Could you help me with these 2 please **Educational Content: Chapter Ten****Instructions:**Show all work on this paper. No work means, No partial credit.---**Chapter Ten**1. **Determining the Significance of Linear Correlation:** Determine the $ r $ critical value from the table and decide if there is a significant linear correlation if $ r = 0.745 $ and $ n = 12 $ at a 0.05 significance level.2. **Predictive Analysis with Regression:** Four pairs of data yield an $ r = 0.912 $ and a regression equation of $ y = 4x + 5 $. Also, the average $ y $-value is 11.45. What is the best predicted value for $ y $ if $ x = 3.7 $?3. **Hypothesis Testing for Correlation:** Use the given data to find the correlation coefficient $ r $ (using a formula or calculator), then perform a hypothesis test, making sure to include and label all five steps. Test at a 0.05 significance level to determine if there is a significant linear correlation.---**Graph/Diagram Explanation:**There are no graphs or diagrams provided in this content. However, if there are tables of $ r $ critical values (not shown in the image), ensure to reference those when performing the calculations for the first task. **Instructions for the Hypothesis Test (Part 3):**1. **State the hypotheses:** - Null hypothesis ($ H_0 $): There is no significant linear correlation ($ \rho = 0 $). - Alternative hypothesis ($ H_1 $): There is a significant linear correlation ($ \rho \neq 0 $).2. **Choose the significance level ($ \alpha $):** - Usually, $ \alpha = 0.05 $ is used.3. **Find the critical value and identify the rejection region:** - Use a critical value table or a calculator to find the critical value for $ n - 2 $ degrees of freedom.4. **Calculate the test statistic:** - Using the formula for the correlation coefficient $ r $.5. **Make a decision:** - Compare the test statistic to the critical value and determine whether to reject the null hypothesis.6. **Conclusion:** - Provide a clear conclusion in

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Chapter Ten 1) Determine the r critical value from the table and decide if there is a significant linear correlation if r = .745 and n = 12 use a .05 significance level

MATLAB: An Introduction with Applications

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ISBN:9781119256830

Author:Amos Gilat

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Concept explainers

Types of Bias

Statistics is the study of data collection, organization, analysis, interpretation, and presentation. Statistical bias is a characteristic of a statistical technique or its findings in which the expected value deviates from the actual root quantitative parameter being estimated. According to the actual definition of bias, it refers to the tendency of a statistic to overestimate or underestimate a parameter.

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Could you help me with these 2 please

**Educational Content: Chapter Ten**

**Instructions:**
Show all work on this paper. No work means, No partial credit.

---

**Chapter Ten**

1. **Determining the Significance of Linear Correlation:**
Determine the $ r $ critical value from the table and decide if there is a significant linear correlation if $ r = 0.745 $ and $ n = 12 $ at a 0.05 significance level.

2. **Predictive Analysis with Regression:**
Four pairs of data yield an $ r = 0.912 $ and a regression equation of $ y = 4x + 5 $. Also, the average $ y $-value is 11.45. What is the best predicted value for $ y $ if $ x = 3.7 $?

3. **Hypothesis Testing for Correlation:**
Use the given data to find the correlation coefficient $ r $ (using a formula or calculator), then perform a hypothesis test, making sure to include and label all five steps. Test at a 0.05 significance level to determine if there is a significant linear correlation.

---

**Graph/Diagram Explanation:**
There are no graphs or diagrams provided in this content. However, if there are tables of $ r $ critical values (not shown in the image), ensure to reference those when performing the calculations for the first task.

**Instructions for the Hypothesis Test (Part 3):**
1. **State the hypotheses:**
- Null hypothesis ($ H_0 $): There is no significant linear correlation ($ \rho = 0 $).
- Alternative hypothesis ($ H_1 $): There is a significant linear correlation ($ \rho \neq 0 $).

2. **Choose the significance level ($ \alpha $):**
- Usually, $ \alpha = 0.05 $ is used.

3. **Find the critical value and identify the rejection region:**
- Use a critical value table or a calculator to find the critical value for $ n - 2 $ degrees of freedom.

4. **Calculate the test statistic:**
- Using the formula for the correlation coefficient $ r $.

5. **Make a decision:**
- Compare the test statistic to the critical value and determine whether to reject the null hypothesis.

6. **Conclusion:**
- Provide a clear conclusion in

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