Refer to the IEICE Transactions on Information & Systems (Jan. 2005) experiment to monitor the impedance to leg movement, Exercise 2.46. Recall that engineers attached electrodes to the ankles and knees of volunteers and measured the signal-to-noise ratio (SNR) of impedance changes. For the optimum ankle-knee electrode pair, the engineers examined the relationship between knee joint angle, x (degrees), and knee impedance change, y (ohms). A quadratic model was fit to the data with the following results:

ŷ = 24.83 + .041x +.005x², R² = .903

a. Sketch the least-squares prediction equation. Identify the nature of the curvature estimated by the model.

b. Predict the knee impedance change (y) for an electrode pair with a knee joint angle of x = 50 degrees.

c. Interpret the value of R².

Data from Exercise 2.46

In an experiment to monitor the impedance to leg movement, Korean engineers attached electrodes to the ankles and knees of volunteers. Of interest was the signal-to-noise ratio (SNR) of impedance changes, where the signal is the magnitude of the leg movement and noise is the impedance change resulting from interferences such as knee flexes and hip extensions. For a particular ankle–knee electrode pair, a sample of 10 volunteers had SNR values with a mean of 19.5 and a standard deviation of 4.7. (IEICE Transactions on Information & Systems, Jan. 2005.) Assuming the distribution of SNR values in the population is mound shaped and symmetric, give an interval that contains about 95% of all SNR values in the population.