Question

Consider the following data for a dependent variable y and two independent variables, x1and x2. x1...

Consider the following data for a dependent variable y and two independent variables, x1and x2.

x1

x2

y
30 12 96
47 10 108
25 17 112
51 16 178
40 5 94
51 19 175
74 7 170
36 12 117
59 13 142
76 16 211

The estimated regression equation for these data is ŷ = −17.33 + 2.00x1 + 4.73x2.

Here, SST = 15,002.1, SSR = 13,887.5, sb1 = 0.2454,and sb2 = 0.9417.

(a)Test for a significant relationship among x1, x2, and y. Use α = 0.05.State the null and alternative hypotheses.

(b)Find the value of the test statistic. (Round your answer to two decimal places.)

(c)Find the p-value. (Round your answer to three decimal places.)

(d)State your conclusion.

-Reject H0. There is sufficient evidence to conclude that there is a significant relationship among the variables.

-Reject H0. There is insufficient evidence to conclude that there is a significant relationship among the variables.  

-Do not reject H0. There is insufficient evidence to conclude that there is a significant relationship among the variables

-Do not reject H0. There is sufficient evidence to conclude that there is a significant relationship among the variables.

(e) Is β1 significant? Use α = 0.05.State the null and alternative hypotheses.

(f) Find the value of the test statistic. (Round your answer to two decimal places.)

(g) Find the p-value. (Round your answer to three decimal places.)

(h)State your conclusion.

-Do not reject H0. There is sufficient evidence to conclude that β1 is significant.

-Reject H0. There is insufficient evidence to conclude that β1 is significant.

-Do not reject H0. There is insufficient evidence to conclude that β1 is significant.

-Reject H0. There is sufficient evidence to conclude that β1 is significant.

(i) Is β2 significant? Use α = 0.05. State the null and alternative hypotheses.

(j) Find the value of the test statistic. (Round your answer to two decimal places.)

(k)Find the p-value. (Round your answer to three decimal places.)

(L) State your conclusion.

-Do not reject H0. There is sufficient evidence to conclude that β2 is significant.

-Reject H0. There is insufficient evidence to conclude that β2 is significant.

-Do not reject H0. There is insufficient evidence to conclude that β2 is significant

-Reject H0. There is sufficient evidence to conclude that β2 is significant.

Homework Answers

Answer #1
Ho: ß1=ß2 =0
Ha:at least one ßi is not equal to 0

b_)

p=number of independent variables= 2
MSR =SSR/p = 6943.750
MSE=(SSE/(n-p-1))= 159.229
F test statistic =MSR/MSE= 43.61

c) p value =0.000

d) -Reject H0. There is sufficient evidence to conclude that there is a significant relationship among the variables.

e_)

Ho: ß1=0

Ha:ß10

f)

value of the test statistic =2/0.2454 =8.15 (please try 8.13 if this comes wrong)

g) p value =0.000

h) -Reject H0. There is sufficient evidence to conclude that β1 is significant.

i)

Ho: ß2=0

Ha:ß20

j)

value of the test statistic =4.73/0.9417 =5.02

k)

p value =0.002

l) -Reject H0. There is sufficient evidence to conclude that β2 is significant.

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