Run a regression analysis on the following bivariate set of data with y as the response variable. Verify that the correlation is significant at an α=0.05. If the correlation is indeed significant, predict what value (on average) for the explanatory variable will give you a value of 43 on the response variable.
Correlation
Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.
Linear Correlation
A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.
Regression Analysis
Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.
Run a
![**Regression Analysis: Understanding Bivariate Data**
In this exercise, you are tasked with running a regression analysis on the given bivariate set of data. The data consists of two variables, \( x \) and \( y \), where \( y \) serves as the response variable.
**Data Table:**
| \( x \) | \( y \) |
|--------|-------|
| 75.9 | 42.1 |
| 82.2 | 42.2 |
| 75.2 | 42.5 |
| 82.2 | 42.2 |
| 69.3 | 43.4 |
| 75.1 | 43.4 |
| 62.6 | 44 |
| 79.4 | 40.4 |
| 78.7 | 40 |
| 61.8 | 45.3 |
| 74.5 | 43.4 |
| 91 | 41.1 |
| 65.1 | 44.4 |
| 69.6 | 44.5 |
| 71.7 | 45 |
| 83.9 | 43.5 |
| 53.8 | 48.9 |
| 78.4 | 41.6 |
| 56.3 | 45.9 |
**Tasks:**
1. **Verify the significance of correlation** at a significance level (\( \alpha \)) of 0.05.
2. If the correlation is significant, determine the average value of the explanatory variable (\( x \)) that predicts a response variable (\( y \)) value of 43.
**Question:**
What is the predicted explanatory value \( x \) for a response variable value of 43?
\[ x = \_\_\_\_ \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F961e5e88-22ea-4869-b279-3bff5edd9f45%2F9dab39ee-94e9-482d-ad5b-0f8d7fad4925%2Fp71r0zo_processed.jpeg&w=3840&q=75)
Trending now
This is a popular solution!
Step by step
Solved in 2 steps
