What does the regression line represent in a simple linear regression analysis?
A) The line that perfectly fits all sample data points.
B) The average of all data points.
C) The maximum distance between the data points and the line.
D) The line of best fit that models the relationship between the independent and dependent variables.
Answer (2)
In a simple linear regression analysis, the regression line represents the line of best fit that models the relationship between the independent and dependent variables. Therefore, the correct choice is D) The line of best fit that models the relationship between the independent and dependent variables.
Here's a detailed explanation:
Simple Linear Regression : This is a statistical method used to understand the relationship between two continuous variables. One is the independent variable (predictor or explanatory variable), and the other is the dependent variable (response or outcome variable).
The Line of Best Fit : In simple linear regression, the goal is to draw a straight line that best fits the data points on a scatter plot. This line is known as the regression line.
Mathematical Representation : The regression line is typically represented by the equation y = m x + b , where:
y represents the estimated value of the dependent variable.
m is the slope of the line, indicating the change in y for a one-unit change in x .
x is the independent variable.
b is the y-intercept, which is the value of y when x is zero.
Purpose : The regression line is used to predict the value of the dependent variable based on the value of the independent variable. It also helps in understanding the strength and direction of the relationship between the variables.
Why It's Called 'Best Fit' : The line is derived by minimizing the sum of the squared differences between the observed values and the values predicted by the line (least squares method).
This process ensures that the total of all these squared differences is as small as possible, making it an optimal choice in summarizing the data's trend.
The regression line in a simple linear regression analysis represents the line of best fit, which models the relationship between the independent and dependent variables. Therefore, the correct answer is D) The line of best fit that models the relationship between the independent and dependent variables.
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