7131596&id3D1001593722&snapshotld%3D189937 following estimated regression equation relating
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.
#a. Predict the sales resulting from a $15,000 investment in inventory and an advertising budget of $10,000.
![# Educational Text: Regression Analysis in Retail
## Understanding Regression Equations
A shoe store developed the following estimated regression equation to relate sales to inventory investment and advertising expenditures:
\[ \hat{y} = 20 + 9x_1 + 7x_2 \]
### Variables Explained:
- \( x_1 \) = Inventory Investment (in thousands of dollars)
- \( x_2 \) = Advertising Expenditures (in thousands of dollars)
- \( y \) = Sales (in thousands of dollars)
### Tasks:
**a. Predict Sales:**
Calculate the sales resulting from a $15,000 investment in inventory and an advertising budget of $10,000.
**b. Interpret Coefficients \( b_1 \) and \( b_2 \):**
- \( b_1 \): Sales are expected to change by $9 for every dollar increase in inventory investment, assuming advertising expenditures are held constant.
- \( b_2 \): Sales are expected to change by $7 for every dollar increase in advertising expenditures, assuming inventory investment is held constant.
### Notes for Students:
- The task involves utilizing the regression equation to determine how changes in inventory and advertising influence sales.
- Interpretation of coefficients provides insight into the relationship between the independent variables and the dependent variable.
Complete the exercises to enhance your understanding of how investments in different areas can impact sales outcomes in a retail setting.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffc8e2d68-695c-49ad-a9b1-8d66f1d1c9ea%2F032dcc74-b587-4a06-947b-abcd8d68b578%2Focndlup_processed.jpeg&w=3840&q=75)
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