This presentation all about the regression and multiple regression equation of multiple regression and the most important thing is the research question of multiple regression with examples

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2. Multiple Regression
Presented by:
Muhammad Imran
Rashna Asif
Sonia Javed
Tahira Gillani 2

3. Content
General purpose and Description
Kinds of Research Question
Limitation to Regression Analysis
Fundamental Equations for
Multiple Regressions
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4. Multiple Regression
• Multiple regression is an extension of simple regression.
• It is a study of more than two variables.
• It is used for prediction.
• It is used when we want to predict the value of a variable based on the value of
two or more other variables.
• The variable we want to predict is called the dependent variable and the variable
we are using to predict the dependent variable is called independent variables.
• The dependent variable is variously known as explained variables, predictand
and response variables.
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• While the independent variable is known as explanatory and regressor variable.
• Here we try to predict the change in Dependent variable according to change in
independent variable.
• The objective of multiple regression is to develop a prediction equation that
permits the estimation of the value of the dependent variable based on the
knowledge of multiple independent variables.
• It is used to estimate the relationship that exists, on the average between the
dependent variable and independent variable.
• It is used to determine the effect of the each independent variable on the
dependent variable, controlling the effects of all other independent variables.
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6. Example 1:
Predicting Final Exam Grades
Assignments
Midterm
Multiple
Regression
Final
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7. Example 2:
“Does ‘ignoring problems’ (IV1) and ‘worrying’ (IV2)
predict
‘psychological distress’ (DV)”
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8. Example 3:
Effect of violence, stress, social support
On
internalizing behavior problems
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9. Kinds of Research Question
Research Question 1
How well do these three IVs:
• No of cigarettes / day (IV1)
• Exercise (IV2) and
• Cholesterol (IV3)
predict
• CHD (Cigarettes & coronary
heart disease) mortality (DV)?
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Cigarettes
Exercise CHD Mortality
Cholesterol

10. Research Question 2
To what extent do personality factors (IVs) predict annual income (DV)?
Extraversion
Neuroticism Income
Psychoticism
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11. Research Question 3
“Does the # of years of formal study of psychology (IV1) and the no. of
years of experience as a psychologist (IV2) predict clinical psychologists’
effectiveness in treating mental illness (DV)?”
Study
Experience
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Effectiveness

12. Limitation to Regression Analysis
Multiple regression is the most powerful technique available to researchers. But
powerful techniques have high demands. So, this technique requires:
• Every variable is measured at the interval-ratio level
• Independent variable does not interact with each other
• Independent variables are uncorrelated with each other
• More difficult to implement
• Best to have a lot of data points
• It involves very lengthy and complicated procedure of calculations and analysis.
• It cannot be used in case of qualitative phenomenon.
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13. Fundamental Equation for Multiple
Regressions
𝑦 = 𝛽0 + 𝛽1 𝑥1 + 𝛽2 𝑥2 + ⋯ 𝛽 𝑛 𝑥 𝑛 + 𝜀
𝒚 = 𝜷 𝟎 + 𝜷 𝟏 𝒙 𝟏 + 𝜷 𝟐 𝒙 𝟐 + ⋯ 𝜷 𝒏 𝒙 𝒏 + 𝜺
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Dependent
Variable
Coefficients
Independent
Variable
Number of
Observations
Random
Error Term

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• Dependent Variable: The single variable being predicted by the
regression model
• Independent Variable: The independent variables used to predict the
dependent variable.
• Coefficients (β): Values, computed by the regression tool, reflecting
independent variable to dependent variable relationships.
• Random Error Term (ε): The portion of the dependent variable that isn’t
explained by the model; the model under and over predictions.
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