You may need to use the appropriate technology to answer this question.Consider the following data for a dependent variable y and two independent variables, x1 and x2.x1x2y301293471010825171125116178405945119175747170361211759131427616210The estimated regression equation for these data isŷ = −18.21 + 2.01x1 + 4.72x2.Here, SST = 15,134.9, SSR = 13,994.6, sb1 = 0.2482, and sb2 = 0.9524.THIS PART IS C.Is β2 significant? Use ? = 0.05.State the null and alternative hypotheses.- H0: β2 < 0Ha: β2 ≥ 0H0: β2 ≠ 0- Ha: β2 = 0 H0: β2 = 0Ha: β2 > 0H0: β2 > 0- Ha: β2 ≤ 0H0: β2 = 0Ha: β2 ≠ 0Find the value of the test statistic. (Round your answer to two decimal places.) Find the p-value. (Round your answer to three decimal places.)Conclusion:Reject H0. There is insufficient evidence to conclude that β2 is significant.Reject H0. There is sufficient evidence to conclude that β2 is significant. Do not reject H0. There is insufficient evidence to conclude that β2 is significant.Do not reject H0. There is sufficient evidence to conclude that β2 is significant. (a) Test for a significant relationship among x, X3, and y. Use a = 0.05.State the null and alternative hypotheses.O Ho: B1 < B2O Họ: B1 > B2Hgi Bq S BzO Ho: B1 = B2 = 0H: One or more of the parameters is not equal to zero.O Ho: B, * 0 and B, = 0H: B, = 0 and B, * 0O Ho: B, * 0 and B, # 0H: One or more of the parameters is equal to zero.Find the value of the test statistic. (Round your answer to two decimal places.)Find the p-value. (Round your answer to three decimal places.)p-value =State your conclusion.O Reject Ho. There is sufficient evidence to conclude that there is a significant relationship among the variables.O Do not reject H. There is sufficient evidence to conclude that there is a significant relationship among the variables.O Reject H,. There is insufficient evidence to conclude that there is a significant relationship among the variables.O Do not reject H. There is insufficient evidence to conclude that there is a significant relationship among the variables. (b) Is B, significant? Use a = 0.05.State the null and alternative hypotheses.O Ho: B1 * 0H: B, = 0O Ho: B, > 0O Ho: B1 = 0H: B, * 0O Ho: B1 = 0Hi ß, > 0O Ho: B, < 0a'1Find the value of the test statistic. (Round your answer to two decimal places.)Find the p-value. (Round your answer to three decimal places.)p-value =State your conclusion.O Do not reject Hp: There is sufficient evidence to conclude that B, is significant.Do not reject H,. There is insufficient evidence to conclude that B, is significant.Reject Ho.There is insufficient evidence to conclude that B, is significant.Reject Ho.There is sufficient evidence to conclude that B, is significant.

Solution: Given information: n= 10 observation k=2 independent variables β1^=2.01 β2^=4.72 S.E(β1^)=0.2482 S.E(β2^)=0.9524SST= 15134.9SSR=13994.6SST=SSR+SSESSE=SST-SSRSSE=15134.9-13994.6=1140.3 a) Test for significant relationship among x1 , x2 and y The null and alternative hypothesis is Ho:β1=β2=0 Vs Ha : one or more parameter is not equal to zero Option C is correct Test statistic F=SSR/kSSE/n-(k+1)F=13994.6/21140.3/7F=6997.3162.9=42.954573F=42.95 Test statistic F = 42.95 P value = 0.000117 From excel P value = 0.000 Decision : P value α=0.05 Reject Ho Conclusion: Reject Ho there is sufficient evidence to conclude that there is significant relationship among the variables Option A is correct b) Test for significant of β1 The null and alternative hypothesis is Ho:β1=0 VS Ha:β1≠0 Option C is correct Test statistic t=β1^S.E(β1^)t=2.010.2482=8.0983078t = 8.10 Test statistic t = 8.10 P value = 0.000084 From excel P value = 0.000 Decision: P value < α=0.05 Reject Ho Conclusion: Reject Ho there is sufficient evidence to conclude that β1 is significant Option D is correct c) Test for significant of β2 The null and alternative hypothesis is Ho:β2=0 VS Ha:β2≠0 Test statistic t=β2^S.E(β2^)t=4.720.9524=4.9559008t = 4.96 Test statistic t = 4.96 P value =0.001638 From excel P value = 0.002 Decision: P value < α=0.05 Reject Ho Conclusion: Reject Ho there is sufficient evidence to conclude that β1 is significant

Answered: ou may need to use the appropriate…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

You may need to use the appropriate technology to answer this question.

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

x₁

and

x₂.

x₁	x₂	y
30	12	93
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	210

The estimated regression equation for these data is

ŷ = −18.21 + 2.01x₁ + 4.72x₂.

Here, SST = 15,134.9, SSR = 13,994.6,

s_b1 = 0.2482,

and

s_b2 = 0.9524.

THIS PART IS C.

Is β₂significant? Use ? = 0.05.

State the null and alternative hypotheses.

- H₀: β₂ < 0
H_a: β₂ ≥ 0H₀: β₂ ≠ 0
- H_a: β₂ = 0 H₀: β₂ = 0
H_a: β₂ > 0H₀: β₂ > 0
- H_a: β₂ ≤ 0H₀: β₂ = 0
H_a: β₂ ≠ 0

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

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

Conclusion:

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

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

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

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

(a) Test for a significant relationship among x, X3, and y. Use a = 0.05.
State the null and alternative hypotheses.
O Ho: B1 < B2
O Họ: B1 > B2
Hgi Bq S Bz
O Ho: B1 = B2 = 0
H: One or more of the parameters is not equal to zero.
O Ho: B, * 0 and B, = 0
H: B, = 0 and B, * 0
O Ho: B, * 0 and B, # 0
H: One or more of the parameters is equal to zero.
Find the value of the test statistic. (Round your answer to two decimal places.)
Find the p-value. (Round your answer to three decimal places.)
p-value =
State your conclusion.
O Reject Ho. There is sufficient evidence to conclude that there is a significant relationship among the variables.
O Do not reject H. There is sufficient evidence to conclude that there is a significant relationship among the variables.
O Reject H,. There is insufficient evidence to conclude that there is a significant relationship among the variables.
O Do not reject H. There is insufficient evidence to conclude that there is a significant relationship among the variables.

(b) Is B, significant? Use a = 0.05.
State the null and alternative hypotheses.
O Ho: B1 * 0
H: B, = 0
O Ho: B, > 0
O Ho: B1 = 0
H: B, * 0
O Ho: B1 = 0
Hi ß, > 0
O Ho: B, < 0
a'
1
Find the value of the test statistic. (Round your answer to two decimal places.)
Find the p-value. (Round your answer to three decimal places.)
p-value =
State your conclusion.
O Do not reject Hp: There is sufficient evidence to conclude that B, is significant.
Do not reject H,. There is insufficient evidence to conclude that B, is significant.
Reject Ho.
There is insufficient evidence to conclude that B, is significant.
Reject Ho.
There is sufficient evidence to conclude that B, is significant.

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Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.

x₁	x₂	y
30	12	93
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	210

x₁	x₂	y
30	12	93
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	210

ou may need to use the appropriate technology to answer this question. Consider the following data for a dependent variable y and two independent variables, x1 and x2. x1 x2 y 30 12 93 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 16 210

x₁	x₂	y
30	12	93
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	210