Question: When a regression model is nonlinear or the error terms are not normally distributed, the standard hypothesis testing methods and confidence intervals do not apply.

When a regression model is nonlinear or the error terms are not normally distributed, the standard hypothesis testing methods and confidence intervals do not apply. However, it is possible to solve the problem by bootstrapping.

How might you bootstrap the data in a regression model? [Hint: There are two ways that have been tried. Consider the equation Y = + 1X1 +

2X2 + 3X3 + 4X4 + and think about using the vector (Y, X1, X2, X3, X4).

Alternatively, to help you apply the bootstrap, what do you know about the properties of and its relationship to the estimated residuals e = Y – (a +

b1X1 + b2X2 + b3X3 + b4X4), where

a, b1, b2, b3, and b4 are the least squares estimates of the parameters , 1, 2, 3, and 4, respectively.] Refer to Table 12.1 in Section 12.3. Calculate r between systolic and diastolic blood pressure. Calculate the regression equation between systolic and diastolic blood pressure. Is the relationship statistically significant at the 0.05 level?

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