For Problems 1 and 2: Suppose an organizational talent manager and/or trainer is interested in studying the relationship between the “quality” of a lesson and/or training as a function of “mode” of delivery. The internal consultant randomly assigns 33 employees to one of 3 groups: 1) Group 1 (the treatment group) receives the information interactively from an on-line website, Group 2 (control group 1) receives the training from a trainer, and 3) Group 3 (control group 2) receives the information from a video tape made by the same trainer. To determine if there is a difference in the mode of presentation, the internal consultant looks at 3 different ratings of the presentation: 1) difficulty, 2) usefulness, and 3) importance.

Problem 1: Test the assumptions surrounding MANOVA before using “trainer.dta” to assess quality by mode.

Problem 2: If your MANOVA gives statistically significant results, run 3 separate ANOVAs to assess whether statistically significant results exist between each measure of quality by mode. Interpret your results.

For Problems 3 to 7: Use the following data to answer the questions below:

id	cards	size	income	autos
1	4	2	14	1
2	6	2	16	2
3	6	4	14	2
1	7	4	17	1
5	8	5	18	1
6	7	5	21	2
7	8	6	17	1
8	10	6	25	2

Cards = number of credit cards used by a family (the main dependent variable)

Size = number of individuals in a family (independent variable)

Income = family income measured in thousands of dollars (independent variable)

Autos = number of automobiles owned per family (independent variable)

Problem 3. Use the correlation matrix to determine which independent variable has the strongest relationship with the dependent variable.

Problem 4. Confirm your results running 3 separate regressions (run three bivariate regressions).

Problem 5. Use your regression of “cards” on “size” to interpret the following: 1) the intercept coefficient, 2) the slope coefficient, and 3) the coefficient of determination. Construct a scattergram that relates predicted values and actual values to “size” (make sure that you “connect” predicted values).

Problem 6. Now, regress “cards” on both “size” and “income” before reinterpreting the results. Is income statistically significant? Should “income” be retained in the model?

Problem 7. Regress “cards” on all 3 independent variables. Use Stata to estimate the model before explaining the results in terms of the size, sign, and significance of coefficients along w/ model diagnostics including the adjusted coefficient of determination (also known as the adjusted R-squared). Which model is best?