Question

A 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 castigs produced in excess of 100 over a four week period. The multiple regression model is γ=β0+pǐX1 + β2X2 + β3X3 + β4X1X2 + β5XiX3 + e, where Xi is the salary incentive, X,-1 for a dayshift worker and 0 otherwise, X3=1 if the worker is unionized and 0 otherwise. Data were collected for a random sample of 200 workers over a four week period. Four models were fit to the data. Model The corresponding SSEs are below Model SSE 388 396 420 412 For which model is R the lowest? 03 [2 pt(s)) Submit Answer Tries 0/1 Test to see whether interaction terms should be included in the model What is the value of the test-statistic? [3 pt(s)] Submit Answer Tries 0/3 What are the degrees of freedom associated with the test-statistic? Numerator: Denominator: 1 pt(s)) Submit Answer Tries 0/3 Select the interval below that contains the p-value for this test. O p-value s 0.001 0.001 0.01 o.05 p-value s o.1 0.1 p-value s 0.25 p-value s 0.01 p-value s o.05 O p-value>0.25 [3 pt(s)] Submit Answer Tries 0/3 Test to see if productivity differs between unionized and non-unionized workers. What is the value of the test-statistic? [3 pt(s) Submit Answer Tries 0/3 What are the degrees of freedom associated with the test-statistic? Numerator: Denominator: [1 pt(s)1 Submit Answer Tries 0/3 Select the interval below that contains the p-value for this test. O p-value s 0.001 0.001

Answer 1

Answer: The larger SSE is, the smaller is RA2 Hence model 3 has largest R 2 Model 1 is unreduced, Model 2 is reduced Test-Statistic = ((SSR r-SSR uryq) / (SSR ur / (n-k-1)) (396- 388)/2)/(388/(200-5-1)) TS-2 q-2, n 200, k 5 (Numerator) dfl- 2 (Denominator) df2-194 p-value-P(F p-value -0.14 0.1 < p-value <= 0.25 > TS) = 1-0.86 = 0.1 3 8

ho: b3-0 Unreduced model -2 reduced model-4 dfi 1, df2 200-3-1 = 1 96 Test-statistic ((412-396)/1)/(396 (196) TS 7.9191919 p-value = 1-0.995-0.005 p-value-0.005 0.001 -p-value<-0.01