Linear Regression Line (Line of Best Fit)
(3 points)
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A. What is the equation for the Linear Regression Line? Response area
B. There is a Response area correlation between the test marks and the homework marks.
C. The slope of the line of best fit can be used to make a probabilistic interpretation that states Response area
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A. What is the equation for the Linear Regression Line? Response area
B. There is a Response area correlation between the test marks and the homework marks.
C. The slope of the line of best fit can be used to make a probabilistic interpretation that states Response area
A. The equation for the Linear Regression Line is y = mx + b, where y is the dependent variable (usually the variable being predicted), x is the independent variable (usually the variable used to make predictions), m is the slope of the line, and b is the y-intercept.
B. There is a positive/negative correlation between the test marks and the homework marks. (Choose either positive or negative depending on the given data).
C. The slope of the line of best fit can be used to make a probabilistic interpretation that states for every one unit increase in the independent variable (x), the dependent variable (y) is expected to increase/decrease by the slope value (m). (Choose either increase or decrease depending on the given data).
A. The equation for the Linear Regression Line can be found using the formula:
\[y = mx + b\]
where \(y\) is the dependent variable (in this case, the test marks), \(x\) is the independent variable (in this case, the homework marks), \(m\) is the slope of the line, and \(b\) is the y-intercept. To find the equation for the Linear Regression Line, you need to calculate the values of \(m\) and \(b\) based on the given data points.
B. There is a correlation between the test marks and the homework marks. Correlation measures the relationship between two variables and ranges from -1 to 1. A positive correlation (values close to 1) means that as one variable increases, the other also increases. In the context of a Linear Regression Line, if there is a positive correlation between the test marks and the homework marks, it suggests that as the homework marks increase, the test marks also tend to increase.
C. The slope of the line of best fit can be used to make a probabilistic interpretation that states for every one unit increase in the independent variable (homework marks in this case), the dependent variable (test marks) is expected to increase/decrease by the value of the slope. This interpretation is based on the assumption that the relationship between the two variables is linear and holds for the given data set.