on coefficient was –0.99. Would it be accurate to use this equ because that would be extrapolation. because the correlation is very strong. because the value of cars is unpredictable over time.
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.
![**Problem Context:**
A statistics professor purchased a new car for $35,000. Over the next 5 years, she estimated the car's value using various automotive websites. She derived the least-squares regression line for this data as:
\[ \hat{y} = 35035.71 - 4142.86x \]
where \(\hat{y}\) represents the estimated car value, and \(x\) represents the number of years since the car was purchased. The correlation coefficient was found to be \(-0.99\).
**Question:**
Would it be accurate to use this equation to predict the value of the car after 10 years?
**Options:**
- **No, because that would be extrapolation.** (Selected option)
- **Yes, because the correlation is very strong.**
- **No, because the value of cars is unpredictable over time.**
**Explanation:**
The selected answer indicates that using the regression line to predict the car's value after 10 years would involve extrapolation beyond the range of the data initially used to create the model (i.e., the first 5 years). Extrapolation can often lead to inaccurate and unreliable predictions, even if the correlation is strong.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F378c15bf-c180-4b3b-bfe7-2cb46e39be68%2F2b2fc2ae-ab25-460c-baf3-dc06323b80c7%2F57s5lko.png&w=3840&q=75)
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