Variable Combinations

Data

    weight age.years        lat   site
1 12615.13        41   2.690077 Site 1
2 12539.55        50   2.974857 Site 2
3 13753.97        21  -4.868759 Site 1
4 17269.26        50 -28.437431 Site 2
5 16945.27        16 -26.414605 Site 1
6 14723.24        39 -11.392111 Site 2

Questions

1. What model syntax allows for the effect of age.years to be different at each level of site?

first =  glm(weight ~ age.years + site + age.years:site
second = glm(weight ~ age.years + site)
third =  glm(weight ~ age.years * site)
fourth = glm(weight ~ poly(age.years,2) + site


2. Draw an x-y plot showing the relationship b/w weight and the additive effect of site and age.years. Assume a negative slope of age.years with weight and two levels of the variable site. Assume the intercept mle is 13000 and the estimated effect of siteSite2 = -2000. Label axes and slopes for each site.

glm(weight ~ age.years + site)


3. Looking at the data table above, write out the design matrix for the two models below.

glm(weight ~ age.years + site)
glm(weight ~ age.years * site)

4. When might it be good to assume an additive effect b/w a categorical and continuous variable over an interaction?


5. Define what each coefficient means. Make sure to make clear the units.

dat$age.yeras.sc = scale(dat$age.years,center=TRUE, scale=TRUE)
summary(glm(weight ~ age.yeras.sc * site, data = dat))

Call:
glm(formula = weight ~ age.yeras.sc * site, data = dat)

Coefficients:
                        Estimate Std. Error t value Pr(>|t|)    
(Intercept)              14574.8      241.9  60.245  < 2e-16 ***
age.yeras.sc              -706.4      263.3  -2.682  0.00861 ** 
siteSite 2                -188.1      342.0  -0.550  0.58367    
age.yeras.sc:siteSite 2   1173.1      347.5   3.375  0.00107 ** 
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

(Dispersion parameter for gaussian family taken to be 2908337)

    Null deviance: 313494594  on 99  degrees of freedom
Residual deviance: 279200364  on 96  degrees of freedom
AIC: 1778

Number of Fisher Scoring iterations: 2