Advance Biostats SPSS (Multiple Linear Regression)
vwccspt12
WK4PART4_4.4_PracticeStep-by-StepGuide.docPART4
Step-by-Step Guide Assignment Problem 4.4
Multivariate Linear Regression
Problem 4. Discuss whether or not there is interaction (effect modification) first between Age and BMI and second between BMI and Coffee.
Discussion:
If the effect of an independent variable on a dependent variable depends on another independent variable, the third independent variable is an “effect modifier”.
Statistically, effect modification is best assessed by simple linear regression with each independent variable separately and the dependent variable. A difference in the R, R2, and the β for that variable alone versus these values for that same variable in the multiple linear regression model with the variables of interest indicates effect modification by the combined variables. This is because the effects of the other variables are not being held constant or controlled in the simple linear regression model.
Step 1. Simple linear regression for age and birth weight: go to Analyze ( Regression ( Linear.
Step 2. Simple linear regression with age: Click Reset to remove the previous input. Transfer birthw to Dependent and transfer age to the Independent(s). Click Statistics.
Step 3. Check Estimates, Confidence intervals Level(%) 95 and Model fit. Click Continue. Click OK.
SPSS Output:
|
Model Summary |
||||
|
Model |
R |
R Square |
Adjusted R Square |
Std. Error of the Estimate |
|
1 |
.400a |
.160 |
.152 |
420.779 |
|
a. Predictors: (Constant), age at conception |
|
Coefficientsa |
||||||||
|
Model |
Unstandardized Coefficients |
Standardized Coefficients |
t |
Sig. |
95.0% Confidence Interval for B |
|||
|
|
B |
Std. Error |
Beta |
|
|
Lower Bound |
Upper Bound |
|
|
1 |
(Constant) |
2543.252 |
258.844 |
|
9.825 |
.000 |
2029.585 |
3056.919 |
|
|
age at conception |
38.867 |
8.987 |
.400 |
4.325 |
.000 |
21.033 |
56.701 |
|
a. Dependent Variable: birth weight |
Step 4. Simple linear regression with BMI: Repeat steps 1 through 3 with BMI.
SPSS Output:
|
Model Summary |
||||||||
|
Model |
R |
R Square |
Adjusted R Square |
Std. Error of the Estimate |
||||
|
1 |
.313a |
.098 |
.089 |
440.567 |
||||
|
a. Predictors: (Constant), body mass index |
||||||||
|
Coefficientsa |
||||||||
|
Model |
Unstandardized Coefficients |
Standardized Coefficients |
t |
Sig. |
95.0% Confidence Interval for B |
|||
|
|
B |
Std. Error |
Beta |
|
|
Lower Bound |
Upper Bound |
|
|
1 |
(Constant) |
2828.244 |
257.296 |
|
10.992 |
.000 |
2317.515 |
3338.972 |
|
|
body mass index |
33.215 |
10.275 |
.313 |
3.233 |
.002 |
12.820 |
53.611 |
|
a. Dependent Variable: birth weight |
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|
|
Step 5. Simple linear regression with cups per day: Repeat steps 1 through 3 with cups per day.
SPSS Output:
|
Model Summary |
||||
|
Model |
R |
R Square |
Adjusted R Square |
Std. Error of the Estimate |
|
1 |
.187a |
.035 |
.024 |
455.721 |
|
a. Predictors: (Constant), cups per day |
|
Coefficientsa |
||||||||
|
Model |
Unstandardized Coefficients |
Standardized Coefficients |
t |
Sig. |
95.0% Confidence Interval for B |
|||
|
|
B |
Std. Error |
Beta |
|
|
Lower Bound |
Upper Bound |
|
|
1 |
(Constant) |
3716.978 |
56.369 |
|
65.940 |
.000 |
3605.008 |
3828.948 |
|
|
cups per day |
-35.027 |
19.310 |
-.187 |
-1.814 |
.073 |
-73.384 |
3.330 |
|
a. Dependent Variable: birth weight |
Step 6. Repeat step 1. Remove cups per day from Independent(s) then transfer age and BMI to Independent(s). Click OK.
SPSS Output:
|
Model Summary |
||||
|
Model |
R |
R Square |
Adjusted R Square |
Std. Error of the Estimate |
|
1 |
.515a |
.265 |
.250 |
399.711 |
|
a. Predictors: (Constant), body mass index, age at conception |
|
Coefficientsa |
||||||||
|
Model |
Unstandardized Coefficients |
Standardized Coefficients |
t |
Sig. |
95.0% Confidence Interval for B |
|||
|
|
B |
Std. Error |
Beta |
|
|
Lower Bound |
Upper Bound |
|
|
1 |
(Constant) |
1673.932 |
340.733 |
|
4.913 |
.000 |
997.491 |
2350.373 |
|
|
age at conception |
39.946 |
8.589 |
.409 |
4.651 |
.000 |
22.894 |
56.998 |
|
|
body mass index |
33.957 |
9.324 |
.320 |
3.642 |
.000 |
15.447 |
52.467 |
|
a. Dependent Variable: birth weight |
Step 7. Repeat step 1. Remove age from Independent(s) and transfer cups per day to Independent(s) with bmi. Click OK.
SPSS Output:
|
Model Summary |
||||
|
Model |
R |
R Square |
Adjusted R Square |
Std. Error of the Estimate |
|
1 |
.365a |
.133 |
.114 |
439.152 |
|
a. Predictors: (Constant), cups per day, body mass index |
|
Coefficientsa |
||||||||
|
Model |
Unstandardized Coefficients |
Standardized Coefficients |
t |
Sig. |
95.0% Confidence Interval for B |
|||
|
|
B |
Std. Error |
Beta |
|
|
Lower Bound |
Upper Bound |
|
|
1 |
(Constant) |
2891.228 |
267.491 |
|
10.809 |
.000 |
2359.646 |
3422.810 |
|
|
body mass index |
33.034 |
10.464 |
.314 |
3.157 |
.002 |
12.238 |
53.830 |
|
|
cups per day |
-30.790 |
18.707 |
-.164 |
-1.646 |
.103 |
-67.966 |
6.386 |
|
a. Dependent Variable: birth weight |
Interpretation:
Your interpretation must cover issues including:
· The meaning of R and R square in the association between each independent variable (age, BMI, cup per day,) and birth weight The meaning of R and R square for the model with all independent variables combined
· Whether there is evidence that there was an effect modification with the addition of the independent variables
· Which model you would chose to report as the final model in your research
