The rowan (Sorbus aucuparia) is a tree that grows in a wide range of altitudes. To study how the tree adapts to its varying habitats, researchers collected twigs with attached buds from 12 trees growing at various altitudes in North Angus, Scotland. The buds were brought back to the laboratory, and measurements were made of the dark respiration rate. The accompanying table shows the altitude of origin (in meters) of each batch of buds and the dark respiration rate (expressed as pi of oxygen per hour per mg dry weight of tissue).15

(a) Calculate the linear regression of Yon X.
(b) Plot the data and the regression line.
(c) Interpret the value of the slope of the regression line, by1, in the context of this setting.
(d) Calculate the residual standard deviation.

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Altitude origin X (m) rate Y (ul/hr X mg) of Respiration 90 230 240 260 330 400 410 550 590 610 700 790 433.333 214.617 0.11 0.20 0.13 0.15 0.18 0.16 023 0.18 0.23 0.26 032 0.37 0.21000 007711 Mean SD r0.88665 SS( resid ) 0.01 3986