> (74.212-62.635)/3/1.940446
[1] 1.988718
> pf(.Last.value,3,30,lower=T)
[1] 0.8631158
> pf(.Last.value,3,30,lower=F)
[1] 0.470936
> pf(1.988718,3,30,lower=F)
[1] 0.1368842
> summary(toxo.glm)

Call:
glm(formula = cbind(r, m - r) ~ poly(rain, 3), family = binomial, 
    data = toxo)

Deviance Residuals: 
    Min       1Q   Median       3Q      Max  
-2.7620  -1.2166  -0.5079   0.3538   2.6204  

Coefficients:
               Estimate Std. Error z value Pr(>|z|)    
(Intercept)     0.02427    0.07693   0.315 0.752401    
poly(rain, 3)1 -0.08606    0.45870  -0.188 0.851172    
poly(rain, 3)2 -0.19269    0.46739  -0.412 0.680141    
poly(rain, 3)3  1.37875    0.41150   3.351 0.000806 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

(Dispersion parameter for binomial family taken to be 1)

    Null deviance: 74.212  on 33  degrees of freedom
Residual deviance: 62.635  on 30  degrees of freedom
AIC: 161.33

Number of Fisher Scoring iterations: 3

> summary(toxo.glm2)

Call:
glm(formula = cbind(r, m - r) ~ rain + I(rain^2) + I(rain^3), 
    family = binomial, data = toxo)

Deviance Residuals: 
    Min       1Q   Median       3Q      Max  
-2.7620  -1.2166  -0.5079   0.3538   2.6204  

Coefficients:
              Estimate Std. Error z value Pr(>|z|)    
(Intercept) -2.902e+02  8.722e+01  -3.327 0.000878 ***
rain         4.500e-01  1.347e-01   3.341 0.000836 ***
I(rain^2)   -2.311e-04  6.903e-05  -3.348 0.000813 ***
I(rain^3)    3.932e-08  1.174e-08   3.351 0.000806 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

(Dispersion parameter for binomial family taken to be 1)

    Null deviance: 74.212  on 33  degrees of freedom
Residual deviance: 62.635  on 30  degrees of freedom
AIC: 161.33

Number of Fisher Scoring iterations: 3

> summary(toxo.quasi2)

Call:
glm(formula = cbind(r, m - r) ~ rain + I(rain^2) + I(rain^3), 
    family = quasibinomial, data = toxo)

Deviance Residuals: 
    Min       1Q   Median       3Q      Max  
-2.7620  -1.2166  -0.5079   0.3538   2.6204  

Coefficients:
              Estimate Std. Error t value Pr(>|t|)  
(Intercept) -2.902e+02  1.215e+02  -2.388   0.0234 *
rain         4.500e-01  1.876e-01   2.398   0.0229 *
I(rain^2)   -2.311e-04  9.616e-05  -2.404   0.0226 *
I(rain^3)    3.932e-08  1.635e-08   2.405   0.0225 *
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

(Dispersion parameter for quasibinomial family taken to be 1.940446)

    Null deviance: 74.212  on 33  degrees of freedom
Residual deviance: 62.635  on 30  degrees of freedom
AIC: NA

Number of Fisher Scoring iterations: 3

> (74.212-62.635)/3/1.940446
[1] 1.988718
> pf(.Last.value, 3, 30, lower=F)
[1] 0.1368842
> summary(toxo.quasi)

Call:
glm(formula = cbind(r, m - r) ~ poly(rain, 3), family = quasibinomial, 
    data = toxo)

Deviance Residuals: 
    Min       1Q   Median       3Q      Max  
-2.7620  -1.2166  -0.5079   0.3538   2.6204  

Coefficients:
               Estimate Std. Error t value Pr(>|t|)  
(Intercept)     0.02427    0.10716   0.226   0.8224  
poly(rain, 3)1 -0.08606    0.63897  -0.135   0.8938  
poly(rain, 3)2 -0.19269    0.65108  -0.296   0.7693  
poly(rain, 3)3  1.37875    0.57321   2.405   0.0225 *
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

(Dispersion parameter for quasibinomial family taken to be 1.940446)

    Null deviance: 74.212  on 33  degrees of freedom
Residual deviance: 62.635  on 30  degrees of freedom
AIC: NA

Number of Fisher Scoring iterations: 3