The document explains regression analysis, focusing on the dependence of a dependent variable on one or more independent variables. It distinguishes between simple and multiple regression models, and provides examples to determine regression equations and predictions based on given data points. Additionally, it includes a practice problem related to inductive reactance in electrical circuits.

1. STATISTICS & PROBABILITY
COURSE CODE: MTH317

2. REGRESSION
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□ Regression investigates dependence of one
variable, called dependent variable, on one or
more other variables, called the independent
variables.
□ Regression provides an equation for estimating or
predicting value of dependent variable
the value of independent
corresponding
to variable.
□ The dependence of one variable
on variable is
known as
a
single
simple
independent
regression.

3. □ The dependence of one variable on two or more
independent variables is called multiple regression.
□ When the dependence is represented by a straight
line equation, the regression is said to be linear,
otherwise curvilinear.
□ The dependent variable is also called the regressand,
the predictand, the response or the explained
variable. The independent variable is also referred to
as the regressor, the predictor, the regression
variable or the explanatory variable.
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4. SIMPLE LINEAR REGRESSION MODEL
□
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5. EXAMPLE 1
Determine equation of regression line for Y on X for the
following data:
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X 14 18 23 30 50
Y 900 1200 1600 2100 3800
Use regression equation to estimate Y at X = 20.
Solution
X Y X2
XY
14 900 196 12600
18 1200 324 21600
23 1600 529 36800
30 2100 900 63000
50 3800 2500 190000

6. □
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7. Thus, the regression equation is
Y = -256.119+80.597X
At X = 20,
Y = -256.119+80.597(20) = 1355.821
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8. EXAMPLE 2
Consider the following data:
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X 2 4 6 8 10 12 14
Y 5 11 15 19 24 28 33
Find regression equation for Y on X. Estimate Y at X = 3.
Solution
X Y X2
XY
2 5 4 10
4 11 16 44
6 15 36 90
8 19 64 152
10 24 100 240
12 28 144 336
14 33 196 462

9. □
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10. Thus, the regression equation is
Y = 1.142 + 2.268X
At X = 3,
Y = 1.142 + 2.268 (3) = 7.946
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11. PRACTICE PROBLEM
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In an experiment to determine the relationship
between frequency and the inductive reactance of an
electrical circuit, the following results were obtained:
Frequency (Hz) 50 100 150 200 250 300 350
Inductive reactance (Ω) 30 65 90 130 150 190 200
Determine the equation of the regression line of
inductive reactance on frequency. Find the inductive
reactance when frequency is 175 Hz.

12. THANKS
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