Example of Orthogonal Regression

An engineer at a medical device company wants to determine whether the company's new blood pressure monitor is equivalent to a similar monitor that is made by a different company. The engineer measures the systolic blood pressure of a random sample of 60 people using both monitors.

To determine whether the two monitors are equivalent, the engineer uses orthogonal regression. Previous to the data collection for the orthogonal regression, the engineer did separate studies on each monitor to estimate the variances. The variance for the new monitor was 1.08. The variance for the other company's monitor was 1.2. The engineer decides to assign the new monitor to be the response variable and the other company's monitor to be the predictor variable. With these assignments, the error variance ratio is 1.08 / 1.2 = 0.9.
Note

If the engineer decided to reverse the assignments, the error variance ratio would be 1.2 / 1.08 = 1.1111.

  1. Open the sample data, BloodPressure.MTW.
  2. Choose Stat > Regression > Orthogonal Regression.
  3. In Response (Y), enter New.
  4. In Predictor (X), enter Current.
  5. In Error variance ratio (Y/X), enter 0.90.
  6. Click OK.

Interpret the results

If either of the following conditions is true, the results provide evidence that the blood pressure monitors are not equivalent:
  • The confidence interval for the slope does not contain 1.
  • The confidence interval for the constant does not contain 0.
The results show that the confidence interval for the constant, which is from approximately -2.78 to 4.06, contains 0. The confidence interval for the slope, Current, which is from approximately 0.97 to 1.02, contains 1. These results do not provide evidence that the measurements from the monitors differ. The fitted line plot shows that the points fall close to the regression line, which indicates that the model fits the data.

Orthogonal Regression Analysis: New versus Current

Error Variance Ratio (New/Current): 0.9

Regression Equation New = 0.644 + 0.995 Current
Coefficients Predictor Coef SE Coef Z P Approx 95% CI Constant 0.64441 1.74470 0.3694 0.712 (-2.77513, 4.06395) Current 0.99542 0.01415 70.3461 0.000 ( 0.96769, 1.02315)
Error Variances Variable Variance New 1.07856 Current 1.19840
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