics.laerd.com/features-assumptions.php
• https://www.analyticsvidhya.com/blog/2021/07/practical-applications-of-linear-
regression-models/
• https://statistics.laerd.com/spss-tutorials/linear-regression-using-spss-
statistics.php
• https://www.youtube.com/watch?v=NOVfLIyY_CA
• https://www.collegeraptor.com/find-colleges/articles/tips-tools-advice/choose-
right-research-topic-5-easy-steps/
• https://sites.google.com/site/econometricsacademy/econometrics-
models/linear-regression

15. For your time and patience