Stat Regression Report

8/18/2019 Stat Regression Report

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SUBJECT: BASIC AND INFERENTIAL STATISTICS

REPORTER:SHIELA ROBETH B. VINARAO

TOPIC: REGRESSION ANALYSIS

PROFESSOR: DR. GLORIA T. MIANO

REGRESSION

ANALYSIS


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THE SIMPLE LINEAR

REGESSION ANALYSIS

The simple linear regression

analysis is used when there is a

signifcant relationshipbetween and variables.

This is used in predicting thevalue o a dependent variable

given the value o the

independent variable .

D

E

F

I

N

I

T

I

O

N


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THE SIMPLE LINEAR

REGESSION ANALYSIS

Suppose the advertising cost

and sales are correlated, then

we can predict the uture sales

in terms o advertising cost .Another type o problem which

uses regression analysis is when

variables corresponding to yearsare given, it is possible to

predict the value o that variable

several years hence or several

E

X

A

M

P

LE


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THE SIMPLE LINEAR

REGESSION ANALYSIS

F

O

R

M

U

LA


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ExampleConsider the following data:

1 6

2 4

3 3

4 5

5 4

6 2

1 6

2 4

3 3

4 5

5 4

6 2

0 1 2 3 4 5 6 70

1

2

3

4

5

6

7

x-axis

y-axis

Straight line indicates that the two variables are to some

extent LINEARLY RELATED

The variable we are basing our predictions on is called the

predictor variable and is referred to as . When there is only

one predictor variable, the prediction method is called


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1 6 6 1

2 4 8 4

3 3 9 9

4 5 20 16

5 4 20 25

6 2 12 36

3.5

4

= 4

75

1 6 6 1

2 4 8 4

3 3 9 9

4 5 20 16

5 4 20 25

6 2 12 36

SIMPLE LINEAR REGESSION


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3.5

4

= 4

75


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05Example A study isconducted on the

relationship of the

number of absences

and the grades of

the students in

English.

Determine the

relationship using

the following data.

•

Number of Absences Grades in English

1 90

2 852 80

3 75

3 80

8 65

6 70

1 95

4 80

5 80

5 75

1 92

2 89

1 80

9 65

1 90

2 85

2 80

3 75

3 80

8 65

6 70

1 95

4 80

5 80

5 75

1 92

2 89

1 80

9 65


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Number of

Absences

Grades in

English

1 90

2 85

2 80

3 75

3 80

8 65

6 70

1 95

4 80

5 805 75

1 92

2 89

1 80

9 65

1 90

2 85

2 80

3 75

3 80

8 65

6 70

1 95

4 80

5 805 75

1 92

2 89

1 80

9 65

0 1 2 3 4 5 6 7 8 9 100

10

20

30

40

50

60

70

80

90

100

Number of absences

x

ra!es in "n#lis$

y

Scatter Diagram


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Solving by the Stepwise Method

Problem :Is there a significant relationship betweenthe number of absences and the grades of15 students in English class?

Hypotheses :

Level of significance :

There is no significant relationship between the

number of absences and the grades of 15 students

in English class. Ho:

There is a significant relationship between the

number of absences and the grades of 15 students

in Englishclass.

H1:

df = n – 2

= 15 – 2

= 13


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ST

A

TI

S

T

I

C

S

Pearson Product Moment

Coefficient of Correlation

281 7335 3950


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The computedr value of is beyond the critical value

of at level of significance with degrees of freedom, so the

null hypothesis is rejected.

This means that there is a significant relationship

between the number of absences and the grades of

students in English. Since the value ofr is negative, it

implies that students who had more absences had lower

grades.

Decision Rule :

If ther computed value is greater than or beyondthe critical value, reject Ho.

Conclusion :


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Suppose we want to predict the grade of the student

who has incurred7 absences. To get the value of x, the

simple linear regression analysis will be used.

69 is the grade of

the student with

7 absences.


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Remarks: It is important to remember that thevalues of a and b are only estimates of the

corresponding parameters of a and b.

To justify the assumption of linearity, atest for linearity of regression should be

performed.

If there are two or more independent

variables, the regression equation becomes

+


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The significance ofthe slope ofthe regression line is to determine if

the regression model is usable.

If theslope is not equal to zero, then we can usethe regression

model to predict the dependent variable for any value of the

independent variable.

If theslope is equal to zero, we do not usethe model to makepredictions.

The scatter plot amounts to determining whether or not the slope

of the line of the best fit is significantly different from a horizontal

line or not.

A horizontal line means there is no association between two

variables, that is

In testing for significance in simple linear regression, the null

hypothesis is H0: and the alternative hypothesis is H1:

Significance Test in Simple

Linear Regression


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0%5 1 1%5 2 2%5 3 3%5 4 4%5 5 5%50

0%2

0%4

0%6

0%8

1

1%2

x-axis

y-axis

If

A horizontal line means there is no

association between two variables.

Slope of

Linear Regression


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Linear Regression

The t-test is conducted for testing the significance of r todetermine if the relationship is not a zero correlation.

Where:

FO

RM

U

L

A

1


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Linear Regression

The t-test is conducted for testing the significance of r todetermine if the relationship is not a zero correlation.

Where:

is the estimated standard deviation of

is the standard deviation of the values about

the regression line.

FO

RM

U

L

A

2


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ExampleGiven are two sets of data on the number of customers(in hundreds) and sales (in thousand of pesos) for a given

period of time from ten eateries. Find the equation of the

regression line which can predict the amount of sales

from the number of customers. Can we conclude that wecan use the model to make such a prediction?

Eatery 1 2 3 4 5 6 7 8 9 10

x2 6 8 8 12 16 20 20 22 26

y 58 105 88 118 117 137 157 169 149 202


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2 58 116 4 3364

6 105 630 36 11025

8 88 704 64 7744

8 118 944 64 13924

12 117 1404 144 13689

16 137 2192 256 18769

20 157 3140 400 24649

20 169 3380 400 28561

22 149 3278 484 22201

26 202 5252 676 40804

2 58 116 4 3364

6 105 630 36 11025

8 88 704 64 7744

8 118 944 64 13924

12 117 1404 144 13689

16 137 2192 256 18769

20 157 3140 400 24649

20 169 3380 400 28561

22 149 3278 484 22201

26 202 5252 676 40804


Linear Regression

Given:


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2 58 116 4 3364 70 144 144

6 105 630 36 11025 90 64 225

8 88 704 64 7744 100 36 144

8 118 944 64 13924 100 36 324

12 117 1404 144 13689 120 4 9

16 137 2192 256 18769 140 4 9

20 157 3140 400 24649 160 36 9

20 169 3380 400 28561 160 36 81

22 149 3278 484 22201 170 64 441

26 202 5252 676 40804 190 144 144

2 58 116 4 3364 70 144 144

6 105 630 36 11025 90 64 225

8 88 704 64 7744 100 36 144

8 118 944 64 13924 100 36 324

12 117 1404 144 13689 120 4 9

16 137 2192 256 18769 140 4 9

20 157 3140 400 24649 160 36 9

20 169 3380 400 28561 160 36 81

22 149 3278 484 22201 170 64 441

26 202 5252 676 40804 190 144 144


Linear Regression


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Since8.62 is greater than 3.355, wereject the H0 or accept the H1. Thus,

the obtained relationship is

significant or is non zero using .005level.

We can conclude that we can usethe model to predict sales from

population.

Decision:


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COMPUTATION USING

MICROSOFT EXCEL

Pearsonr

Slopeb

Intercepta

Syntax

+pearson(array1,array2)

or+correl(array1,array2)

+slope(known_y’s,known_x’s)

+intercept(known_y’s,known_x’s)


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PEARSONr


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SLOPEb INTERCEPTa


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THANK YOU

Stat Regression Report

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