Psychology 406 Assignment #9

This assignment is based on the data given in Assignment #8 and requires the results and information from #8. Treat variable 1 as the dependent variable Y and variable 2 as the independent variable X.

Correlational Model: Suppose the pairs of values given by X and Y represent independent ob-

servations from a bivariate normal distribution.

a) Test H_{0} : ρ_{xy} = 0 versus H_{1} : ρ_{xy} ≠ 0 using the t-statistic.

b) Test H_{0} : ρ_{xy} = .8 versus H_{1} : ρ_{xy} ≠ .8 using Fisher’s Z-transformation.

c) Using Fisher’s Z-transformation, find a 95% confidence interval for ρ_{xy}.

Regression Model: Suppose the data on X and Y are assumed to follow the usual linear re-

gression model with the X variable fixed.

d) Construct a 95% confidence interval on β_{1} and test the hypothesis that H_{0} : β_{1} = 0 versus H_{1} : β_{1} ≠ 0 at α = .05. What is the relation of this latter test to that done in (a).

e) Construct a 95% confidence interval on β_{0}.

f) Construct a 95% confidence interval on the “true mean” for Y given that X = 33.

g) Construct a 95% prediction interval for a new observation with an X value of 33.

h) Partition the Total Sum of Squares for Y into the Regression and Error Sum of Squares. Construct the analysis-of-variance table and carry out the appropriate F-test for testing H_{0} : β_{1} = 0 versus H_{1} : β_{1} ≠ 0. What is the relation of the latter to what was done in (a) and (d)?

i) Partition the Error Sum of Squares into the Sum of Squares for Pure Error and for lack of fit. Construct the analysis-of-variance table for assessing lack of fit and carry out the appropriate F-test.