Regression Analysis | Assignment | New
Added on 2022-09-14
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QUESTION ONE
The General Linear model is expressed as follows,
Y=B0 + B1X1 + B2X2 +...+BNXN Where X1, X2, ... XN are the independent
variables and
B0, B1...BN are the coefficients (Kiebel, 2003).
Let
y be Peak expiratory flow (PEF) y=PEF
X1 be Diabetes
X2 be Area
X3 be Age
Then our General Linear Model becomes
PEF=B0 + B1*Diabetes + B2*Area +B3*Age + e
Where PEF Is dependent variable, while Diabetes, Area and Age are
Independent variables
We begin our Analysis by understanding the demographic nature of the data
GENERAL RGRESSION MODEL
The General Linear model is expressed as follows,
Y=B0 + B1X1 + B2X2 +...+BNXN Where X1, X2, ... XN are the independent
variables and
B0, B1...BN are the coefficients (Kiebel, 2003).
Let
y be Peak expiratory flow (PEF) y=PEF
X1 be Diabetes
X2 be Area
X3 be Age
Then our General Linear Model becomes
PEF=B0 + B1*Diabetes + B2*Area +B3*Age + e
Where PEF Is dependent variable, while Diabetes, Area and Age are
Independent variables
We begin our Analysis by understanding the demographic nature of the data
GENERAL RGRESSION MODEL
From our analysis, we have model 1 and Model 2
MODEL ONE
SUMMARY OF THE MODEL ONE
Model Summaryc
Model R R2 Adjusted R2 Std. Error of
the Estimate
Durbin-Watson
1 .865a .747 .745 147.499
2 .864b .747 .746 147.429 1.989
a. Predictors: (Constant), Age, Diabetes, Area
b. Predictors: (Constant), Diabetes, Area
c. Dependent Variable: PEF
Reliability of the data
R2 of the data is 0.747. This means that the independent variables explain 74.7%
of the dependent variable. Hence our data is reliable
B0 =431.381 B1=-300.510 B2=406.463 B3=0.197
PEF=431.381 + B1*Diabetes + B2*Area +B3*Age + e
Model 1 becomesPEF=431.381 - 300.510*Diabetes + 406.463* Area + 0.197 Age + e
However, let us check on the statistical significance of the variables.
The sig. for Diabetes and area is 0.000 which is less than 0.05, hence they
are statistically significant while Age =0.430 which is greater that 0.05 is
statistically significant.
MODEL ONE
SUMMARY OF THE MODEL ONE
Model Summaryc
Model R R2 Adjusted R2 Std. Error of
the Estimate
Durbin-Watson
1 .865a .747 .745 147.499
2 .864b .747 .746 147.429 1.989
a. Predictors: (Constant), Age, Diabetes, Area
b. Predictors: (Constant), Diabetes, Area
c. Dependent Variable: PEF
Reliability of the data
R2 of the data is 0.747. This means that the independent variables explain 74.7%
of the dependent variable. Hence our data is reliable
B0 =431.381 B1=-300.510 B2=406.463 B3=0.197
PEF=431.381 + B1*Diabetes + B2*Area +B3*Age + e
Model 1 becomesPEF=431.381 - 300.510*Diabetes + 406.463* Area + 0.197 Age + e
However, let us check on the statistical significance of the variables.
The sig. for Diabetes and area is 0.000 which is less than 0.05, hence they
are statistically significant while Age =0.430 which is greater that 0.05 is
statistically significant.
Elimination of the Age Variable
Since Age is not statistically significant, the variable is excluded from the
model
Excluded Variablesa
Model Beta In t Sig. Partial
Correlation
Collinearity Statistics
Toleran
ce
VIF Minimum
Tolerance
2 Age .020b .789 .430 .040 .996 1.004 .996
a. Dependent Variable: PEF
b. Predictors in the Model: (Constant), Diabetes, Area
Therefore, proceed with Diabetes and Area
MODEL 2 (SECOND ANALYSIS AFTER ELIMINATION OF AGE VARIABLE)
B0 =614.820 B1=376.510 B2=-329.430
Our Model becomes
PEF=441.790 + 376.510*Diabetes -329.430*Area -152.680*Diabetes*Area
Since Age is not statistically significant, the variable is excluded from the
model
Excluded Variablesa
Model Beta In t Sig. Partial
Correlation
Collinearity Statistics
Toleran
ce
VIF Minimum
Tolerance
2 Age .020b .789 .430 .040 .996 1.004 .996
a. Dependent Variable: PEF
b. Predictors in the Model: (Constant), Diabetes, Area
Therefore, proceed with Diabetes and Area
MODEL 2 (SECOND ANALYSIS AFTER ELIMINATION OF AGE VARIABLE)
B0 =614.820 B1=376.510 B2=-329.430
Our Model becomes
PEF=441.790 + 376.510*Diabetes -329.430*Area -152.680*Diabetes*Area
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