How has brain volume changed over time in the hominin lineage? The hominin taxon

Question

How has brain volume changed over time in the hominin lineage? The hominin taxon includes Homo sapiens and about 20 extinct species that are more closely related to humans than they are to the closest living relative of humans, the chimpanzee. Researchers have found that the brain volume of the earliest hominins ranged between 300 and 450 cm3, similar to the brain volume of chimpanzees. The brain volumes of modern humans range between 1,200 and 1,800 cm3. In this exercise, you’ll examine how mean brain volume changed over time and across various hominin species. You’ll perform a linear regression, which is a technique for determining the equation for the straight line that provides a “best fit” to a set of data.

Part A - Calculating the correlation coefficient

The first step to determining if there is a linear (straight-line) relationship between brain volume and fossil age is to calculate the correlation coefficient for the data shown in the table below. The data table provides xi (mean age in millions of years ago) and yi (mean brain volume in cm3) of 8 hominin species. Ages with negative values represent millions of years before the present (which has an age of 0.0).

Calculating the correlation coefficient for this data is a multi-step process.

Start by calculating the mean of all the mean values for age (x¯). (This mean is the sum of the eight values (xi) divided by n, the number of species.) Calculate the same for brain volume (y¯). Round your answers to one decimal place.

Next calculate the values for (xix¯) and (yiy¯) for Ardipithecus ramidus. Round your answers to one decimal place.

Next calculate the values for (xix¯)2 and (yiy¯)2 for Ardipithecus ramidus. Round your answers to the nearest whole number.

Mean age (%) in millions of years Mean brain volume (y) in cm Hominin species (xi-x) (x, -x)2 (Y;-2 (x,-R) (y,- Ardipithecus ramidus -4.4 325 -3.4 375 afarensis Homo habilis 550 Homo ergaster 850 Homo erectus 1,000 Homo heidelbergensis -0.5 1,200 -0.1 1,400 Homo sapiens 0.0 1,350

Explanation / Answer

X~ = -13.5/8=-1.65

Y~ = 7050/8 = 881

r = 4490 / Square root (17.3 * 1280938)

r = 4490 / 4707

r= 0.95

Mean age (Xi-(-1.6)) (Xi - X~)2 Mean Brain (Yi - 881) (Yi - Y~)2 (Xi - X~) (Yi - Y~) 1 -4.4 -2.8 7.8 325 -556 309136 1556 -3.4 -1.8 3.2 375 -506 256036 910 -1.9 -0.3 0.09 550 -331 109561 99 -1.6 0 0 850 -31 961 0 -1.2 0.4 0.16 1000 119 14161 47 -0.5 1.1 1.21 1200 319 101761 350 -0.1 1.5 2.25 1400 519 269361 778 0 1.6 2.56 1350 469 219961 750 X~ = -1.65 17.3 Y~ = 881 1280938 4490

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