Question

An analyst analysed 102 trips of a travel company. He studied the relation between travel expenses (y) and the duration (x) of these trips. He found that the relation between x and y was linear. Given the following data, find the regression equation of y on x.

`sumx` = 510, `sumy` = 7140, `sumx^2` = 4150, `sumy^2` = 740200, `sumxy` = 54900

Answer 1

Given n = 102

`sumx` = 510,

`sumy` = 7140,

`sumx^2` = 4150,

`sumy^2` = 740200

and `sumxy` = 54900

∵ `barx = (sumx)/n`

= `510/102`

= 5

`bary = (sumy)/n`

= `7140/102`

= 70

b_yx = `(sumxy - (sumxsumy)/n)/(sumx^2 - (sumx)^2/n)`

= `(54900 - (510 xx 7140)/102)/(4150 - (510)^2/102`

= `(54900 - 35700)/(4150 - 2550)`

= `19200/1600`

∴ b_yx = 12

Now, the regression line for y on x is

`y - bary = b_(yx)(x - barx)`

y – 70 = 12(x – 5)

y – 70 = 12x – 60

y = 12x + 10