Residuals vs fitted plots can be used to assess whether the four key assumptions for a simple linear regression have been met. Each of the plots below displays an instance where at least one of these assumptions may not have been met. For each plot, identify which assumption has been most violated, if any.
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.
Residuals vs fitted plots can be used to assess whether the four key assumptions for a simple linear regression have been met. Each of the plots below displays an instance where at least one of these assumptions may not have been met. For each plot, identify which assumption has been most violated, if any.
![2.8
3.0
3.2
3.4
3.6
3.8
Fitted value
2.
? v 2.
-10
-5
5
10
A. The data does not appear to be from independent observations.
Fitted value
B. No assumptions have been violated.
C. The relationship between x and y cannot be assumed to be linear.
D. The variability of points around the least-squares line is not roughly constant.
? v 3.
-0.4
-0.2
0.0
0.2
0.4
Fitted value
Residual
-0.5
0'0
S'O](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4745af79-0155-486b-8f61-53121b7c4ee4%2Fb7b7f95d-5404-4b79-9215-2ab39576efdd%2F2vd4aiw_processed.png&w=3840&q=75)
![-0.4
-0.2
0.0
0.2
0.4
Fitted value
20
-10
-5
10
Fitted value
OL
Residual
4.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4745af79-0155-486b-8f61-53121b7c4ee4%2Fb7b7f95d-5404-4b79-9215-2ab39576efdd%2Ff08ylor_processed.png&w=3840&q=75)
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