Question

the number of bird specie living in an industrial region have been declining during the past thirty years. Here are the number of bird specie inhabiting the region from 1960 to 1984.

Year 1960 1963 1966 1969 1972 1975 1978 1981 1984

Species 132 129 122 104 102 105 94 81 70

1)Give the equation of the least square regression line of the number of species

2)Find the predicted number of species in 1987.

3)Give the correlation coefficient and coefficient of determination

4)Comment on the direction, form and strength of the relatio between Midterm and Final Scores

5)Is the answer to part c reasonable? Give reason for your answer

6)What fraction of the observed variation is accounted for by the linear change over time?

Answer 1

Let x: year y: Species Sr. No. 1960 1963 1966 1969 1972 1975 132258720384160017424 129 2532273853369 16641 1222398523865156 14884 104 204776 3876961 10816 102 201144 3888784 10404 105 207375 390062511025 1978 94 185932 39124848836 6561 1984 | 70中| | 4900 939 1850367 34999596 101491 2 4 6 7 8 81 1604613924361 1388803936256 1981 Total 17748

Foum he abive cell ations ZXY= 1250363- 小い。 x- 34999596 二、8503 6구-) 1972x g39 B E -2.4833 z ro4.3333 248 33 x 1971 R l east squase 96ession line is

Y= Soo)-467-24833 X 1987- 6709029 We x now Thus Thus, costelathon beween Yeas anl Species S-0-9724 NoW 0.9455 4'

which ndicates that thee is negahve oelation Thus, we 24 can say that, as, Yeoð Incơe mumbeo of sPeces axe decoeases. we con aso say that thehive velabidn betvein Midtem2 Final Scose cut expleuns gy.s5% vanability 'm tne model thus, thu answers In Partie a犯配ason able aecovnted b the lmeas change ove ime