case study by using multiple linear regression..how to full fill the assumption to use this method..

1. NADZIRAH HANIS ZA IN OR D IN P75182
MARWAN OMAR JALAMBO P75376
ASHOK SIVAJI P77800
DWI BUDININGSARI P75375
HAMZAH WALI P74918
OOI THENG CHOON P75129
HARUNA EMMANUEL P73270
SURESH MANI P77104
Multiple Linear Regression
NNPD 6014

2. Introduction
In developing countries, high BP is one of the
risk factors for CVD, and the estimated 7.1
million deaths especially among middle, and
old-age adults is due to high BP (Mungreiphy et
al. 2011).
 Overweight and obesity increase the risk of
elevated blood pressure (Drøyvold et al.
2005).

3. Introduction
 Positive association BMI and BP have also been
reported among Asian populations.
 Several studies indicate that high BP is associated
with age (Mungreiphy et al. 2011).

4. Research Question
 How well the BMI and age predict systolic blood
pressure?
 Which is the best predictor of perceived systolic
blood pressure; BMI or age?

5. Research hypothesis
 The systolic blood pressure change can predict by
BMI and Age among population.
 Statistic hypothesis
Ho : ᵝ BMI = 0, ᵝ age = 0
Ha : ᵝ BMI ≠ ᵝ age ≠ 0

6. Normality test

7. Multi Linear Regression - Assumptions
 Sample size
 Multicollinearity
 Outliers
 Normality, linearity, homoscedasticity, independence of
residuals

8. Assumptions- sample size
Use formula;
N > 50 + 8m (where m = number of independent
variables)
In our case study;
N> 50 + 8 (2)
N> 66
Our sample size is 96

9. Assumptions- Multicollinearity
 To test the multicollinearity
 between independent variables,
 we should test correlation by Pearson’s factor to
assume the relationship between the independent
variables

10. Assumptions- Multicollinearity
Correlation between
independent variable:
Correlation should not
exceed 0.9
The result indicates
Pearson’s correlation
factor = -0.122 (not
significant)
No correlation assumed
Correlations between
independent
P- value not significant .236

11. Assumptions- Multicollinearity
To avoid multicollinearity in MLR between the independent variables:
1- Variance inflation factor (VIF) < 10
2- Tolerance factor lie between (0-1); closed to zero means multicollinearity
Multicollinearity indicates that a variable is almost a linear combination of
other independent variable.
Results:
Age: Tolerance far away of Zero (=0.985) and VIF= 1.015
BMI: Tolerance far away of Zero (=0.985) and VIF= 1.015
Result: No multicollinearity has assumed (Independent variables)

12. Assumptions- Outliers
From option of statistics of Linear Reg.
Choose casewise diagnostics and standard deviation equal 3.
From the Table:
Std. Residual should lie between (-3.3 to +3.3) for (Minimum
to Maximum)
Our results interval (-2.482 to +3.217)
Result: No outliers

13. Assumptions- Outliers
 Using Mahalanobis distance (the value less than 13.82)
 It show multivariate outliers among independent
variable

14. Assumptions- Normality
Normal
distribution;
Points lie in a
straight line form
bottom left to top
right

15. Assumptions- Linearity
The distribution
of observation
up and down the
line of total
indicates equal
values or
similarities in
the distribution
that mean the
linearity
assumption has
been assumed

16. Assumptions-homoscedasticity
 By homoscedasticity: we test the equal variance
between up and down distributed observations in
scatter plot,
 In our results equal variance has assumed.

17. Assumptions-homoscedasticity

18. Test of Independence
 By Durbin-Watson test
 The Durbin-Watson estimate ranges from zero to four.
 Values hovering around two showed that the data points
were independent.
 Values near zero means strong positive correlations and
four indicates strong negative.

19. Test of Independence
Here, the independence assumption is satisfied as
the value of Durbin-Watson equal 1.668.

20. Assumption
Assumption Check
Sample size
Multicollinearity
Outliers
Normality
Linearity
Homoscedasticity
Independence of
residuals
Multiple
linear
regression

21. Multiple linear regression
Using multi regression standard
- All independent variable ( BMI and age) are entered into
the equation simultaneously.
- We want to know how much variance in dependent variable
were able to explain as group or block.

22. Evaluating the model
Adjusted R2
= 0.09 x 100 = 9 %
Age and BMI explains 9 % of variances in perceived systolic
blood pressure .

23. ANOVA
 Df (2)
 F-ratio (F) = 5.699
 Sig = 0.005 (p<0.05), significant enough to predict
dependent variable
 Report as; F (2,93) = 5.699; p<0.05

24. Evaluating each of the independent variable
To comparing the contribution of each independent
we use Beta value.
The larger Beta 0.258 (p<0.05) in BMI shows
more contribution in explaining systolic as
compared to the age.

25. Regression equations
Systolic = 84.769 + (0.983*BMI)+(0.368*age)

26. Answering research question
 How well the BMI and age predict systolic blood
pressure?
- BMI and age predicts 9% (p<0.05) of the variance
in systolic blood pressure
 Which is the best predictor of perceived systolic blood
pressure; BMI or age?
- Both BMI (Beta 0.258 ) and age (Beta 0.241)
are predictor systolic blood pressure.

27. Conclusion (APA Style)
 To predict the relationship between BMI and Age on Systolic
blood pressure, multiple linear regression was performed.
 Prior to interpretation (MLR) several assumptions evaluated.
 First, appropriate sample size was assumed(≥66).
 Second multicolinearity assumed by Pearson correlation,
VIF and Tolerance.
 Third, Mahalanobis distance did not exceed the critical X2
for df=2(at α = .05) of 13.82 for any cases in the data file.
 Fourth, inspection of the normal probability plot of
standardized residual against standardized predicted
value indicated the assumption of normality, linearity
and homoscedasticity of residuals were met.

28. Continue Conclusion
Systolic = 84.769 + (0.983*BMI)+(0.368*age)
 The multi-linear regression model predicts 9% of the
variance in systolic blood pressure. Adjusted R2
= 0.09
 This is statistically significant using MRL.
 The independent variables ( age and BMI) that are
significant predictors of the dependent variables (systolic)
at alpha=0.05.
 F(2, 93)= 5.699, p<0.05

29. References
 WB Drøyvold, K Midthjell, TIL Nilsen and J Holmen. 2005. International Journal of
Obesity 29, 650–655.
 N. K. Mungreiphy, Satwanti Kapoor, and Rashmi Sinha. 2011. Journal of Anthropology
Volume 2011, Article ID 748147, 6
 Mungreiphy, N., S. Kapoor & R. Sinha 2011. Association between BMI, blood pressure, and
age: study among Tangkhul Naga tribal males of Northeast India. Journal of Anthropology
 Allen, P. & Bennett, K. 2012. SPSS Statistic: A Practical Guide Version 20. Australia:
Cengage Learning Australia Pty.
 Coakes, S. J. 2013. SPSS vrsion20.0 for Windows. Analysis without Anguish. Milton : John
Wiley & Sons Ltd.
 Morgan, G. A., Leech, N. L., Cloeckner, G. W. & Barrett, K. C. 2013. IBM SPSS for
introductory statistic; Use and interpretation ( 5th edn). New York; Routledge Taylor &
Francis Group.
 Piaw, C. Y. 2013. Mastering research statistics. Selangor ; McGraw-Hill Education
(Malaysia) Sdn. Bhd,.
 Chan Y. H. 2004. biostatistics 201: Linear regression Analysis. Singapore Med J. 45(2): 55-
61