The data set given below has y^ = 3x - 5 for its regression equation. Find the standard error of estimate.
x 3 2 5 8
y 4 1 10 19
A) 1.29 B) 0 C) 2.06 D) 0.17
B) 0
How do you work problems that ask for the standard error of the estimate Sest of the regression line
To find the standard error of estimate, we need to compare the actual values of y to the predicted values of y^ using the regression equation.
Step 1: Calculate the predicted values of y^.
The regression equation given is y^ = 3x - 5. We can use this equation to calculate the predicted values of y^ for each x value in the dataset.
For x = 3:
y^ = (3 * 3) - 5 = 4
For x = 2:
y^ = (3 * 2) - 5 = 1
For x = 5:
y^ = (3 * 5) - 5 = 10
For x = 8:
y^ = (3 * 8) - 5 = 19
So the predicted values of y^ are 4, 1, 10, and 19.
Step 2: Calculate the difference between the actual values of y and the predicted values of y^.
For each x value, we subtract the corresponding predicted value of y^ from the actual value of y.
For x = 3:
Actual value of y = 4
Difference = 4 - 4 = 0
For x = 2:
Actual value of y = 1
Difference = 1 - 1 = 0
For x = 5:
Actual value of y = 10
Difference = 10 - 10 = 0
For x = 8:
Actual value of y = 19
Difference = 19 - 19 = 0
Step 3: Calculate the sum of the squared differences.
Next, we square each difference calculated in step 2 and then sum them up.
Sum of squared differences = (0^2) + (0^2) + (0^2) + (0^2) = 0
Step 4: Calculate the standard error of estimate.
Finally, we divide the sum of squared differences by the number of data points (n) minus 2, and take the square root.
In this case, n = 4 (since there are 4 data points).
Standard error of estimate = Square root of (sum of squared differences / (n - 2))
= Square root of (0 / 2)
= Square root of 0
= 0
Therefore, the standard error of estimate is 0.
The correct answer is B) 0.