/* Additional SAS code for Chapter 8: */


/* Special Models: */

/* Polynomial regression on the Rabbit Jawbone Data (Table 8.8) */


data rabbit;
input age length;
cards;
0.01 15.5
0.2 26.1
0.2 26.3
0.21 26.7
0.23 27.5
0.24 27
0.24 27
0.25 26
0.26 28.6
0.34 29.8
0.41 29.7
0.83 37.7
1.09 41.5
1.17 41.9
1.39 48.9
1.53 45.4
1.74 48.3
2.01 50.7
2.12 50.6
2.29 49.2
2.52 49
2.61 45.9
2.64 49.8
2.87 49.4
3.39 51.4
3.41 49.7
3.52 49.8
3.65 49.9
;
run;



/* Initial scatterplot of data: */

proc sgplot data=rabbit;
scatter y=length x=age;
run;

/* Not a linear trend? */

* Defining transformed variables for the polynomial terms:;

data rabbit; set rabbit;
age2 = age**2;
age3 = age**3;
age4 = age**4;
run;

proc reg data=rabbit;
model length = age age2 age3 age4; * quartic regression;
run;


** Looks like the fourth-degree term is not needed.;

proc reg data=rabbit;
model length = age age2 age3; * cubic regression;
run;

* Plotting the fitted curve (this plotting approach only works with linear, quadratic, or cubic);

title 'Cubic Regression Plot';
proc sgplot data=rabbit;
reg y=length x=age / degree=3;
run;
title;


***** Multiplicative model with the squid data (Table 8.10):;

data squid;
input obs rl wl rnl nwl w wt;
cards;
1 1.31 1.07 0.44 0.75 0.35 1.95
2 1.55 1.49 0.53 0.9 0.47 2.9
3 0.99 0.84 0.34 0.57 0.32 0.72
4 0.99 0.83 0.34 0.54 0.27 0.81
5 1.05 0.9 0.36 0.64 0.3 1.09
6 1.09 0.93 0.42 0.61 0.31 1.22
7 1.08 0.9 0.4 0.51 0.31 1.02
8 1.27 1.08 0.44 0.77 0.34 1.93
9 0.99 0.85 0.36 0.56 0.29 0.64
10 1.34 1.13 0.45 0.77 0.37 2.08
11 1.3 1.1 0.45 0.76 0.38 1.98
12 1.33 1.1 0.48 0.77 0.38 1.9
13 1.86 1.47 0.6 1.01 0.65 8.56
14 1.58 1.34 0.52 0.95 0.5 4.49
15 1.97 1.59 0.67 1.2 0.59 8.49
16 1.8 1.56 0.66 1.02 0.59 6.17
17 1.75 1.58 0.63 1.09 0.59 7.54
18 1.72 1.43 0.64 1.02 0.63 6.36
19 1.68 1.57 0.72 0.96 0.68 7.63
20 1.75 1.59 0.68 1.08 0.62 7.78
21 2.19 1.86 0.75 1.24 0.72 10.15
22 1.73 1.67 0.64 1.14 0.55 6.88
;
run;



* We will only use weight, rostal length, and width in our model:;

* Untransformed regression model:;

PROC REG data = squid;
MODEL wt = rl w;
run;


* Residual plot shows some violations of model assumptions.;


* Defining transformed variables for the logarithmic terms:;

DATA squid; SET squid;
logwt = log(wt);
logrl = log(rl); 
logw = log(w);

* Transformed regression model:;

PROC REG DATA = squid;
MODEL logwt = logrl  logw;
run;

* Much better!;