Class Notes (1,100,000)

CA (640,000)

UTSC (30,000)

Health Studies (1,000)

HLTB21H3 (200)

Caroline Barakat (100)

Lecture 7

# HLTB21H3 Lecture Notes - Lecture 7: Simple Linear Regression, Confidence Interval, Null Hypothesis

by OC1894511

Department

Health StudiesCourse Code

HLTB21H3Professor

Caroline BarakatLecture

7This

**preview**shows pages 1-3. to view the full**32 pages of the document.**Application 1

A study by Triller et al. (A-14) examined the length of time required for home health-care nurses to

repackage a patient’s medications into various medication organizers (i.e., pill boxes). For the 19 patients

in the study, researchers recorded the time required for repackaging of medications. They also recorded

the number of problems encountered in the repackaging sessions.

Patient No.

No. of

Problems

Repackaging

Time (min)

Patient No.

No. of

Problems

Repackaging

Time (min)

1

9

38

11

1

10

2

2

25

12

2

15

3

0

5

13

1

17

4

6

18

14

0

18

5

5

15

15

0

23

6

3

25

16

10

29

7

3

10

17

0

5

8

1

5

18

1

22

9

2

10

19

1

20

10

0

15

Dependent Variable: Repackaging Time

Independent Variable: Number of Problems

a. scatter diagram

0

5

10

15

20

25

30

35

40

0 2 4 6 8 10 12

Repackacking Time

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Only pages 1-3 are available for preview. Some parts have been intentionally blurred.

b. Assuming a linear relationship, find the simple linear regression equation.

(Excel Summary Output of the Regression Analysis)

SUMMARY OUTPUT

Regression Statistics

Multiple R

0.616798

R Square

0.38044

Adjusted R

Square

0.343995

Standard Error

7.080977

Observations

19

ANOVA

df

SS

MS

F

Significance

F

Regression

1

523.4054

523.4054

10.43883

0.00491

Residual

17

852.3841

50.14024

Total

18

1375.789

Coefficients

Standard

Error

t Stat

P-value

Lower 95%

Upper

95%

Lower

95.0%

Upper

95.0%

Intercept

12.64145

2.132547

5.927867

1.65E-05

8.142173

17.14073

8.142173

17.14073

X Variable 1

1.804519

0.558516

3.230918

0.00491

0.626153

2.982884

0.626153

2.982884

The regression equation is

c. Interpret the meaning of the Y intercept bo and the slope b1 in this problem.

bo= the portion of repackaging time not explained by number of problems encountered

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b1= for each additional one problem encountered there is an average increase of 1.8 min spent repackaging by nurse.

d. Use the regression equation developed to predict the time spent for a nurse who has 10

problems.

e. Determine the coefficient of correlation r. Interpret its meaning in this application.

r=.617 tells you that there is a moderately strong association (linear) between number of

problems encountered and repackaging time.

f. Determine the coefficient of determination r2 and interpret its meaning in the context of this

application.

r2=0.38 38% of the variation in the repackaging time is explained by the variation in the

number of problems encountered by a nurse.

g. Determine the standard error of the estimate and interpret its meaning in the context of this

application.

SYX= 7.081 is the standard deviation of the observed repackaging times spent (by nurses)

around the line of regression. 95% of the observed times spent will fall within 2 x 7.081of

the least squares line (regression line).

h. At the 0.01 level of significance, is there evidence of a linear relationship between the time

spent and the number of topics researched?

Perform the t test for the significance of slope between number of problems encountered

and time spent by nurses repackaging. (2 tail. test)

H0:=0 there is not a linear relationship between repackaging time and number of

problems encountered.

H1:≠0 there is a linear relationship between repackaging time and number of problems

encountered.

Critical value for the test

Conclusion: At There is a linear relationship between number of

problems encountered and repackaging time.

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