Find the explained variation for the paired data. The equation of the regression line for the paired data below is y-hat = 3x. Find the explained variation. x= 2 4 5 6 y= 7 11 13 20
To find the explained variation, we need to calculate the sum of squared differences between the predicted values (y-hat) from the regression line and the actual values of y.
First, let's calculate the predicted values (y-hat) for each x using the equation of the regression line y-hat = 3x:
For x = 2:
y-hat = 3 * 2 = 6
For x = 4:
y-hat = 3 * 4 = 12
For x = 5:
y-hat = 3 * 5 = 15
For x = 6:
y-hat = 3 * 6 = 18
Now, let's calculate the squared differences between the predicted values and the actual values of y:
For x = 2:
Squared difference = (6 - 7)^2 = 1
For x = 4:
Squared difference = (12 - 11)^2 = 1
For x = 5:
Squared difference = (15 - 13)^2 = 4
For x = 6:
Squared difference = (18 - 20)^2 = 4
Next, add up these squared differences:
1 + 1 + 4 + 4 = 10
Therefore, the explained variation is 10.