case0701: The Big Bang

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

Description

Hubble's initial data on 24 nebulae outside the Milky Way.

Usage

case0701

Format

A data frame with 24 observations on the following 2 variables.

Velocity

recession velocity (in kilometres per second)

Distance

distance from earth (in magaparsec)

Source

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

References

Hubble, E. (1929). A Relation Between Distance and Radial Velocity Among Extragalactic Nebulae, Proceedings of the National Academy of Science 15: 168–173.

See Also

ex0725

Examples

str(case0701) 
attach(case0701)  

## EXPLORATION
plot(Distance ~ Velocity)   
myLm <- lm(Distance ~ Velocity)  
abline(myLm) 

myResiduals <- myLm$res  
myFits  <- myLm$fit  
plot(myResiduals ~ myFits)   # Plot residuals versus estimated means.
abline(h=0)  # Draw a horizontal line at 0.     
# OR, use this shortcut...
plot(myLm, which=1) # Residual plot (red curve is a scatterplot smooother)

## INFERENCE
summary(myLm)  
confint(myLm,level=.95)   
myLm2 <- lm(Distance ~ Velocity - 1)   # Drop the intercept.
summary(myLm2) 
confint(myLm2) 

## DISPLAY FOR PRESENTATION
plot(Distance ~ Velocity, xlab="Recession Velocity (km/sec)", 
  ylab="Distance from Earth (megaparsecs)", 
  main="Measured Distance Versus Velocity for 24 Extra-Galactic Nebulae", 
  pch=21, lwd=2, bg="green", cex=1.5 )  
abline(myLm, lty=2, col="blue", lwd=2) 
abline(myLm2, lty=3, col="red", lwd=2) 
legend(-250,2.05, 
  c("unrestricted regression line","regression through the origin"),  
  lty=c(2,3), lwd=c(2,2), col=c("blue","red")) 

detach(case0701)   

Example output

'data.frame':	24 obs. of  2 variables:
 $ Velocity: int  170 290 -130 -70 -185 -220 200 290 270 200 ...
 $ Distance: num  0.03 0.03 0.21 0.26 0.28 0.28 0.45 0.5 0.5 0.63 ...

Call:
lm(formula = Distance ~ Velocity)

Residuals:
     Min       1Q   Median       3Q      Max 
-0.76717 -0.23517 -0.01083  0.21081  0.91463 

Coefficients:
             Estimate Std. Error t value Pr(>|t|)    
(Intercept) 0.3991704  0.1186662   3.364   0.0028 ** 
Velocity    0.0013724  0.0002278   6.024 4.61e-06 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 0.4056 on 22 degrees of freedom
Multiple R-squared:  0.6226,	Adjusted R-squared:  0.6054 
F-statistic: 36.29 on 1 and 22 DF,  p-value: 4.608e-06

                   2.5 %     97.5 %
(Intercept) 0.1530719058 0.64526897
Velocity    0.0008999349 0.00184488

Call:
lm(formula = Distance ~ Velocity - 1)

Residuals:
     Min       1Q   Median       3Q      Max 
-0.76767 -0.06909  0.22948  0.46056  1.03931 

Coefficients:
          Estimate Std. Error t value Pr(>|t|)    
Velocity 0.0019214  0.0001913   10.04 7.05e-10 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 0.4882 on 23 degrees of freedom
Multiple R-squared:  0.8143,	Adjusted R-squared:  0.8062 
F-statistic: 100.9 on 1 and 23 DF,  p-value: 7.05e-10

               2.5 %      97.5 %
Velocity 0.001525611 0.002317143

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