CORRELATION & REGRESSION

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EASWARI ENGINEERING COLLEGE
(AUTONOMOUS)
GROUP PRESENTATION
STATISTICS FOR MANAGERIAL DECISIONS

2. CORRELATION AND
REGRESSION

3. CORRELATION
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 Correlation is a statistical term describing the degree to which two
variables move in coordination with one another.
 If the two variables move in the same direction, then those variables
are said to have a positive correlation.
 If they move in opposite directions, then they have a negative
correlation.
 There is no association or relevant relationship between the two
variables.

4. Model of 3 types of correlation
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5. REAL LIFE APPLICATION
POSITIVE CORRELATION:
◉ When the demand for a product goes up, the price also goes up; when demand
decreases, the price decreases as well.
◉ When an employee works more hours, their paycheck also increases.
◉ Hiring more salespeople will result in the company making more sales.
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6. NEGATIVE CORRELATION:
◉ If a car decreases speed, travel time to a destination increases.
◉ The more time you study or prepare for a test, the fewer mistakes you'll make.
◉ The more you pay off a loan, the less debt you'll be in.
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7. ZERO CORRELATION:
◉ The weight of the student and his/her score in the exams, i.e., one can not
analyze the scores of a person will obtain in any exam by knowing the
weight of that person.
◉ The height of a person and the salary he/she earn, i.e., if you know the
height of a person you can not estimate the income of that person.
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8. REGRESSION
 Regression analysis is a predictive modeling technique that
analyzes the relation between the target or dependent
variable and independent variable in a dataset.
 It involves determining the best fit line, which is a line that
passes through all the data points in such a way that
distance of the line from each data point is minimized.
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9. TYPES OF REGRESSION
1. Linear Regression
2. Logistic Regression
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10. LINEAR REGRESSION:
It is 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.
FOR EXAMPLE,
Suppose we want to predict the price of a house based on its Area, Garage
Area, Land Contour, Utilities, etc. So here “price” will be the dependent variable
and “Area, Garage Area, Land Contour, Utilities” will be the independent variable.

11. REAL LIFE EXAMPLES OF LINEAR REGRESSION
◉ Businesses frequently use Linear regression to comprehend the
connection between advertising spending and revenue.
For example, they might use the Liner regression model using
advertising spend as an independent variable or predictor variable and
revenue as the response variable.
◉ Agriculture scientists frequently use Linear regression to see the
impact of rainfall and fertilizer on the number of fruits/vegetables
yielded
For example, scientists might use different amounts of fertilizer and
see the effect of rain on different fields and see how it affects crop
yield. They might fit a multiple linear regression using rainfall and
fertilizer as the predictor variables and crop yield as the dependent
variable or response variable.
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12. KINDS OF RELATIONSHIP OF A LINEAR REGRESSION
1. Positive Relationship :
When the regression line between the two variables moves in the
same direction with an upward slope then the variables are said to be
in a Positive Relationship, it means that if we increase the value of x
(independent variable) then we will see an increase in our dependent
variable.
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2. Negative Relationship :
When the regression line between the two variables moves in the
same direction with a downward slope then the variables are said to
be in a Negative Relationship it means that if we increase the value of
an independent variable (x) then we will see a decrease in our
dependent variable (y)

14. 3. No Relationship :
If the best fit line is flat (not sloped) then we can say that there is no
relationship among the variables. It means there will be no change in
our dependent variable (y) by increasing or decreasing our
independent variable (x) value.
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15. LOGISTIC REGRESSION:
 Logistic regression is one of the types of regression analysis technique, which gets
used when the dependent variable is discrete. Example: 0 or 1, true or false, etc.
 Logistic regression predicts the probability of an outcome that can only have two values
(i.e. a dichotomy). The prediction is based on the use of one or several predictors
(numerical and categorical).
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REAL LIFE EXAMPLE OF LOGISTIC REGRESSION
Medical researchers want to know how exercise and weight impact the probability of having a heart
attack. To understand the relationship between the predictor variables and the probability of having a
heart attack, researchers can perform logistic regression.
The response variable in the model will be heart attack and it has two potential outcomes:
• A heart attack occurs.
• A heart attack does not occur.
The results of the model will tell researchers exactly how changes in exercise and weight affect the
probability that a given individual has a heart attack. The researchers can also use the fitted logistic
regression model to predict the probability that a given individual has a heart attacked, based on their
weight and their time spent exercising.

17. LEAST SQUARE METHOD
The least-squares method is a form of mathematical
regression analysis used to determine the line of best fit
for a set of data, providing a visual demonstration of the
relationship between the data points. Each point of data
represents the relationship between a known
independent variable and an unknown dependent
variable.
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18. APPLICATION OF LEAST SQUARE
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To illustrate, consider the case of an investment considering whether to invest in a
gold mining company. The investor might wish to know how sensitive the company’s
stock price is to changes in the market price of gold. To study this, the investor could
use the least-squares method to trace the relationship between those two variables
over time onto a scatter plot. This analysis could help the investor predict the degree
to which the stock’s price would likely rise or fall for any given increase or decrease
in the price of gold.

19. THANK YOU
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