a. Make a scatter plot of this data. Which point is an outlier? Enter as an ordered pair, e.g., (x,y). (x, y) b. Find the regression equation for the data set without the outlier. Enter the equation of the form mx + b rounded to three decimal places. ŷ wo c. Find the regression equation for the data set with the outlier. Enter the equation of the form mx + b rounded to three decimal places. Y w
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
![### Analyzing Data with Regression
Here is a set of data with **y** as the response variable:
#### Data Table:
| **x** | **y** |
|----------|----------|
| 64.7 | 123.6 |
| 98.4 | -57.9 |
| -126.5 | 619.2 |
| 76.2 | 32.3 |
| 61.7 | 49.1 |
| 103.9 | -77.8 |
| 52.7 | 12.4 |
| 89.6 | -10.4 |
| 71 | 58.7 |
| 90.7 | -71.7 |
### Tasks:
#### a. Scatter Plot and Outlier Identification
Using the data provided, create a scatter plot to visualize the relationship between **x** and **y**. After plotting, identify the point that appears to be an outlier.
**Outlier point (x, y) =** [Input box]
#### b. Regression Equation without the Outlier
Determine the regression equation for the data set **without** the identified outlier. Express the regression equation in the form \( \hat{y}_{wo} = mx + b \), rounded to three decimal places.
**Regression equation without outlier \( \hat{y}_{wo} = \)** [Input box]
#### c. Regression Equation with the Outlier
Calculate the regression equation for the data set **with** the outlier included. Represent the regression equation in the form \( \hat{y}_{w} = mx + b \), rounded to three decimal places.
**Regression equation with outlier \( \hat{y}_{w} = \)** [Input box]
Understanding the impact of outliers on the regression equation will help in analyzing and improving the accuracy of predictive models.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F443e45af-3927-4fd9-baca-290567a407b3%2F6dfd9db6-dadf-4f0c-a0d9-b2905938cf14%2Fqmai92t_processed.png&w=3840&q=75)
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