For 50 randomly selected speed dates, attractiveness ratings by males of their female date partners (x) are recorded along with the attractiveness ratings by females of their male date partners (y); the ratings range from 1 to 10. the 50 paired ratings yield x overbarxequals=6.46.4, y overbaryequals=6.06.0, requals=negative 0.281−0.281, p-valueequals=0.0480.048, and modifyingabove y with caretyequals=8.128.12negative 0.323−0.323x. find the best predicted value of modifyingabove y with carety (attractiveness rating by female of male) for a date in which the attractiveness rating by the male of the female is xequals=55. use a 0.100.10 significance level.

Question

10-05-2018
Mathematics

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For 50 randomly selected speed dates, attractiveness ratings by males of their female date partners (x) are recorded along with the attractiveness ratings by females of their male date partners (y); the ratings range from 1 to 10. the 50 paired ratings yield x overbarxequals=6.46.4, y overbaryequals=6.06.0, requals=negative 0.281−0.281, p-valueequals=0.0480.048, and modifyingabove y with caretyequals=8.128.12negative 0.323−0.323x. find the best predicted value of modifyingabove y with carety (attractiveness rating by female of male) for a date in which the attractiveness rating by the male of the female is xequals=55. use a 0.100.10 significance level.

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Mamasu Mamasu · Answer 1 · 2018-05-23T17:46:54+02:00

This is a linear regression problem. We are given the linear regression equation already, and that is [tex]\hat{y\:}=8.12-0.323x[/tex]. So, we are asked to find the value of y, when the value of x is equal to 5.

To do this, we just need to substitute the value of x to the given linear regression equation. That is
[tex]\hat{y\:}=8.12-0.323\left(5\right)=6.505[/tex]

Therefore, when the value of x is 5, the value of y is predicted to be about 6.5.