Asking for help! Thank you ### Part 1: Analyzing a Random Sample of ObservationsThe following data represent a random sample of 5 observations. Assume that $ Y $ is a linear function of $ X $ and a normally distributed disturbance term with a mean of zero and a constant variance. In other words:\[ Y = a + bX + u, \quad u \sim N(0, \sigma^2) \]#### Observational Data:| Observation | Y | X ||-------------|---|---|| 1. | 1 | 17|| 2. | 3 | 13|| 3. | 5 | 8 || 4. | 7 | 10|| 5. | 9 | 2 |### Tasks1. **Create a Scatterplot**: - **Objective**: Create a scatterplot of this dataset (either manually, or by using Excel graphing functions). - **Steps**: Plot the values of $ Y $ on the vertical axis and $ X $ on the horizontal axis.2. **Calculate Statistical Parameters**: - **Objective**: Calculate the sample means, variances, and standard deviations of the variables $ X $ and $ Y $ either “by hand” or using Excel. Write one sentence describing what each of these means in the context of the dataset. - **Definitions**: - **Sample Mean**: The average value of the observations. - **Variance**: A measure of the dispersion of the observations from the mean. - **Standard Deviation**: The square root of the variance, indicating the average distance of the observations from the mean.### CalculationsThe calculations below should be done by applying the bivariate regression formulas. In other words, do them “by hand” using a calculator, or in Excel in a manner that clearly reveals the formulas used. Additionally, verify your calculations by entering the data into an Excel sheet and using the regression analysis function under Data Tools.1. **Regression Coefficients**: - **Show how to calculate $ a $ and $ b $**. Write one sentence discussing the interpretation of each of them. - $ a $: The intercept of the regression line, representing the expected value of $ Y $ when $ X $ is zero. - $ b $: The

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Description: Asking for help! Thank you ### Part 1: Analyzing a Random Sample of ObservationsThe following data represent a random sample of 5 observations. Assume that $ Y $ is a linear function of $ X $ and a normally distributed disturbance term with a mea

If there is any functional relationship between two variable, the points we marked in the scatter…

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Create a scatterplot of this dataset (either manually, or by using Excel graphing functions) Calculate the sample means, variances, and standard deviations of the variables X and Y either "by hand" or by using Excel and write one sentence describing what each of these mean in terms of the dataset. The calculations below should be done by applying the bivariate regression formulas. In other words, do them “by hand" using a calculator or in Excel in a manner that I can clearly see the formulas you have used. You should also check your calculations by entering the data into an Excel sheet and using the regression analysis function under Data Tools. 1. Show how to calculate a and b. In a sentence, discuss the interpretation of each of them. 2. Calculate the predicted value of 3. Calculate the Sum of Square Errors (SSE), Mean Square Error (MSE) and the Standard and the residual for each observation. Error (s) Explain the meaning of each of them

Create a scatterplot of this dataset (either manually, or by using Excel graphing functions) Calculate the sample means, variances, and standard deviations of the variables X and Y either "by hand" or by using Excel and write one sentence describing what each of these mean in terms of the dataset. The calculations below should be done by applying the bivariate regression formulas. In other words, do them “by hand" using a calculator or in Excel in a manner that I can clearly see the formulas you have used. You should also check your calculations by entering the data into an Excel sheet and using the regression analysis function under Data Tools. 1. Show how to calculate a and b. In a sentence, discuss the interpretation of each of them. 2. Calculate the predicted value of 3. Calculate the Sum of Square Errors (SSE), Mean Square Error (MSE) and the Standard and the residual for each observation. Error (s) Explain the meaning of each of them

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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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Asking for help! Thank you

### Part 1: Analyzing a Random Sample of Observations

The following data represent a random sample of 5 observations. Assume that $ Y $ is a linear function of $ X $ and a normally distributed disturbance term with a mean of zero and a constant variance. In other words:

\[ Y = a + bX + u, \quad u \sim N(0, \sigma^2) \]

#### Observational Data:
| Observation | Y | X |
|-------------|---|---|
| 1. | 1 | 17|
| 2. | 3 | 13|
| 3. | 5 | 8 |
| 4. | 7 | 10|
| 5. | 9 | 2 |

### Tasks

1. **Create a Scatterplot**:
- **Objective**: Create a scatterplot of this dataset (either manually, or by using Excel graphing functions).
- **Steps**: Plot the values of $ Y $ on the vertical axis and $ X $ on the horizontal axis.

2. **Calculate Statistical Parameters**:
- **Objective**: Calculate the sample means, variances, and standard deviations of the variables $ X $ and $ Y $ either “by hand” or using Excel. Write one sentence describing what each of these means in the context of the dataset.
- **Definitions**:
- **Sample Mean**: The average value of the observations.
- **Variance**: A measure of the dispersion of the observations from the mean.
- **Standard Deviation**: The square root of the variance, indicating the average distance of the observations from the mean.

### Calculations

The calculations below should be done by applying the bivariate regression formulas. In other words, do them “by hand” using a calculator, or in Excel in a manner that clearly reveals the formulas used. Additionally, verify your calculations by entering the data into an Excel sheet and using the regression analysis function under Data Tools.

1. **Regression Coefficients**:
- **Show how to calculate $ a $ and $ b $**. Write one sentence discussing the interpretation of each of them.
- $ a $: The intercept of the regression line, representing the expected value of $ Y $ when $ X $ is zero.
- $ b $: The

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