MAT207 – Roback
Spring 2002
MAT207: Multiple Regression
Case Study 9.1.1 – Effect of Light on Meadowfoam Flowering
Description:
Meadowfoam is a small plant found growing in moist meadows of the U.S. Pacific Northwest. It has been
domesticated at Oregon State University for its seed oil, which is unique among vegetable oils for its long carbon
strings, which make the oil nongreasy and highly stable. Researchers reported the results from one study in a series
designed to find out how to elevate meadowfoam production to a profitable crop (M. Seddigh and G.D. Jolliff,
“Light Intensity Effects on Meadowfoam Growth and Flowering,” Crop Science 34 (1994): 497-503.) In a
controlled growth chamber, they focused on the effects of two light-related factors: light intensity, at the 6 levels of
150, 300, 450, 600, 750, and 900 umol/m2/sec; and the timing of the onset of the light treatment, either at
photoperiodic floral induction (PFI)—the time at which the photo period was increased from 8 to 16 hours per day
to induce flowering—or 24 days before PFI.
The design consists of 12 treatment groups—the 6 light intensities at each of the two timing levels. 10 seedlings
were randomly assigned to each treatment group. The number of flowers per plant is the primary measure of
production, and it was measured by averaging the numbers of flowers produced by the 10 seedlings in each group.
The entire experiment was replicated, yielding 24 total observations. The researchers wanted to determine: What
are the effects of differing light intensity levels? What is the effect of the timing? Does the effect of intensity
depend on the timing?
Graphical Description of Data:
Graphs…Scatter…Matrix, then put all variables of interest under Matrix Variables. To get the 3D
plot, go to Graphs…Scatter…3D, with Y=light, X=time, and Z=flowers. Or, to get a cool
interactive 3D plot that you can spin around, go to Graphs…Interactive…Scatterplot. To get the
plot of separate regression lines, go to Graphs…Scatter…Simple with Y=flowers, X=light, and Set
Markers By = time, then under Chart Options hit Fit Line…Subgroups.
FLOWERS
1000
800
LIGHT
TIME
600
400
200
30
INTENS
20
10
TIME
Regression Lines fit Separately
80
70
60
50
Prior Timing
40
24 days
30
O days
0
200
400
600
800
1000
Light Intensity (umol/m2/sec)
Page 1
0
30
80
60 70
40 50
FLOWERS
90
MAT207 – Roback
Spring 2002
Regression Analysis:
Analyze…Regression…Linear (Dependent = flowers; Independent = light).
Model Summaryb
Model
1
R
.771a
R Square
.595
Adjusted
R Square
.576
Std. Error of
the Estimate
8.9397
a. Predictors: (Constant), LIGHT
b. Dependent Variable: FLOWERS
Coefficientsa
Model
1
(Constant)
LIGHT
Unstandardized
Coefficients
B
Std. Error
77.385
4.161
-4.05E-02
.007
Standardi
zed
Coefficien
ts
Beta
t
18.597
-5.682
-.771
Sig.
.000
.000
95% Confidence Interval for B
Lower Bound Upper Bound
68.755
86.015
-.055
-.026
a. Dependent Variable: FLOWERS
Residual Plot for model with light only
20
10
0
-10
Prior Timing
24 days
-20
0 Days
40
50
60
70
80
Unstandardized Predicted V alue
Analyze…Regression…Linear (Dependent = flowers; Independent = early).
Model Summaryb
Model
1
R
.452a
R Square
.204
Adjusted
R Square
.168
Std. Error of
the Estimate
12.5245
a. Predictors: (Constant), EARLY
b. Dependent Variable: FLOWERS
Coefficientsa
Model
1
(Constant)
EARLY
Unstandardized
Coefficients
B
Std. Error
62.217
3.616
-12.158
5.113
Standardi
zed
Coefficien
ts
Beta
-.452
t
17.208
-2.378
Sig.
.000
.027
a. Dependent Variable: FLOWERS
Page 2
95% Confidence Interval for B
Lower Bound Upper Bound
54.719
69.715
-22.762
-1.554
MAT207 – Roback
Spring 2002
Analyze…Regression…Linear (Dependent = flowers; Independent = light, early).
Model Summaryb
Descriptive Statistics
FLOWERS
LIGHT
EARLY
Mean
56.1375
525.0000
.5000
Std. Deviation
13.7334
261.6835
.5108
N
24
24
24
Model
1
R
.894a
R Square
.799
Adjusted
R Square
.780
Std. Error of
the Estimate
6.4411
a. Predictors: (Constant), EARLY, LIGHT
b. Dependent Variable: FLOWERS
Correl ations
Pearson Correlation
Sig. (1-tailed)
N
FLOW ERS
LIGHT
EARLY
FLOW ERS
LIGHT
EARLY
FLOW ERS
LIGHT
EARLY
FLOW ERS
1.000
-.771
-.452
.
.000
.013
24
24
24
LIGHT
-.771
1.000
.000
.000
.
.500
24
24
24
EARLY
-.452
.000
1.000
.013
.500
.
24
24
24
Coeffi cientsa
Model
1
(Const ant)
LIGHT
EARLY
Unstandardized
Coeffic ient s
B
St d. Error
83.464
3.274
-4. 05E-02
.005
-12.158
2.630
St andardi
zed
Coeffic ien
ts
Beta
-.771
-.452
t
25.495
-7. 886
-4. 624
Sig.
.000
.000
.000
95% Confidenc e Interval for B
Lower Bound Upper Bound
76.656
90.272
-.051
-.030
-17.627
-6. 690
a. Dependent Variable: FLOW ERS
Analyze…Regression…Linear (Dependent = flowers; Independent = day24,l300,…,l900).
Model Summary
Model
1
R
.907a
R Square
.823
Adjusted
R Square
.761
Std. Error of
the Estimate
6.7190
a. Predictors: (Constant), L900, DAY24, L750, L600,
L450, L300
Coefficientsa
Model
1
(Constant)
DAY24
L300
L450
L600
L750
L900
Unstandardized
Coefficients
B
Std. Error
67.196
3.629
.507
.114
-9.125
4.751
-13.375
4.751
-23.225
4.751
-27.750
4.751
-29.350
4.751
Standardi
zed
Coefficien
ts
Beta
.452
-.253
-.371
-.644
-.769
-.814
t
18.518
4.432
-1.921
-2.815
-4.888
-5.841
-6.178
Sig.
.000
.000
.072
.012
.000
.000
.000
a. Dependent Variable: FLOWERS
Page 3
95% Confidence Interval for B
Lower Bound Upper Bound
59.540
74.852
.265
.748
-19.149
.899
-23.399
-3.351
-33.249
-13.201
-37.774
-17.726
-39.374
-19.326
MAT207 – Roback
Spring 2002
Analyze…Regression…Linear (Dependent = flowers; Independent = light, early, int).
Transform…Compute to create int=light*early.
Must first
Model Summary
Model
1
R
.894a
R Square
.799
Adjusted
R Square
.769
Std. Error of
the Estimate
6.5980
a. Predictors: (Constant), INT, LIGHT, EARLY
Coeffi cientsa
Model
1
(Const ant)
LIGHT
EARLY
INT
Unstandardized
Coeffic ient s
B
St d. Error
83.147
4.343
-3. 99E-02
.007
-11.523
6.142
-1. 21E-03
.011
St andardi
zed
Coeffic ien
ts
Beta
-.760
-.429
-.029
t
19.144
-5. 362
-1. 876
-.115
Sig.
.000
.000
.075
.910
95% Confidenc e Interval for B
Lower Bound Upper Bound
74.087
92.207
-.055
-.024
-24.336
1.289
-.023
.021
a. Dependent Variable: FLOW ERS
flower
62.30
77.40
55.30
54.20
49.60
61.90
39.40
45.70
31.30
44.90
36.80
41.90
77.80
75.60
69.10
78.00
57.00
71.10
62.90
52.20
60.30
45.60
52.60
44.40
timeor
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
light
150.00
150.00
300.00
300.00
450.00
450.00
600.00
600.00
750.00
750.00
900.00
900.00
150.00
150.00
300.00
300.00
450.00
450.00
600.00
600.00
750.00
750.00
900.00
900.00
day24
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
early
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
time
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
24.0
24.0
24.0
24.0
24.0
24.0
24.0
24.0
24.0
24.0
24.0
24.0
l150
1.00
1.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
1.00
1.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
Page 4
l300
.00
.00
1.00
1.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
1.00
1.00
.00
.00
.00
.00
.00
.00
.00
.00
l450
.00
.00
.00
.00
1.00
1.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
1.00
1.00
.00
.00
.00
.00
.00
.00
l600
.00
.00
.00
.00
.00
.00
1.00
1.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
1.00
1.00
.00
.00
.00
.00
l750
.00
.00
.00
.00
.00
.00
.00
.00
1.00
1.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
1.00
1.00
.00
.00
l900
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
1.00
1.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
1.00
1.00
int
150.00
150.00
300.00
300.00
450.00
450.00
600.00
600.00
750.00
750.00
900.00
900.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00