Consider the data below.

These data were collected in an experiment where \(x_{1}=\) reaction time in minutes and \(x_{2}=\) temperature in degrees Celsius. The response variable \(y\) is concentration (grams per liter). The engineer is considering the model
\[
y=\theta_{1}\left(x_{1}\right)^{\theta_{2}}\left(x_{2}\right)^{\theta_{3}}+\varepsilon
\]
a. Note that we can linearize the expectation function by taking logarithms. Fit the resulting linear regression model to the data.
b. Test for significance of regression. Does it appear that both variables \(x_{1}\) and \(x_{2}\) have important effects?
c. Analyze the residuals and comment on model adequacy.

X2 50 75 100 4.70 5.52 3.98 2 2.68 3.75 4.22 6.35 5.88 6.28 x1 4 6.10 7.69 7.12 7.85 9.00 11.43 6 9.25 9.78 9.62