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A city in Texas wants to know the relationship between house size and the number of...

A city in Texas wants to know the relationship between house size and the number of residents living in the house. The city has sampled 15 houses. Table below presents the number of residents and the house size. Obtain a regression equation and predict the house size required for a family of 5 residents?

Number of Residents

House size (Sq. ft)

3

1992

3

1754

3

1766

5

2060

6

2293

6

2139

3

1836

4

1924

6

2321

4

2060

3

1769

4

1955

5

2309

4

1857

4

1972
business   Operations-Management   
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Answer #1

Let the number of residents be defined by x and house size by y

Let the Regression line be y = bo + b1x

where,

bo = ( Σy Σx2 - Σx Σxy ) / ( nΣx2 - (Σx)2 )

b1 = ( nΣxy - ΣxΣy ) / ( nΣx2 - (Σx)2 )

Residents (x) House Size (y) x2 xy
3 1992 9 5976
3 1754 9 5262
3 1766 9 5298
5 2060 25 10300
6 2293 36 13758
6 2139 36 12834
3 1836 9 5508
4 1924 16 7696
6 2321 36 13926
4 2060 16 8240
3 1769 9 5307
4 1955 16 7820
5 2309 25 11545
4 1857 16 7428
4 1972 16 7888
Σ 63 30007 283 128786

bo = ( 30007*283 - 63*128786 ) / ( 15*283 - 632 ) = 1371.24

b1 = ( 15*128786 - 63*30007 ) / ( 15*283 - 632 ) = 149.82

=> y = 1371.24 + 149.82x

when x = 5, y = 1371.24 + 149.82*5 = 2120.34

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