Question

Consider the multiple linear regression (MLR) model that satisfies the classical assumptions: Yi = Bo + B1Xil +...+Bkxik + Ui estimated by OLS/MOM. Let the estimators beßo, Ŝ1,..., ØK. Question 1 (1 point) The p-value for undertaking a hypothesis test is the smallest significance level for which we reject a null hypothesis that is correct. True False Question 2 (1 point) To test Ho: B3 = 34 vs H1 : B3 – B4 > 0, we form the test statistic B3-² se (B3-BA) examining whether the sample value of the test statistic is more extreme than a critical value, chosen at some appropriate significance level, based on a Student-t null distribution with 1 degree of freedom. t= True False

Answer 1

Given data: Assume multiple lineas segression (MLR) model is : Y = Bo+ Bxit. ...+ Bx dik + 4i where edimators le BK 1 Multiple linear segression: : It is used to estimate the relation between two con more independent var alles and one dependent Variable a Question 1: Given statement is the p-value for undertaking hypothers test is the smallest significance level for which we reject a null hypothesis is correct. STRUE So, the p-value is the smallest (least possible) significance Level. Question 2 : Given data! Ho: B2 = By VIS HP₂-By > 0 Test statistic it = B3 - By selp - fu) To examine whether the sample value its more extreme than a critical value at some significance level based on student -t null distribution with a degree freedom

Test stadistic is. = p.2 - By & talnok) se (B3-B4) where n= number of observations k= number of estimated coefficients Hence, we are not able define aboud kand a values, therefore degrees of freedom may not be 1 Therefore, FALSEL Question 3 : By considering whypothesu test in above question, the p-value is defined as: P- Value - Pr (+ (n-k-1) > t samp) Where; t(n-k-i) = Studentt sandom variable degrees of freedom (n-k-1) = Degrees of freedom Sample value of the test statistic tsamp with pl. Because to uppee taited is greater than o, we use greater to find p value, Therefore, TRUE