case0901: Effects of Light on Meadowfoam Flowering

In Sleuth3: Data Sets from Ramsey and Schafer's "Statistical Sleuth (3rd Ed)"

Description

Meadowfoam is a small plant found growing in moist meadows of the US Pacific Northwest. Researchers reported the results from one study in a series designed to find out how to elevate meadowfoam production to a profitable crop. In a controlled growth chamber, they focused on the effects of two light–related factors: light intensity and the timeing of the onset of the ligth treatment.

Usage

case0901

Format

A data frame with 24 observations on the following 3 variables.

Flowers

average number of flowers per meadowfoam plant

Time

time light intensity regiments started; 1=Late, 2=Early

Intensity

light intensity (in mumol/m^2/sec)

Source

Ramsey, F.L. and Schafer, D.W. (2013). The Statistical Sleuth: A Course in Methods of Data Analysis (3rd ed), Cengage Learning.

Examples

str(case0901)
attach(case0901)

## EXPLORATION
plot(Flowers ~ Intensity, pch=ifelse(Time ==1, 19, 21))
myLm <- lm(Flowers ~ Intensity + factor(Time) + Intensity:factor(Time)) 
plot(myLm, which=1) 
summary(myLm)  # Note p-value for interaction term

# INFERENCE
myLm2 <- lm(Flowers ~ Intensity + factor(Time)) 
summary(myLm2)         
confint(myLm2)         

# DISPLAY FOR PRESENTATION
plot(Flowers ~ jitter(Intensity,.3),   
  xlab=expression("Light Intensity ("*mu*"mol/"*m^2*"/sec)"), # Include symbols
  ylab="Average Number of Flowers per Plant",
  main="Effect of Light Intensity and Timing on Meadowfoam Flowering",
  pch=ifelse(Time ==1, 21, 22), bg=ifelse(Time==1, "orange","green"),
  cex=1.7, lwd=2)          
beta <- myLm2$coef  
abline(beta[1],beta[2],lwd=2, lty=2) 
abline(beta[1]+beta[3],beta[2],lwd=2,lty=3) 
legend(700,79,c("Early Start","Late Start"),  
  pch=c(22,21),lwd=2,pt.bg=c("green","orange"),pt.cex=1.7,lty=c(3,2))

detach(case0901)

Example output

'data.frame':	24 obs. of  3 variables:
 $ Flowers  : num  62.3 77.4 55.3 54.2 49.6 61.9 39.4 45.7 31.3 44.9 ...
 $ Time     : int  1 1 1 1 1 1 1 1 1 1 ...
 $ Intensity: int  150 150 300 300 450 450 600 600 750 750 ...

Call:
lm(formula = Flowers ~ Intensity + factor(Time) + Intensity:factor(Time))

Residuals:
   Min     1Q Median     3Q    Max 
-9.516 -4.276 -1.422  5.473 11.938 

Coefficients:
                         Estimate Std. Error t value Pr(>|t|)    
(Intercept)             71.623333   4.343305  16.491 4.14e-13 ***
Intensity               -0.041076   0.007435  -5.525 2.08e-05 ***
factor(Time)2           11.523333   6.142360   1.876   0.0753 .  
Intensity:factor(Time)2  0.001210   0.010515   0.115   0.9096    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 6.598 on 20 degrees of freedom
Multiple R-squared:  0.7993,	Adjusted R-squared:  0.7692 
F-statistic: 26.55 on 3 and 20 DF,  p-value: 3.549e-07


Call:
lm(formula = Flowers ~ Intensity + factor(Time))

Residuals:
   Min     1Q Median     3Q    Max 
-9.652 -4.139 -1.558  5.632 12.165 

Coefficients:
               Estimate Std. Error t value Pr(>|t|)    
(Intercept)   71.305833   3.273772  21.781 6.77e-16 ***
Intensity     -0.040471   0.005132  -7.886 1.04e-07 ***
factor(Time)2 12.158333   2.629557   4.624 0.000146 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 6.441 on 21 degrees of freedom
Multiple R-squared:  0.7992,	Adjusted R-squared:   0.78 
F-statistic: 41.78 on 2 and 21 DF,  p-value: 4.786e-08

                    2.5 %      97.5 %
(Intercept)   64.49765172 78.11401495
Intensity     -0.05114478 -0.02979808
factor(Time)2  6.68987027 17.62679640

Sleuth3 documentation built on May 2, 2019, 6:41 a.m.