Listed below are the log body weights and log brain weights of the primates spec

Question

Listed below are the log body weights and log brain weights of the primates species in the data set ”mammals”. Find the equation of the least squares line with y = log brain weight and x = log body weight. Do it by hand, by constructing a table like the one in Example 9.1. Then do it with your calculator as efficiently as possible. Finally, use the lm function in R to do it by creating a linear model object ”primates.lm”. The model formula is ”log(brain)log(body)”. You can select the primates and put them in a new data frame by first listing the primate species names:

> primatenames=c(”Owl monkey”, ”Patas monkey”, ”Gorilla”, etc.)

and then

> primates=mammals[primatenames, ]

Your ”data” argument in calling lm would be ”data=primates”, as in

> primates.lm=lm(log(brain)log(body),data=primates)

Alternatively, you can just use ”mammals[primatenames, ]” as the data argument in lm, that is,

> primates.lm=lm(log(brain)log(body), data=mammals[primatenames,])

log body               log brain

Owl monkey                       -0.7339692         2.740840

Patas monkey                    2.3025851           4.744932

Gorilla                                   5.3327188           6.006353

Human                                 4.1271344           7.185387

Rhesus monkey                                1.9169226           5.187386

Chimpanzee                                       3.9543159           6.086775

Baboon                                                 2.3561259           5.190175

Verbet                                                  1.4327007           4.060443

Galago                                                  -1.6094379        1.609438

Slow loris                                             0.3364722           2.525729

Explanation / Answer

The dataset is not given hence we use the mammalssleep data set ,

the r code is as below

data("mammalsleep")

primatenames <- c("Owl monkey", "Patas monkey", "Gorilla")

primates= mammalsleep %>% filter(species %in% primatenames)
#Your ”data” argument in calling lm would be ”data=primates”, as in
primates.lm=lm(log(brw)~log(bw),data=primates)

summary(primates.lm)

The results of the regression is

summary(primates.lm)

Call:

lm(formula = log(brw) ~ log(bw), data = primates)

Residuals:

1 2 3

-0.1233 -0.1231 0.2464

Coefficients:

Estimate Std. Error t value Pr(>|t|)  

(Intercept) 3.25902 0.23780 13.705 0.0464 *

log(bw) 0.53831 0.07035 7.652 0.0827 .

---

Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.3018 on 1 degrees of freedom

Multiple R-squared: 0.9832, Adjusted R-squared: 0.9664

F-statistic: 58.55 on 1 and 1 DF, p-value: 0.08273

The regression equation is formed using the

as

log(brw) = 3.25 +0.5383*log(bw)

the r2 value is 0.9832 , this means that the model is very good, higher the value better the model range is 0 to 1

also note that r2 means that about 98.32 % variation in data is explained by the model

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