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Pitagorjev izrek - PowerPoint PPT Presentation

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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attempts to ascertain the

nature of the statistical

relationship, if any,

between variables.

For a Population:

For a Population:

For a Sample:

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.

(X) (Y)

1 1

2 5

3 4

4 7

5 10

6 8

7 9

8 13

9 14

10 13

11 18

Study Time in Minutes

} Error

Study Time in Minutes

Study Time in Minutes

t-distribution with n-2 degrees of freedom.

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

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%

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)

A (1-a)% Confidence Interval on b1

slope = 1.44

slope = 1.11

may be used to predict:

1. the mean response E{Yh}

or

2. a new observation Yh(new)

A (1-a)% Confidence Interval

for E{Yh}

A (1-a)% Prediction Interval

for Yh(new)

Fit StDev. Fit

10.709 0.486

95% CI 95% PI

(9.610, 11.808) (7.064, 14.354)

Fit StDev. Fit

15.018 0.747

95% CI 95% PI

(13.329,16.708) (11.154,18.882)

Y=13

Study Time in Minutes

Y=13

Total deviation =

Study Time in Minutes

Regression =

Study Time in Minutes

Y=13

Error =

Study Time in Minutes

F-distribution with 1 and n-2

degrees of freedom.

Spearman’s Rank Correlation Coefficient

Where di is the difference between the

rank of y and the rank of x

for the ith observation.

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

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

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.

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%

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)