Question

That animal species produce more offspring when their supply of food goes up isn't surprising. That some animals appear able to anticipate unusual food abundance is more surprising. Red squirrels eat seeds from pine cones, a food source that occasionally has very large crops (called seed masting). What is striking is that the offspring are conceived in the spring, before the cones mature in the fall to feed the new young squirrels through the winter. Here are data on an index of the abundance of pine cones and average number of offspring per female over 16 years: Pine Index (x) 0 2.02 0.25 3.22 4.68 0.31 3.37 3.09 2.44 4.81 1.88 0.31 1.61 1.88 0.91 1.04 Offspring (y) 1.49 1.1 1.29 2.71 4.07 1.29 3.36 2.41 1.97 3.41 1.49 2.02 3.34 2.41 2.15 2.12 (a) Describe the relation between the variable x (Pine index) and the variable y (offspring) using the correlation factor r. Explain what r tells us about the relation. (b) Find the expected y value for a year when the Pine index is 3.6

          That animal species produce more offspring when their supply of food goes up isn't surprising. That some animals appear able to anticipate unusual food abundance is more surprising. Red squirrels eat seeds from pine cones, a food source that occasionally has very large crops (called seed masting). What is striking is that the offspring are conceived in the spring, before the cones mature in the fall to feed the new young squirrels through the winter. Here are data on an index of the abundance of pine cones and average number of offspring per female over 16 years:

Pine Index (x)
0
2.02
0.25
3.22
4.68
0.31
3.37
3.09
2.44
4.81
1.88
0.31
1.61
1.88
0.91
1.04

Offspring (y)
1.49
1.1
1.29
2.71
4.07
1.29
3.36
2.41
1.97
3.41
1.49
2.02
3.34
2.41
2.15
2.12

(a) Describe the relation between the variable x (Pine index) and the variable y (offspring) using the correlation factor r. Explain what r tells us about the relation.

(b) Find the expected y value for a year when the Pine index is 3.6

Added by Mark E.

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