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In: Statistics and Probability

The rowan (Sorbus aucuparia) is a tree that grows in a wide range of altitudes. To...

  1. 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 µl of oxygen per hour per mg dry weight of tissue).
  2. Compute the correlation coefficient
  3. calculate the least squares regression line of Y on X (y-hat= a +bx)
  4. Predict the respiration rate at an altitude of origin 720

Altitude of

origin X (m)

Respiration rate

Y (µl/hr x mg)

XY

X2

Y2

90

0.11

9.9

8100

.0121

230

0.20

46.0

52900

.0400

240

0.13

31.2

57600

.0169

260

0.15

39.0

67600

.0225

330

0.18

59.4

108900

.0324

400

0.16

64.0

160000

.0256

410

0.23

94.3

168100

.0529

550

0.18

99.0

302500

.0324

590

0.23

135.7

348100

.0529

610

0.26

158.6

372100

.0676

700

0.32

224.0

490000

.1024

790

0.37

292.3

624100

.1369

Sum: 5200

2.52

1253.4

2760000

.5946

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Expert Solution

orchestra answered 1 year ago
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