(c) Assuming the residuals are normally distributed, construct a 90% confidence interval for the slope of the true least-squares regression line. Lower bound: 0.2343 (Round to four decimal places as needed.) Upper bound: 1.2901 (Round to four decimal places as needed.) (d) What is the mean rate of return for the company stock if the rate of return of the index is 3.15%? The mean rate of return for the company stock if the rate of return of the index is 3.15% is (Round to three decimal places as needed.) %.

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### Statistical Analysis in Finance

#### P-Value and Significance Testing

- **P-value**: 0.027 (Rounded to three decimal places as needed)

#### Conclusion Based on P-Value

- **Significance Level (α)**: 0.10

**Options:**
- A. **Reject H₀**: There is sufficient evidence to conclude that a linear relation exists between the rate of return of the index and the rate of return of the company stock.
- B. **Reject H₀**: There is not sufficient evidence to conclude that a linear relation exists between the rate of return of the index and the rate of return of the company stock.
- C. **Do not reject H₀**: There is not sufficient evidence to conclude that a linear relation exists between the rate of return of the index and the rate of return of the company stock.
- D. **Do not reject H₀**: There is sufficient evidence to conclude that a linear relation exists between the rate of return of the index and the rate of return of the company stock.

**Correct Answer**: Option A is the appropriate conclusion since the P-value (0.027) is less than the significance level (0.10).

#### Confidence Interval for Slope

(c) **90% Confidence Interval for the Slope of the True Least-Squares Regression Line**
- **Lower Bound**: 0.2343 (Rounded to four decimal places as needed)
- **Upper Bound**: 1.2901 (Rounded to four decimal places as needed)

#### Mean Rate of Return Calculation

(d) **Mean Rate of Return for Company Stock**
- **Given**: Rate of return of the index is 3.15%

- **Solution**: Calculate the mean rate of return for the company stock based on the index rate of 3.15%.

**Note**: The result should be rounded to three decimal places as needed.

#### Visual Elements
There are no graphs or diagrams in the provided image. The text involves options for statistical conclusions and the calculation of confidence intervals and expected returns.
Transcribed Image Text:### Statistical Analysis in Finance #### P-Value and Significance Testing - **P-value**: 0.027 (Rounded to three decimal places as needed) #### Conclusion Based on P-Value - **Significance Level (α)**: 0.10 **Options:** - A. **Reject H₀**: There is sufficient evidence to conclude that a linear relation exists between the rate of return of the index and the rate of return of the company stock. - B. **Reject H₀**: There is not sufficient evidence to conclude that a linear relation exists between the rate of return of the index and the rate of return of the company stock. - C. **Do not reject H₀**: There is not sufficient evidence to conclude that a linear relation exists between the rate of return of the index and the rate of return of the company stock. - D. **Do not reject H₀**: There is sufficient evidence to conclude that a linear relation exists between the rate of return of the index and the rate of return of the company stock. **Correct Answer**: Option A is the appropriate conclusion since the P-value (0.027) is less than the significance level (0.10). #### Confidence Interval for Slope (c) **90% Confidence Interval for the Slope of the True Least-Squares Regression Line** - **Lower Bound**: 0.2343 (Rounded to four decimal places as needed) - **Upper Bound**: 1.2901 (Rounded to four decimal places as needed) #### Mean Rate of Return Calculation (d) **Mean Rate of Return for Company Stock** - **Given**: Rate of return of the index is 3.15% - **Solution**: Calculate the mean rate of return for the company stock based on the index rate of 3.15%. **Note**: The result should be rounded to three decimal places as needed. #### Visual Elements There are no graphs or diagrams in the provided image. The text involves options for statistical conclusions and the calculation of confidence intervals and expected returns.
# Data Analysis: Comparing Rates of Return

This educational content delves into the analysis of the rate of return of a company's stock over 11 months, comparing it to the rate of return of a specific index comprising 500 stocks.

### Hypothesis Testing

**Objective:** Determine if there is a significant linear relationship between the company's stock return and the index.

- **P-value**: 0.027 (Rounded to three decimal places)

### Conclusion at α = 0.10 Significance Level

Choose the correct conclusion regarding the hypothesis:

A. **Reject \(H_0\).** There is sufficient evidence to conclude that a linear relationship exists between the rate of return of the company stock and the index.

B. Reject \(H_0\). There is not sufficient evidence to conclude that a linear relationship exists.

C. Do not reject \(H_0\). There is not sufficient evidence to conclude that a linear relationship exists.

D. Do not reject \(H_0\). There is sufficient evidence to conclude that a linear relationship exists.

### Confidence Interval

Assuming residuals are normally distributed, a 90% confidence interval for the intercept is:

- **Lower bound**: 0.2343 (Rounded to four decimal places)
- **Upper bound**: 1.2901 (Rounded to four decimal places)

### Calculation of Mean Rate of Return

**Objective:** Estimate the mean rate of return for the company stock when the index's rate of return is 3.1.

- **Result**: (Rounded to three decimal places)

### Rates of Return Data Table

#### Table: Rates of Return

| **Month** | **Rates of return of the index, \(x\)** | **Rates of return of the company stock, \(y\)** |
|-----------|------------------------------------------|-------------------------------------------------|
| Apr-18    | -1.84                                    | 3.28                                            |
| May-18    | 0.97                                     | 5.09                                            |
| Jun-18    | 1.36                                     | 0.54                                            |
| Jul-18    | 2.80                                     | 2.88                                            |
| Aug-18    | -0.57                                    | 2.69                                            |
| Sep-18    | 0.30                                     | -2.98                                           |
| Oct-18    | -1.36                                    | -4.83                                           |
Transcribed Image Text:# Data Analysis: Comparing Rates of Return This educational content delves into the analysis of the rate of return of a company's stock over 11 months, comparing it to the rate of return of a specific index comprising 500 stocks. ### Hypothesis Testing **Objective:** Determine if there is a significant linear relationship between the company's stock return and the index. - **P-value**: 0.027 (Rounded to three decimal places) ### Conclusion at α = 0.10 Significance Level Choose the correct conclusion regarding the hypothesis: A. **Reject \(H_0\).** There is sufficient evidence to conclude that a linear relationship exists between the rate of return of the company stock and the index. B. Reject \(H_0\). There is not sufficient evidence to conclude that a linear relationship exists. C. Do not reject \(H_0\). There is not sufficient evidence to conclude that a linear relationship exists. D. Do not reject \(H_0\). There is sufficient evidence to conclude that a linear relationship exists. ### Confidence Interval Assuming residuals are normally distributed, a 90% confidence interval for the intercept is: - **Lower bound**: 0.2343 (Rounded to four decimal places) - **Upper bound**: 1.2901 (Rounded to four decimal places) ### Calculation of Mean Rate of Return **Objective:** Estimate the mean rate of return for the company stock when the index's rate of return is 3.1. - **Result**: (Rounded to three decimal places) ### Rates of Return Data Table #### Table: Rates of Return | **Month** | **Rates of return of the index, \(x\)** | **Rates of return of the company stock, \(y\)** | |-----------|------------------------------------------|-------------------------------------------------| | Apr-18 | -1.84 | 3.28 | | May-18 | 0.97 | 5.09 | | Jun-18 | 1.36 | 0.54 | | Jul-18 | 2.80 | 2.88 | | Aug-18 | -0.57 | 2.69 | | Sep-18 | 0.30 | -2.98 | | Oct-18 | -1.36 | -4.83 |
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