y A) Interpret the slope of the regression equation in a complete 0.93313 sentence. B) According to the linear regression equation, the bone density of someone who drinks 24 colas per week is 0.9363 4 0.93447 5. 0 92364
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.
I need help to interpret the slope of the
![### Bone Mineral Density and Cola Consumption Analysis
#### Scatter Plot Analysis
The scatter plot presented is titled "Bone mineral density and cola consumption" and displays the relationship between the number of colas consumed per week (x-axis) and bone mineral density in grams per cubic centimeter (y-axis).
- **X-Axis:** Number of colas consumed per week (ranging from 0 to 13).
- **Y-Axis:** Bone mineral density in grams per cubic centimeter (ranging from 0.905 to 0.94).
A trend line is added to the scatter plot with the linear regression equation:
\[ y = -0.0025x + 0.9413 \]
The coefficient of determination (\(R^2\)) is 0.7374, indicating that approximately 73.74% of the variation in bone density is explained by cola consumption.
#### Data Table
The table below provides individual data points:
| x (Number of colas per week) | y (Bone mineral density) |
|------------------------------|--------------------------|
| 2 | 0.93313 |
| 3 | 0.9363 |
| 4 | 0.93447 |
| 5 | 0.92364 |
| 6 | 0.91981 |
| 7 | 0.93698 |
| 8 | 0.92415 |
| 9 | 0.91832 |
| 10 | 0.91549 |
| 11 | 0.90966 |
| 12 | 0.91483 |
| 13 | 0.908 |
The correlation coefficient (r) is -0.858717559, indicating a strong negative correlation between cola consumption and bone mineral density.
#### Interpretation Questions
**A) Interpretation of the Slope:**
The slope of the regression line is -0.0025, indicating that for each additional cola consumed per week, bone mineral density decreases by 0.0025 grams per cubic centimeter, on average.
**B) Prediction for 24 Colas Per Week:**
To estimate the bone density of someone who drinks 24 colas per week, substitute \(x = 24\) into the regression equation:
\[ y = -0.0025(24) + 0.941](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fab6a44fb-472d-4115-ae99-90593ad92ba0%2Fc187b1e6-99a0-4e35-8c49-bdac00331378%2F40m12s_processed.png&w=3840&q=75)
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