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Pitagorjev izrek. c. a. b. Consumption funkcija. Regression Analysis attempts to ascertain the nature of the statistical relationship, if any, between variables. Simple Linear Regression For a Population:. Simple Linear Regression For a Population:. Simple Linear Regression

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slide4
Regression Analysis

attempts to ascertain the

nature of the statistical

relationship, if any,

between variables.

slide6

Simple Linear Regression

For a Population:

slide7

Simple Linear Regression

For a Population:

simple linear regression practical exercise
Simple Linear RegressionPractical Exercise

An Army psychological research lab is testing retentive

memory. Eleven soldiers are chosen randomly from a

battalion roster. Each soldier, in isolation, studies a map

for a set time ranging from one to eleven minutes. Fifteen

minutes later, the soldier answers 25 questions

about the map. The soldier’s score is

the number of questions answered correctly.

The results are shown in the table below.

slide10

Study Time Test Score

(X) (Y)

1 1

2 5

3 4

4 7

5 10

6 8

7 9

8 13

9 14

10 13

11 18

slide11

Scatter Plot

Questions Answered Correctly

Study Time in Minutes

slide12

Error in Regression

} Error

Questions Answered Correctly

Study Time in Minutes

slide19

Regression Equation

Questions Answered Correctly

Study Time in Minutes

slide25

This Test Statistic will follow the

t-distribution with n-2 degrees of freedom.

slide27

Data into Minitab

Time Score

1 1

2 5

3 4

4 7

5 10

6 8

7 9

8 13

9 14

10 13

11 18

Study.MTW

slide28

Regression Analysis

The regression equation is

Score = 0.655 + 1.44 Time

Predictor Coef StDev T p

Constant 0.6545 0.9933 0.66 0.526

Time 1.4364 0.1465 9.81 0.000

S = 1.536 R-Sq = 91.4% R-Sq(adj) = 90.5%

slide29

Analysis of Variance

Source DF SS MS F p

Regression 1 226.95 226.95 96.18 0.000

ERROR 9 21.24 2.36

TOTAL 10 248.18

Minitab output (Study.MTW)

slide32

slope = 1.77

slope = 1.44

slope = 1.11

the equation
The equation

may be used to predict:

1. the mean response E{Yh}

or

2. a new observation Yh(new)

slide41

Predicted Values

Fit StDev. Fit

10.709 0.486

95% CI 95% PI

(9.610, 11.808) (7.064, 14.354)

slide42

Predicted Values

Fit StDev. Fit

15.018 0.747

95% CI 95% PI

(13.329,16.708) (11.154,18.882)

slide44

Regression

Y=13

Questions Answered Correctly

Study Time in Minutes

slide45

Regression

Y=13

Questions Answered Correctly

Total deviation =

Study Time in Minutes

slide46

Regression

Questions Answered Correctly

Regression =

Study Time in Minutes

slide47

Regression

Y=13

Error =

Questions Answered Correctly

Study Time in Minutes

slide55

This Test Statistic will follow the

F-distribution with 1 and n-2

degrees of freedom.

slide63

Where di is the difference between the

rank of y and the rank of x

for the ith observation.

slide64

Rank Rank Square of

of of Rank of Y (Rank of Y

X X Y Y - Rank of X - Rank of X)

1 1

2 5

3 4

4 7

5 10

6 8

7 9

8 13

9 14

10 13

11 18

slide65

Rank Rank Square of

of of Rank of Y (Rank of Y

X X Y Y - Rank of X - Rank of X)

1 1 1 1 1-1 = 0 0

2 2 5 3 3-2 = 1 1

3 3 4 2 2-3 = -1 1

4 4 7 4 4-4 = 0 0

5 5 10 7 7-5 = 2 4

6 6 8 5 5-6 = -1 1

7 7 9 6 6-7 = -1 1

8 8 13 8.5 8.5-8= 0.5 0.25

9 9 14 10 10-9 = 1 1

10 10 13 8.5 8.5-10=-1.5 2.25

11 11 18 11 11-11 = 0 0

S di2 =11.5

slide66

Coefficient of Determination

The Coefficient of Determination is the

proportion of the variability in the

dependent variable that is accounted for

by the linear relationship with the

independent variable.

slide68

Regression Analysis

The regression equation is

Score = 0.655 + 1.44 Time

Predictor Coef StDev T p

Constant 0.6545 0.9933 0.66 0.526

Time 1.4364 0.1465 9.81 0.000

S = 1.536 R-Sq = 91.4% R-Sq(adj) = 90.5%

slide69

Analysis of Variance

SOURCE DF SS MS F p

Regression 1 226.95 226.95 96.18 0.000

Error 9 21.24 2.36

Total 10 248.18

Minitab output (Study.MTW)

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