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Questions › DSE › DSE 2020 › Q15
4 marks, −1Econometrics › Linear regression and OLS › The two regression lines and the correlation coefficientModerateabout 3 min

DSE 2020 Question 15: Linear regression and OLS

Let XXX and YYY be jointly normal, (X,Y)∼N(μX,μY,σX2,σY2,ρ)(X,Y)\sim N(\mu_X,\mu_Y,\sigma_X^2,\sigma_Y^2,\rho)(X,Y)∼N(μX​,μY​,σX2​,σY2​,ρ). If σX2=σY2\sigma_X^2=\sigma_Y^2σX2​=σY2​ and 0<ρ<10<\rho<10<ρ<1, then

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Let X and Y be jointly normal, (X,Y)~ N(μ_X,μ_Y,σ_X²,σ_Y²,ρ). If σ_X²=σ_Y² and 0<ρ<1, then (A) the OLS regression of Y on X yields a slope less than unity, and that of X on Y a slope greater than unity (B) the OLS regression of Y on X yields a slope less than unity, and that of X on Y a slope less than unity (C) the OLS regression of Y on X yields a slope greater than unity, and that of X on Y a slope less than unity (D) it is not possible to draw conclusions about the magnitude of the slope with the given information

Also written as: Let X and Y be jointly normal, (X,Y)~ N(mu_X,mu_Y,sigma_X^2,sigma_Y^2,rho). If sigma_X^2=sigma_Y^2 and 0<rho<1, then

Linear regression and OLS has come up 74 times in 7 exams since 2008.

What this question tests

This question is on The two regression lines and the correlation coefficient, part of Linear regression and OLS in Econometrics.

How the regression of y on x and of x on y relate to each other and to correlation.

TestStop has 19 past-paper questions on this subtopic.

Practise Linear regression and OLSMore on The two regression lines and the correlation coefficient

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