Suppose you were checking the normality assumption for a simple linear regressio

Question

Suppose you were checking the normality assumption for a simple linear regression model y = beta_0 + beta_1 x + e. Would it be correct to plot the observations for y on a Q-Q plot, or to test for the normality of y using a test like Shapiro-Wilks?

Yes, if the response variable is normal, the errors will be normal as well. (I would expect this to be correct since one would expect the errors to be normal if the     response variable is normal)

No, the assumption is about the errors, rather than y being normal.

Yes, as long as the explanatory variable x is normally distributed.

Explanation / Answer

Whenever we want to check the assumption of normality we plot the residuals on Q-Q plot and to coherent our conclusion we are using Shapiro-Wilks test for response and residual. Using both the things it gives same result.it can't happen that accrding to Q-Q plot response and residual follows nomality assumption and according to Shapiro-Wilks it does n't fallow normality assumption.We know the additive property of normal distribution that linear combination of two narmal population is agin normal so,y is linear combination of x and e as yand e are normal then we may say that x is also normally distributed.

Related Questions

Navigate

• Browse (All)
• Browse S
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.