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Question
Information on v:ehicles [in thousands) passing through seven different highways during a day (X) and number of accidents reported (Y) is given as follows :
`Sigmax_i` = 105, `Sigmay_i` = 409, n = 7, `Sigmax_i^2` = 1681, `Sigmay_i^2` = 39350 `Sigmax_iy_i` = 8075
Obtain the linear regression of Y on X.
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Solution
`Sigmax_i` = 105, `Sigmay_i` = 409, n = 7, `Sigmax_i^2` = 1681, `Sigmay_i^2` = 39350 `Sigmax_iy_i` = 8075
`bar x (Sigmax_i)/n = 105/7` = 15`
`bar x = 15, bar y = (Sigmay_i)/n = 409/7` = 58.4285
Coefficient of regression Y on X is
`b_yx = (nSigmax_iy_i - Sigmax_iSigmay_i)/(nSigmax_i^2 - Sigmax_i)^2`
= `(7(8075) - 105 (409))/(7(1681) - (105)^2)`
= `(56525 - 42945)/(11767 - 11025)`
= `13580/742`
`b_(yx) = 18.3018`
Equation of regression line Y on X is
`y - bar y = b_yx (x - bar x)`
y - 58.4285 = 18.3018x - 274.5270
y = 18.3018x - 274.5270 + 58.4285
y = 18.3018x - 216.0985
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