Question

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, s_b1 = 0.2454,and s_b2 = 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.

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.