Need help solving a b and c ### Regression Analysis of Dependent and Independent Variables#### Data TableThe following data is provided for a dependent variable \( y \) and two independent variables, \( x_1 \) and \( x_2 \):| \( x_1 \) | \( x_2 \) | \( y \) ||-----------|-----------|---------|| 30 | 12 | 94 || 47 | 10 | 108 || 25 | 17 | 112 || 51 | 16 | 178 || 40 | 5 | 94 || 51 | 19 | 175 || 74 | 17 | 170 || 36 | 12 | 117 || 59 | 13 | 142 || 76 | 16 | 211 |#### Estimated Regression EquationThe estimated regression equation based on the given data is:\[\hat{y} = -18.36827 + 2.01019x_1 + 4.73781x_2\]#### Sum of Squares- Total Sum of Squares (SST): 15,182.9- Regression Sum of Squares (SSR): 14,052.2- Standard error of \( x_1 \) (\( s_{b_1} \)): 0.24712- Standard error of \( x_2 \) (\( s_{b_2} \)): 0.94844#### Hypothesis Testing**Objective:** Test for a significant relationship among \( x_1 \), \( x_2 \), and \( y \). Use \( \alpha = 0.05 \).**Hypothesis:**- **\( H_0 \):** \(\beta_1 = \beta_2 = 0\)- **\( H_a \):** One or more of the parameters is not equal to zero.Choices:- \( H_0 \): \(\beta_1 > \beta_2 \) \( H_a \): \(\beta_1 \leq \beta_2 \) - \( H_0 \): \(\beta_1 \neq 0 \) and \(\beta_2 \neq ### Statistical Significance Testing**(b) Is \( \beta_1 \) significant? Use \(\alpha = 0.05\).**#### Steps to Determine Significance:1. **State the Null and Alternative Hypotheses.** - Choose one of the following options: - \( H_0: \beta_1 = 0 \) \( H_a: \beta_1 \neq 0 \) - \( H_0: \beta_1 \neq 0 \) \( H_a: \beta_1 = 0 \) - \( H_0: \beta_1 < 0 \) \( H_a: \beta_1 \geq 0 \) - \( H_0: \beta_1 > 0 \) \( H_a: \beta_1 \leq 0 \) - \( H_0: \beta_1 = 0 \) \( H_a: \beta_1 > 0 \)2. **Find the Value of the Test Statistic.** - Round your answer to two decimal places. \[ \text{Test Statistic} = \boxed{} \]3. **Find the p-value.** - Round your answer to three decimal places. \[ p\text{-value} = \boxed{} \]4. **State Your Conclusion.** - Choose one of the following options: - Do not reject \( H_0 \). There is insufficient evidence to conclude that \( \beta_1 \) is significant. - Do not reject \( H_0 \). There is sufficient evidence to conclude that \( \beta_1 \) is significant. - Reject \( H_0 \). There is insufficient evidence to conclude that \( \beta_1 \) is significant. - Reject \( H_0 \). There is sufficient evidence to conclude that \( \beta_1 \) is significant.---**(c) Is \( \beta_2 \) significant? Use \(\alpha = 0.05\).**#### Steps to Determine Significance:1. **State the Null and Alternative Hypotheses.** - Choose one of the following options: - \( H_0: \beta_2 = 0 \) \( H_a: \beta_2 > 0

The question is about regression.Given :SST = 15182.9SSR = 14052.2Regression equation :To find :a ) Test the relationship between y and x1, x2b ) Test the significance of c ) Test the significance of No. of independent variables ( k ) = 2Total no. of paired observations ( n ) = 10To find : degree of freedomTo find : Mean squaresand, Compare the given regression equation with So, a )Null and alternative hypothesis :Answer : Option 1Test statistic :p value approach :Since the F distribution is always right skewed.Using excel command, So,Decision rule :i ) Reject H0 if ii ) Do not reject H0 if Given : Here, Hence, reject H0Conclusion :There is sufficient evidence to conclude that there is significant relation among variables.Answer : Option 3b )Null and alternative hypothesis :Answer : Option 1Test statistic :p value approach :Since the alternative hypothesis has ≠ sign, so it is a two tailed test.Using excel command, So,Decision rule :i ) Reject H0 if ii ) Do not reject H0 if Given : Here, Hence, reject H0Conclusion :There is sufficient evidence to conclude that the is significant.Answer : Option 4 c )Null and alternative hypothesis :Answer : Option 5Test statistic :p value approach :Since the alternative hypothesis has ≠ sign, so it is a two tailed test.Using excel command, So,Decision rule :i ) Reject H0 if ii ) Do not reject H0 if Given : Here, Hence, reject H0Conclusion :There is sufficient evidence to conclude that the is significant.Answer : Option 4a )Answer : Option 1Test statistic = 43.50p value = 0.000Conclusion :Reject H0. There is sufficient evidence to conclude that there is significant relation among variables.Answer : Option 3b )Answer : Option 1Test statistic = 8.13p value = 0.000Conclusion :Reject H0 . There is sufficient evidence to conclude that the is significant.Answer : Option 4 c )Test statistic = 5.00p value = 0.002Conclusion :Reject H0 . There is sufficient evidence to conclude that the is significant.Answer : Option 4

Math

Statistics

Consider the following data for a dependent variable y and two independent variables, x₁ and x₂. X1 X2 30 47 25 51 51 74 36 59 12 94 10 108. 17 40 5 94 y 16 178 112 19 175 7 170 12 117 13 142 76 16 211 me estimated regression equation for these data is y = -18.36827 +2.01019x₁ +4.73781x2. ere, SST = 15,182.9, SSR = 14,052.2, Sb₁ = 0.24712, and Sp₂ = 0.94844. (SST represents the Total Sum of Squares presents the Regression Sum of Squares) a) Test for a significant relationship among X₁, X₂, and y. Use α = 0.05. State the null and alternative hypotheses. O Ho: B1 = B2 = 0 o Ho Bì > B2 H₂: B₁ ≤ B₂ H₂: : One or more of the parameters is not equal to zero. o Ho Bi

Consider the following data for a dependent variable y and two independent variables, x₁ and x₂. X1 X2 30 47 25 51 51 74 36 59 12 94 10 108. 17 40 5 94 y 16 178 112 19 175 7 170 12 117 13 142 76 16 211 me estimated regression equation for these data is y = -18.36827 +2.01019x₁ +4.73781x2. ere, SST = 15,182.9, SSR = 14,052.2, Sb₁ = 0.24712, and Sp₂ = 0.94844. (SST represents the Total Sum of Squares presents the Regression Sum of Squares) a) Test for a significant relationship among X₁, X₂, and y. Use α = 0.05. State the null and alternative hypotheses. O Ho: B1 = B2 = 0 o Ho Bì > B2 H₂: B₁ ≤ B₂ H₂: : One or more of the parameters is not equal to zero. o Ho Bi

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

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Question

Need help solving a b and c

### Regression Analysis of Dependent and Independent Variables

#### Data Table

The following data is provided for a dependent variable \( y \) and two independent variables, \( x_1 \) and \( x_2 \):

| \( x_1 \) | \( x_2 \) | \( y \) |
|-----------|-----------|---------|
| 30 | 12 | 94 |
| 47 | 10 | 108 |
| 25 | 17 | 112 |
| 51 | 16 | 178 |
| 40 | 5 | 94 |
| 51 | 19 | 175 |
| 74 | 17 | 170 |
| 36 | 12 | 117 |
| 59 | 13 | 142 |
| 76 | 16 | 211 |

#### Estimated Regression Equation

The estimated regression equation based on the given data is:
\[
\hat{y} = -18.36827 + 2.01019x_1 + 4.73781x_2
\]

#### Sum of Squares

- Total Sum of Squares (SST): 15,182.9
- Regression Sum of Squares (SSR): 14,052.2
- Standard error of \( x_1 \) (\( s_{b_1} \)): 0.24712
- Standard error of \( x_2 \) (\( s_{b_2} \)): 0.94844

#### Hypothesis Testing

**Objective:** Test for a significant relationship among \( x_1 \), \( x_2 \), and \( y \). Use \( \alpha = 0.05 \).

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

Choices:

- \( H_0 \): \(\beta_1 > \beta_2 \)
\( H_a \): \(\beta_1 \leq \beta_2 \)

- \( H_0 \): \(\beta_1 \neq 0 \) and \(\beta_2 \neq

### Statistical Significance Testing

**(b) Is \( \beta_1 \) significant? Use \(\alpha = 0.05\).**

#### Steps to Determine Significance:

1. **State the Null and Alternative Hypotheses.**
- Choose one of the following options:
- \( H_0: \beta_1 = 0 \)
\( H_a: \beta_1 \neq 0 \)
- \( H_0: \beta_1 \neq 0 \)
\( H_a: \beta_1 = 0 \)
- \( H_0: \beta_1 < 0 \)
\( H_a: \beta_1 \geq 0 \)
- \( H_0: \beta_1 > 0 \)
\( H_a: \beta_1 \leq 0 \)
- \( H_0: \beta_1 = 0 \)
\( H_a: \beta_1 > 0 \)

2. **Find the Value of the Test Statistic.**
- Round your answer to two decimal places.

\[ \text{Test Statistic} = \boxed{} \]

3. **Find the p-value.**
- Round your answer to three decimal places.

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

4. **State Your Conclusion.**
- Choose one of the following options:
- Do not reject \( H_0 \). There is insufficient evidence to conclude that \( \beta_1 \) is significant.
- Do not reject \( H_0 \). There is sufficient evidence to conclude that \( \beta_1 \) is significant.
- Reject \( H_0 \). There is insufficient evidence to conclude that \( \beta_1 \) is significant.
- Reject \( H_0 \). There is sufficient evidence to conclude that \( \beta_1 \) is significant.

---

**(c) Is \( \beta_2 \) significant? Use \(\alpha = 0.05\).**

#### Steps to Determine Significance:

1. **State the Null and Alternative Hypotheses.**
- Choose one of the following options:
- \( H_0: \beta_2 = 0 \)
\( H_a: \beta_2 > 0

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Step 1: Determine the given variables.

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Step 2: Find the b1, b2, MSR and MSE

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Step 3: Test the relationship between y and x1, x2

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Step 4: Test the signifcance of beta1.

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