Curvilinear Regression Example - Portland State University

Newsom, USP 654 Data Analysis II, Fall 2015 1

Curvilinear Regression Example
Canadian NPHS Check-up Recency Regressed on Weight

SPSS
Plot

8
7

Recency of Physical Check-up 6
5

4

3
2

1

0
10 20 30 40 50

Body Mass Index

Syntax

output close *.

get file='c:\jason\spsswin\da2\hbs_2.sav'.
* Random sample of approx 1200 older adults from the Canadian NPHS.

*make sure n the mean is based on is the same used in the regression model.
count nmiss=checkup weight (missing).
select if nmiss=0.

*mean center the weight variable.
compute id=$casenum.
aggregate /mweight=MEAN(weight).
compute cweight=weight - mweight.

*compute quadratic effect variable.
compute cweight2=cweight*cweight.

regression vars=checkup cweight cweight2
/descriptives=mean stdev n sig corr
/statistics=anova r coeff ses cha
/dependent=checkup
/method=enter cweight cweight2.

Newsom, USP 654 Data Analysis II, Fall 2015 2

Output

Regression N�
1191�
Descriptive Statistics�
Mean� Std. Deviation� 1191�
1191�
2.28� 2.027�

cweight� .00000� 4.114211�
cweight2� 16.91252� 29.174028�

Correlations

CHECKUP CWEIGHT CWEIGHT2
Physical
Check-up

Pearson Correlation CHECKUP 1.000 .000 .027
Sig. (1-tailed) Physical Check-up
N CWEIGHT .000 1.000 .361
CWEIGHT2 .027 .361 1.000
CHECKUP
Physical Check-up . .496 .179
CWEIGHT
CWEIGHT2 .496 . .000
CHECKUP .179 .000 .
Physical Check-up
CWEIGHT 1191 1191 1191
CWEIGHT2
1191 1191 1191
1191 1191 1191

Model Summary

Change Statistics

Model R R Square Adjusted Std. Error of R Square F Change df1 df2 Sig. F Change
1 R Square the Estimate Change .481 2 1188 .618
.028a .001
-.001 2.028 .001

a. Predictors: (Constant), CWEIGHT2, CWEIGHT

ANOVAb

Model Regression Sum of df Mean Square F Sig.
1 Residual Squares 2 1.979 .481 .618a
Total 4.113
3.959 1188
4886.375 1190
4890.334

a. Predictors: (Constant), CWEIGHT2, CWEIGHT

b. Dependent Variable: CHECKUP Physical Check-up

Coefficientsa

Unstandardized Standardized
Coefficients Coefficients

Model B Std. Error Beta Std. Error t Sig.
1 (Constant) 32.436 .000
2.245 .069 .731
-.344 .327
CWEIGHT -.005 .015 -.011 .031 .981

CWEIGHT2 .002 .002 .031 .031

a. Dependent Variable: CHECKUP Physical Check-up

Newsom, USP 654 Data Analysis II, Fall 2015 3

R (some output omitted for brevity)

> #clear active frame from previous analyses
> rm(mydata)
>
>
> library(lessR)
> mydata = Read("c:/jason/spsswin/da2/hbs_2.sav",quiet=TRUE)

> #Random sample of approx 1200 older adults from the Canadian NPHS.
>

> #need to convert data types in order to compute a correlation in R--lessR function
> mydata <-Transform(CHECKUP = as.numeric(CHECKUP))

>
> library(car)
>
> #test simple regression first and examine residual plot
> residualPlots(lm(CHECKUP ~ WEIGHT, data = mydata), fitted=FALSE)

Initial Plot of the Residuals from Linear Regression

Pearson residuals
1234

-1 0

15 20 25 30 35 40

WEIGHT

> #listwise deletion to match n from regression when centering
> mydata <-Subset(WEIGHT!='NA' & CHECKUP!='NA')

> #mean center WEIGHT
> mydata$cweight <- scale(mydata$WEIGHT, center = TRUE, scale = FALSE)
> ss.brief(mydata) #check that mean of cweight is zero

> #compute quadratic effect variable
> mydata$weight2=mydata$cweight^2
>

> #test linear with quadratic effect
> Regression(CHECKUP ~ cweight + weight2, res.sort="off")

Newsom, USP 654 Data Analysis II, Fall 2015 4

Response Variable: CHECKUP, Physical Check-up
Predictor 1: cweight,
Predictor 2: weight2,

Number of cases (rows) of data: 1191
Number of cases retained for analysis: 1191

BASIC ANALYSIS

Estimated Model

(Intercept) Estimate Std Err t-value p-value Lower 95% Upper 95%
cweight 2.24 0.07 32.436 0.000 2.11 2.38
weight2 0.02 -0.344 0.731 0.02
-0.01 0.00 0.981 0.327 -0.04 0.01
0.00 -0.00

Model Fit

Standard deviation of residuals: 2.03 for 1188 degrees of freedom

R-squared: 0.001 Adjusted R-squared: -0.001 PRESS R-squared: -0.005

Null hypothesis that all population slope coefficients are 0:

F-statistic: 0.481 df: 2 and 1188 p-value: 0.618

Analysis of Variance

cweight df Sum Sq Mean Sq F-value p-value
weight2 1 0.00 0.00 0.00 0.991
Model 1 3.96 3.96 0.96 0.327
2 3.96 1.98 0.48 0.618

Residual Plot for Model with Quadratic Effect (flat fit line, but, ooh, I don't like those outliers much!)

Residuals 10
-2 -1 0 1 2 3 4 5

2.3 2.4 2.5 2.6 2.7 2.8

Fitted Values

Largest Cook's Distance, 0.14, is highlighte