Question

For the data set shown​ below, complete parts​ (a) through​ (d) below. x 3 4 5 7 8 y 5 7 6 13 14 ​(a)  Find the estimates of beta 0 and beta 1. beta 0almost equalsb 0equals nothing ​(Round to three decimal places as​ needed.) beta 1almost equalsb 1equals nothing ​(Round to three decimal places as​ needed.) ​(b)  Compute the standard​ error, the point estimate for sigma. s Subscript eequals nothing ​(Round to four decimal places as​ needed.) ​(c)  Assuming the residuals are normally​ distributed, determine s Subscript b 1 Baseline . s Subscript b 1equals nothing ​(Round to three decimal places as​ needed.) ​(d)  Assuming the residuals are normally​ distributed, test Upper H 0 : beta 1 equals 0 versus Upper H 1 : beta 1 not equals 0 at the alpha equals 0.05 level of significance. Use the​ P-value approach. The​ P-value for this test is nothing. ​(Round to three decimal places as​ needed.) Make a statement regarding the null hypothesis and draw a conclusion for this test. Choose the correct answer below. A. Reject Upper H 0. There is sufficient evidence at the alpha equals 0.05 level of significance to conclude that a linear relation exists between x and y. B. Reject Upper H 0. There is not sufficient evidence at the alpha equals 0.05 level of significance to conclude that a linear relation exists between x and y. C. Do not reject Upper H 0. There is not sufficient evidence at the alpha equals 0.05 level of significance to conclude that a linear relation exists between x and y. D. Do not reject Upper H 0. There is sufficient evidence at the alpha equals 0.05 level of significance to conclude that a linear relation exists between x and y.

Answer 1

a)

beta 0 =-1.3605

beta1 =1.9186

b)

SSE =Syy-(Sxy)2/Sxx=

6.686

	s2 =SSE/(n-2)=	2.2287
std error σ              =	=se =√s2=	1.4929

c)

estimated std error of slope =se(β1) =s/√Sxx=

0.3600

d)

test stat t =	β1/se(β1)=	=	5.330
p value:		=	0.013

reject Ho There is sufficient evidence at the alpha equals 0.05 level of significance to conclude that a linear relation exists between x and y.