Consider the following data for a dependent variable y and two independent variables, x1 and x2. x1 x2 y 30 12 95 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 = −17.85 + 2.00x1 + 4.73x2. Here, SST = 15,091.6, SSR = 13,969.7, sb1 = 0.2462, and sb2 = 0.9447. (a) Test for a significant relationship among x1, x2, and y. Use ? = 0.05. State the null and alternative hypotheses. H0: ?1 ≠ 0 and ?2 ≠ 0 Ha: One or more of the parameters is equal to zero.H0: ?1 < ?2 Ha: ?1 ≥ ?2 H0: ?1 = ?2 = 0 Ha: One or more of the parameters is not equal to zero.H0: ?1 ≠ 0 and ?2 = 0 Ha: ?1 = 0 and ?2 ≠ 0H0: ?1 > ?2 Ha: ?1 ≤ ?2 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. Do not reject H0. There is insufficient 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 sufficient evidence to conclude that there is a significant relationship among the variables.Reject H0. There is sufficient evidence to conclude that there is a significant relationship among the variables. (b) Is ?1 significant? Use ? = 0.05. State the null and alternative hypotheses. H0: ?1 ≠ 0 Ha: ?1 = 0H0: ?1 = 0 Ha: ?1 ≠ 0 H0: ?1 = 0 Ha: ?1 > 0H0: ?1 < 0 Ha: ?1 ≥ 0H0: ?1 > 0 Ha: ?1 ≤ 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.) p-value = State your conclusion. Do not reject H0. There is sufficient evidence to conclude that ?1 is significant.Reject H0. There is insufficient evidence to conclude that ?1 is significant. Do not reject H0. There is insufficient evidence to conclude that ?1 is significant.Reject H0. There is sufficient evidence to conclude that ?1 is significant. (c) Is ?2 significant? Use ? = 0.05. State the null and alternative hypotheses. H0: ?2 > 0 Ha: ?2 ≤ 0H0: ?2 ≠ 0 Ha: ?2 = 0 H0: ?2 < 0 Ha: ?2 ≥ 0H0: ?2 = 0 Ha: ?2 ≠ 0H0: ?2 = 0 Ha: ?2 > 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.) p-value = State your conclusion. Reject H0. There is sufficient evidence to conclude that ?2 is significant.Do not reject H0. There is insufficient evidence to conclude that ?2 is significant. Reject H0. There is insufficient evidence to conclude that ?2 is significant.Do not reject H0. There is sufficient evidence to conclude that ?2 is significant

Consider the following data for a dependent variable y and two independent variables, x1 and x2. x1 x2 y 30 12 95 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 = −17.85 + 2.00x1 + 4.73x2. Here, SST = 15,091.6, SSR = 13,969.7, sb1 = 0.2462, and sb2 = 0.9447. (a) Test for a significant relationship among x1, x2, and y. Use ? = 0.05. State the null and alternative hypotheses. H0: ?1 ≠ 0 and ?2 ≠ 0 Ha: One or more of the parameters is equal to zero.H0: ?1 < ?2 Ha: ?1 ≥ ?2 H0: ?1 = ?2 = 0 Ha: One or more of the parameters is not equal to zero.H0: ?1 ≠ 0 and ?2 = 0 Ha: ?1 = 0 and ?2 ≠ 0H0: ?1 > ?2 Ha: ?1 ≤ ?2 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. Do not reject H0. There is insufficient 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 sufficient evidence to conclude that there is a significant relationship among the variables.Reject H0. There is sufficient evidence to conclude that there is a significant relationship among the variables. (b) Is ?1 significant? Use ? = 0.05. State the null and alternative hypotheses. H0: ?1 ≠ 0 Ha: ?1 = 0H0: ?1 = 0 Ha: ?1 ≠ 0 H0: ?1 = 0 Ha: ?1 > 0H0: ?1 < 0 Ha: ?1 ≥ 0H0: ?1 > 0 Ha: ?1 ≤ 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.) p-value = State your conclusion. Do not reject H0. There is sufficient evidence to conclude that ?1 is significant.Reject H0. There is insufficient evidence to conclude that ?1 is significant. Do not reject H0. There is insufficient evidence to conclude that ?1 is significant.Reject H0. There is sufficient evidence to conclude that ?1 is significant. (c) Is ?2 significant? Use ? = 0.05. State the null and alternative hypotheses. H0: ?2 > 0 Ha: ?2 ≤ 0H0: ?2 ≠ 0 Ha: ?2 = 0 H0: ?2 < 0 Ha: ?2 ≥ 0H0: ?2 = 0 Ha: ?2 ≠ 0H0: ?2 = 0 Ha: ?2 > 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.) p-value = State your conclusion. Reject H0. There is sufficient evidence to conclude that ?2 is significant.Do not reject H0. There is insufficient evidence to conclude that ?2 is significant. Reject H0. There is insufficient evidence to conclude that ?2 is significant.Do not reject H0. There is sufficient evidence to conclude that ?2 is significant

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

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

x₁

and

x₂.

x₁	x₂	y
30	12	95
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 = −17.85 + 2.00x₁ + 4.73x₂.

Here, SST = 15,091.6, SSR = 13,969.7,

s_b1 = 0.2462,

and

s_b2 = 0.9447.

(a)

Test for a significant relationship among

x₁, x₂, and y.

Use ? = 0.05.

State the null and alternative hypotheses.

H₀: ?₁ ≠ 0 and ?₂ ≠ 0
H_a: One or more of the parameters is equal to zero.H₀: ?₁ < ?₂
H_a: ?₁ ≥ ?₂ H₀: ?₁ = ?₂ = 0
H_a: One or more of the parameters is not equal to zero.H₀: ?₁ ≠ 0 and ?₂ = 0
H_a: ?₁ = 0 and ?₂ ≠ 0H₀: ?₁ > ?₂
H_a: ?₁ ≤ ?₂

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.

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

(b)

?₁

significant? Use ? = 0.05.

State the null and alternative hypotheses.

H₀: ?₁ ≠ 0
H_a: ?₁ = 0H₀: ?₁ = 0
H_a: ?₁ ≠ 0 H₀: ?₁ = 0
H_a: ?₁ > 0H₀: ?₁ < 0
H_a: ?₁ ≥ 0H₀: ?₁ > 0
H_a: ?₁ ≤ 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.)

p-value =

State your conclusion.

Do not reject H₀. There is sufficient evidence to conclude that ?₁ is significant.Reject H₀. There is insufficient evidence to conclude that ?₁ is significant. Do not reject H₀. There is insufficient evidence to conclude that ?₁ is significant.Reject H₀. There is sufficient evidence to conclude that ?₁ is significant.

(c)

?₂

significant? Use ? = 0.05.

State the null and alternative hypotheses.

H₀: ?₂ > 0
H_a: ?₂ ≤ 0H₀: ?₂ ≠ 0
H_a: ?₂ = 0 H₀: ?₂ < 0
H_a: ?₂ ≥ 0H₀: ?₂ = 0
H_a: ?₂ ≠ 0H₀: ?₂ = 0
H_a: ?₂ > 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.)

p-value =

State your conclusion.

Reject H₀. There is sufficient evidence to conclude that ?₂ is significant.Do not reject H₀. There is insufficient evidence to conclude that ?₂ is significant. Reject H₀. There is insufficient evidence to conclude that ?₂ is significant.Do not reject H₀. There is sufficient evidence to conclude that ?₂ is significant

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x₁	x₂	y
30	12	95
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

x₁	x₂	y
30	12	95
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

x₁	x₂	y
30	12	95
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