Consider the following observations:

a. Fit the nonlinear regression model
\[
y=\theta_{1} e^{\theta_{2} x}+\varepsilon
\]
to these data. Discuss how you obtained the starting values.
b. Test for significance of regression.
c. Estimate the error variance \(\sigma^{2}\).
d. Test the hypotheses \(H_{0}: \theta_{1}=0\) and \(H_{0}: \theta_{2}=0\). Are both model parameters different from zero? If not, refit an appropriate model.
e. Analyze the residuals from this model. Discuss model adequacy.

x y 0.5 0.68 1.58 124890 0.45 2.66 2.50 2.04 6.19 7.85 56.1 54.2 89.8 90.2 147.7 146.3