The following table shows retail sales in drug stores in billions of dollars in the U.S. for years since 1995. Year Retail Sales 85.851 108.426 6. 141.781 169.256 12 202.297 15 222.266 Let S(t) be the retails sales in billions of dollars in t years since 1995. A linear model for the data is F(t) = 9.44t + 84.182. 220- 210- 200-
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.
![The following table shows retail sales in drug stores in billions of dollars in the U.S. for years since 1995.
| Year | Retail Sales |
|------|--------------|
| 0 | 85.851 |
| 3 | 108.426 |
| 6 | 141.781 |
| 9 | 169.256 |
| 12 | 202.297 |
| 15 | 222.266 |
Let \( S(t) \) be the retail sales in billions of dollars in \( t \) years since 1995. A linear model for the data is \( F(t) = 9.44t + 84.182 \).
**Graph Explanation:**
- The graph includes a scatter plot chart with blue dots representing data points of retail sales over the years.
- The x-axis represents the years since 1995.
- The y-axis represents retail sales in billions of dollars.
- A line of best fit is drawn through the points, indicating the linear model \( F(t) = 9.44t + 84.182 \).
**Model Evaluation:**
- A question prompts users to decide whether the linear model fits the data well.
- The option selected indicates that the function is a good model for the data.
**Questions:**
1. Estimate the retail sales in the U.S. in 2012. [Fill in the blank] billions of dollars.
2. Use the model to predict the year that corresponds to retail sales of $233 billion. [Fill in the blank]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0017d92f-fd5a-4a34-8e16-36b3a20e3d6d%2Fd96db7d1-7d89-41c8-8268-60af9f723001%2F94c4j4x_processed.png&w=3840&q=75)
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