Cat Jumping

Evolutionary biologists Harris and Steudel (2002) investigated factors that are related to the jumping ability of domestic cats. The scientists measured the takeoff velocity (using high-speed cameras) as a proxy for jumping ability in 18 healthy adult cats. Several traits that might be related to takeoff velocity were also recorded including: gender, relative limb length (hindlimb), relative extensor muscle mass (musclemass), body mass, and fat mass relative to lean body mass (percent body fat).

results = read.csv("http://people.hsc.edu/faculty-staff/blins/spring17/math222/data/CatJumping.txt")
results
##    sex bodymass hindlimb musclemass percentbodyfat velocity
## 1    F     3640    29.10      51.15             29    334.5
## 2    F     2670    28.55      46.05             17    387.3
## 3    M     5600    31.74      95.90             31    410.8
## 4    F     4130    26.90      55.65             39    318.6
## 5    F     3020    26.11      57.20             15    368.7
## 6    F     2660    26.69      48.67             11    358.8
## 7    F     3240    26.74      64.55             21    344.6
## 8    M     5140    27.71      78.80             35    324.6
## 9    F     3690    25.47      54.60             33    301.4
## 10   F     3620    28.18      55.50             15    331.8
## 11   F     5310    28.45      68.80             42    312.6
## 12   M     5560    28.65      79.80             37    316.8
## 13   M     3970    29.82      69.40             20    375.6
## 14   F     3770    26.66      60.25             26    372.4
## 15   F     5100    27.84      60.70             41    314.3
## 16   F     2950    27.89      55.65             25    367.5
## 17   M     7930    30.58      98.95             48    286.3
## 18   F     3550    28.06      79.25             16    352.5

  1. What is the response variable and what are the explanatory variables in this data set?

  2. The scatterplots below show the relationships between each explanatory variable and the response variable. For each plot, comment on the (a) direction, (b) linearity, and (c) strength of the trends.

#pairs(results)
par(mfrow=c(2,2))
plot(results$sex,results$velocity)
plot(results$bodymass,results$velocity)
plot(results$musclemass,results$velocity)
plot(results$percentbodyfat,results$velocity)

  1. Use backwards elimination to find the model with the best adjusted-\(R^2\) value. What variables ended up mattering?

  2. Make a 95% prediction interval for the velocity of a female cat with bodymass=3000, hindlimb=28, percentbodyfat=20, and musclemass=50. Which model makes a tighter prediction interval, the full model or the one you got after backwards elimination?