a. The event {X2 y} is equivalent to what event involving X itself? b. If X has a standard normal distribution, use part (a) to write the integral that equals P(X2 y). Then differentiate this with respect to y to obtain the pdf of X2 [the square of a N(0, 1) variable]. Finally, show that X2 has a chi-squared distribution with 1 df [see (4.10)]. [Hint: Use the following identity.] d d y b(y) a(y) f(x) dx f[b(y)] b (y) f[a(y)] a (y)
Chapter 15 Inferences for Regression Chapter 4 was all descriptive statistics (describing the relationship between Y and X in the sample data) and Chapter 15 is inferential statistics (describing the ‘true’ relationship between Y and X in the population) The first few pages of Chapter 15 have two main purposes: o To introduce the population regression model o Briefly review what we did with regression in Chapter 4 The population model is x . The text does a good job of explaining this model. Y 0 1 The population mean of Y has a linear relation with X. 0 is the population Y-intercept and 1Is the population slope Our sample regression equation statistics (ŷ, b O and b 1 will provide estimates of the p
