Chapter 13, Problem 73SE

The accompanying data on x = frequency (MHz) and y = output power (W) for a certain laser configuration was read from a graph in the article “Frequency Dependence in RF Discharge Excited Waveguide CO₂ Lasers" (IEEE J. of Quantum Electronics, 1984: 509-514).

X	60	63	77	100	125	157	186	222
V	16	17	19	21	22	20	15	5

A computer analysis yielded the following information for a quadratic regression model: ${\hat{\beta }}_o$ ⁼ − 1.5127, ${\hat{\beta }}_1$  = .391901, ${\hat{\beta }}_2$  = -.00163141, $s_{{\hat{\beta }}_2}$  = .00003391, SSE = .29, SST =" 202.88, and $s_{\hat{\gamma }}$ = .1141 when x = 100.

1. a. Does the quadratic model appear to be suitable for explaining observed variation in output power by relating it to frequency?
2. b. Would the simple linear regression model be nearly as satisfactory as the quadratic model?
3. c. Do you think it would be worth considering a cubic model?
4. d. Compute a 95% CI for expected power output when frequency is 100.
5. e. Use a 95% PI to predict the power from a single experimental run when frequency is 100.