Use the equation of the regression line to predict y when x = 20.
x - 5 8 6 10 12 9
y - 18 20 15 25 30 25
To predict the value of y when x = 20, we can use the equation of the regression line. The regression line represents the relationship between the independent variable (x) and the dependent variable (y) in a linear regression model.
To obtain the equation of the regression line, we need to perform linear regression analysis on the given data. This analysis helps us find the best-fitting line that represents the relationship between x and y.
Before we proceed, let's organize the given data into two columns: x and y.
x: 5 8 6 10 12 9
y: 18 20 15 25 30 25
We can use software tools like Microsoft Excel, Python libraries like NumPy or SciPy, or online regression calculators to perform the linear regression analysis and obtain the equation of the regression line.
Once we have the equation of the regression line in the form y = mx + b, we can substitute x = 20 into the equation to calculate the predicted value of y.
Therefore, the actual calculation of predicting y when x = 20 involves finding the equation of the regression line, substituting x = 20 into the equation, and solving for y.