Question

For the data set shown? below, complete parts? (a) through? (d) below. x 3 4 5 7 8 y 4 6 8 12 13 ?(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 not sufficient evidence at the alpha equals 0.05 level of significance to conclude that a linear relation exists between x and y. B. 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. C. 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. D. 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

Following table shows the calculations:

	X	Y	X^2	Y^2	XY
	3	4	9	16	12
	4	6	16	36	24
	5	8	25	64	40
	7	12	49	144	84
	8	13	64	169	104
Total	27	43	163	429	264

Sample size: n=5

Now,

Slope of the regression equation is

and intercept of the equation will be

So the regression equation will be

y'=-1.384+1.849x

(b)

Let us find SSE first :

So standard error of estimate will be

(c)

The standard error of slope is

(d)

Hypotheses are:

T-statistics is

Degree of freedom of test is df=n-2=5-2=3

P-value of the test : 0.0002

D. 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.