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.(a)Test for a significant relationship among x1, x2, and y. Use ? = 0.05.State the null and alternative hypotheses.H0: β1 < β2Ha: β1 ≥ β2H0: β1 > β2Ha: β1 ≤ β2 H0: β1 = β2 = 0Ha: One or more of the parameters is not equal to zero.H0: β1 ≠ 0 and β2 = 0Ha: β1 = 0 and β2 ≠ 0H0: β1 ≠ 0 and β2 ≠ 0Ha: 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.Reject H0. There is sufficient 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 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.(b)Is β1 significant? Use ? = 0.05.State the null and alternative hypotheses.H0: β1 ≠ 0Ha: β1 = 0H0: β1 > 0Ha: β1 ≤ 0 H0: β1 = 0Ha: β1 ≠ 0H0: β1 = 0Ha: β1 > 0H0: β1 < 0Ha: β1 ≥ 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.)p-value = State your conclusion.Do not reject H0. There is sufficient 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 insufficient evidence to conclude that β1 is significant.Reject H0. There is sufficient evidence to conclude that β1 is significant.(c)Is β2 significant? Use ? = 0.05.State the null and alternative hypotheses.H0: β2 < 0Ha: β2 ≥ 0H0: β2 ≠ 0Ha: β2 = 0 H0: β2 = 0Ha: β2 > 0H0: β2 > 0Ha: 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.)p-value = State your 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 $x_1$, $x_2$, and $y$. Use $\alpha = 0.05$.**State the null and alternative hypotheses.- $H_0 : \beta_1 < \beta_2$ $H_a : \beta_1 \geq \beta_2$- $H_0 : \beta_1 > \beta_2$ $H_a : \beta_1 \leq \beta_2$- $H_0 : \beta_1 = \beta_2 = 0$ $H_a :$ One or more of the parameters is not equal to zero.- $H_0 : \beta_1 \neq 0 \text{ and } \beta_2 = 0$ $H_a : \beta_1 = 0 \text{ and } \beta_2 \neq 0$- $H_0 : \beta_1 \neq 0 \text{ and } \beta_2 \neq 0$ $H_a :$ One or more of the parameters is equal to zero.Find the value of the test statistic. (Round your answer to two decimal places.) \[ \text{Test Statistic} = \underline{\quad\quad\quad} \]Find the $p$-value. (Round your answer to three decimal places.)\[ p\text{-value} = \underline{\quad\quad\quad} \]State your conclusion.- $ \circ $ Reject $H_0$. There is sufficient evidence to conclude that there is a significant relationship among the variables.- $ \circ $ Do not reject $H_0$. There is sufficient evidence to conclude that there is a significant relationship among the variables.- $ \circ $ Reject $H_0$. There is insufficient evidence to conclude that there is a significant relationship among the variables.- $ \circ $ Do not reject $H_0$. There is insufficient evidence to conclude that there is a significant relationship among the variables. ### Hypothesis Testing for Significance of $\beta_1$#### Is $\beta_1$ significant? Use $\alpha = 0.05$.**State the null and alternative hypotheses:**- $\circ$ $H_0: \beta_1 \neq 0$ $H_a: \beta_1 = 0$- $\circ$ $H_0: \beta_1 > 0$ $H_a: \beta_1 \leq 0$- $\circ$ $H_0: \beta_1 = 0$ $H_a: \beta_1 \neq 0$- $\circ$ $H_0: \beta_1 = 0$ $H_a: \beta_1 > 0$- $\circ$ $H_0: \beta_1 < 0$ $H_a: \beta_1 \geq 0$**Find the value of the test statistic.** *(Round your answer to two decimal places.)*\[ \boxed{\phantom{value}} \]**Find the $ p $-value.** *(Round your answer to three decimal places.)*\[ p\text{-value} = \boxed{\phantom{value}} \]**State your conclusion:**- $\circ$ Do not reject $H_0$. There is sufficient evidence to conclude that $\beta_1$ is significant.- $\circ$ Do not reject $H_0$. There is insufficient evidence to conclude that $\beta_1$ is significant.- $\circ$ Reject $H_0$. There is insufficient evidence to conclude that $\beta_1$ is significant.- $\circ$ Reject $H_0$. There is sufficient evidence to conclude that $\beta_1$ is significant.

a) Null Hypothesis: H0:β1=β2=0 Alternative Hypothesis: H1: At least one coefficient is not equal to…

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

(a)

Test for a significant relationship among

x₁, x₂, and y.

Use ? = 0.05.

State the null and alternative hypotheses.

H₀: β₁ < β₂
H_a: β₁ ≥ β₂H₀: β₁ > β₂
H_a: β₁ ≤ β₂ H₀: β₁ = β₂ = 0
H_a: One or more of the parameters is not equal to zero.H₀: β₁ ≠ 0 and β₂ = 0
H_a: β₁ = 0 and β₂ ≠ 0H₀: β₁ ≠ 0 and β₂ ≠ 0
H_a: 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.

Reject H₀. There is sufficient 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 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.

(b)

β₁

significant? Use ? = 0.05.

State the null and alternative hypotheses.

H₀: β₁ ≠ 0
H_a: β₁ = 0H₀: β₁ > 0
H_a: β₁ ≤ 0 H₀: β₁ = 0
H_a: β₁ ≠ 0H₀: β₁ = 0
H_a: β₁ > 0H₀: β₁ < 0
H_a: β₁ ≥ 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 β₁ is significant.Do not reject H₀. There is insufficient evidence to conclude that β₁ is significant. Reject H₀. There is insufficient evidence to conclude that β₁ is significant.Reject H₀. There is sufficient evidence to conclude that β₁ is significant.

(c)

β₂

significant? 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.)

p-value =

State your 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 $x_1$, $x_2$, and $y$. Use $\alpha = 0.05$.**

State the null and alternative hypotheses.

- $H_0 : \beta_1 < \beta_2$
$H_a : \beta_1 \geq \beta_2$

- $H_0 : \beta_1 > \beta_2$
$H_a : \beta_1 \leq \beta_2$

- $H_0 : \beta_1 = \beta_2 = 0$
$H_a :$ One or more of the parameters is not equal to zero.

- $H_0 : \beta_1 \neq 0 \text{ and } \beta_2 = 0$
$H_a : \beta_1 = 0 \text{ and } \beta_2 \neq 0$

- $H_0 : \beta_1 \neq 0 \text{ and } \beta_2 \neq 0$
$H_a :$ One or more of the parameters is equal to zero.

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

\[ \text{Test Statistic} = \underline{\quad\quad\quad} \]

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

\[ p\text{-value} = \underline{\quad\quad\quad} \]

State your conclusion.

- $ \circ $ Reject $H_0$. There is sufficient evidence to conclude that there is a significant relationship among the variables.

- $ \circ $ Do not reject $H_0$. There is sufficient evidence to conclude that there is a significant relationship among the variables.

- $ \circ $ Reject $H_0$. There is insufficient evidence to conclude that there is a significant relationship among the variables.

- $ \circ $ Do not reject $H_0$. There is insufficient evidence to conclude that there is a significant relationship among the variables.

### Hypothesis Testing for Significance of $\beta_1$

#### Is $\beta_1$ significant? Use $\alpha = 0.05$.

**State the null and alternative hypotheses:**

- $\circ$ $H_0: \beta_1 \neq 0$
$H_a: \beta_1 = 0$

- $\circ$ $H_0: \beta_1 > 0$
$H_a: \beta_1 \leq 0$

- $\circ$ $H_0: \beta_1 = 0$
$H_a: \beta_1 \neq 0$

- $\circ$ $H_0: \beta_1 = 0$
$H_a: \beta_1 > 0$

- $\circ$ $H_0: \beta_1 < 0$
$H_a: \beta_1 \geq 0$

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

\[ \boxed{\phantom{value}} \]

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

\[ p\text{-value} = \boxed{\phantom{value}} \]

**State your conclusion:**

- $\circ$ Do not reject $H_0$. There is sufficient evidence to conclude that $\beta_1$ is significant.

- $\circ$ Do not reject $H_0$. There is insufficient evidence to conclude that $\beta_1$ is significant.

- $\circ$ Reject $H_0$. There is insufficient evidence to conclude that $\beta_1$ is significant.

- $\circ$ Reject $H_0$. There is sufficient evidence to conclude that $\beta_1$ is significant.

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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