psychologist conducted an experiment to investigate the relationship between worker productivity (Y, measured in units of thousands of machine castings), salary incentive shift (day or night), and type of factory (unionized or non-unionized)_ The salary incentive was the bonus paid per worker, in dollars, for all castings produced in excess of 100 over a four week period_ The multiple regression model is Y=Bo+B1X1 Bzx2 B3x3 BaX1X2 BsX1X3 where X1 is the salary incentive X2=1 for dayshift worker and 0 otherwise_ X3=1 if the worker is unionized and 0 otherwise_ Data were collected for random sample of 200 workers over four week period Four models were fit to the data.
Model Y=Bo+B1X1 B2x2 83*3 B4X1X2 B5X1X3 Y=Bo+B1X1 Bzx2 B3*3 3. Y=Bo+Bixi Bax3 Y=Bo+B1X1 Bzx2
The corresponding SSEs are below.
ModellsSE
For which model is R2 the lowest?
Test to see whether interaction terms should be included in the model:
What is the value of the test-statistic?
What are the degrees of freedom associated with the test-statistic? Numerator:
Denominator:
Select the interval below that contains the p-value for this test: P-value $ 0.001 .001 P-value $ 0.01 0.01 P-value 0.05 0.05 P-value 0.1 0.1 p-value < 0.25 P-value 0.25