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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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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 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.


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


Scatter Plot

Questions Answered Correctly

Study Time in Minutes


Error in Regression

} Error

Questions Answered Correctly

Study Time in Minutes



Regression Equation

Questions Answered Correctly

Study Time in Minutes


This Test Statistic will follow the

t-distribution with n-2 degrees of freedom.


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


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%


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)


A (1-a)% Confidence Interval on b1


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)


A (1-a)% Confidence Interval

for E{Yh}


A (1-a)% Prediction Interval

for Yh(new)


Predicted Values

Fit StDev. Fit

10.709 0.486

95% CI 95% PI

(9.610, 11.808) (7.064, 14.354)


Predicted Values

Fit StDev. Fit

15.018 0.747

95% CI 95% PI

(13.329,16.708) (11.154,18.882)


Regression

Y=13

Questions Answered Correctly

Study Time in Minutes


Regression

Y=13

Questions Answered Correctly

Total deviation =

Study Time in Minutes


Regression

Questions Answered Correctly

Regression =

Study Time in Minutes


Regression

Y=13

Error =

Questions Answered Correctly

Study Time in Minutes




This Test Statistic will follow the

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.


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


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


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.


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%


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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