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 3 108.426 6 141.781 9 169.256 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- 190- 180- 170- 160- 150- 140- 130- 120- 110- 100- 90- 6 12 804 Use the above scatter plot to decide whether the linear model fits the data well. The function is a good model for the data. The function is not a good model for the data Estimate the retails sales in the U. S. in 2016. billions of dollars. Use the model to predict the year in which retails sales will be $249 billion.
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.
![### Retail Sales Analysis in Drug Stores (Since 1995)
#### Retail Sales Data
The following table shows retail sales in drug stores in billions of dollars in the U.S. for years since 1995:
| Year | Retail Sales (in billions) |
|------|----------------------------|
| 0 | 85.851 |
| 3 | 108.426 |
| 6 | 141.781 |
| 9 | 169.256 |
| 12 | 202.297 |
| 15 | 222.266 |
#### Linear Model Representation
Let \( S(t) \) be the retail sales in billions of dollars in \( t \) years since 1995. A linear model for the data is given by:
\[ F(t) = 9.44t + 84.182 \]
#### Scatter Plot and Linear Model Fit
The following scatter plot demonstrates the retail sales data points (in blue) along with the linear model \( F(t) \):
<img src="scatter_plot.png" alt="Scatter Plot of Retail Sales and Linear Model" width="500">
1. **X-axis (horizontal):** Represents the years since 1995.
2. **Y-axis (vertical):** Represents the retail sales in billions of dollars.
3. **Blue points:** Actual retail sales data for the respective years.
4. **Straight line:** Represents the linear model \( F(t) \) fitted to the data points.
#### Model Evaluation
Use the above scatter plot to decide whether the linear model fits the data well:
- O The function is a good model for the data.
- O The function is not a good model for the data.
#### Prediction
- Estimate the retail sales in the U.S. in 2016: \( \_\_\_\_\_\_\_\_ \) billions of dollars.
- Use the model to predict the year in which retail sales will be $249 billion: \( \_\_\_\_\_\_\_\_ \)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcebbde0b-56df-456f-b45f-057baf1d3a0f%2F0a0ead61-78e5-4050-ae70-0ebcd2430ae6%2Fkh5g1sn_processed.png&w=3840&q=75)
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