Question

The data in the accompanying table represent the population of a certain country every 10 years...

The data in the accompanying table represent the population of a certain country every 10 years for the years​ 1900-2000. An ecologist is interested in finding an equation that describes the population of the country over time.

Year, x   Population, y
1900   79,212   
1910   92,228   
1920   104,021   
1930   123,202   
1940   132,164   
1950   151,325   
1960   179,323
1970   203,302
1980   226,542
1990   248,709
2000   281,421

​(a) Determine the​ least-squares regression​ equation, treating year as the explanatory variable. Choose the correct answer below.

A.

ŷ =2,011x−1,521,037

B.

ŷ =2,011x−3,755,493

C.

ŷ =−3,755,493x+2,011

D.

ŷ =1,236,362x−3,755,493

Math   Statistics-And-Probability   
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Homework Answers

Answer #1

Correct option:

B.    

Explanation:

From the given data, the following Table is calculated:

X Y XY X2
1900 79212 150502800 3610000
1910 92228 176155480 3648100
1920 104021 199720320 3724900
1930 123202 237779860 3724900
1940 132164 256398160 3763600
1950 151325 295083750 3802500
1960 179323 351473080 3841600
1970 203302 400504940 3880900
1980 226542 448553160 3920400
1990 248709 494930910 3960100
2000 281421 562842000 4000000
Total = 21450 1821449 3573944460 41838500

So

The last square regression equation is:

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