A psychologist conducted an experiment to investigate the relationship between w

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 all castings produced in excess of 100 over a four week period. The multiple regression model is Y=0+1X1 + 2X2 + 3X3 + 4X1X2 + 5X1X3 + e, where X1 is the salary incentive, X2=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.

The corresponding SSEs are below.

Model 1. Y=0+1X1 + 2X2 + 3X3 + 4X1X2 + 5X1X3 + e 2. Y=0+1X1 + 2X2 + 3X3 + e 3. Y=0+1X1 + 3X3 + e 4. Y=0+1X1 + 2X2 + e For which model is R the lowest? O 2 4 [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 O 0.001

Explanation / Answer

the larger SSE is , the smaller is R^2
hence model 3 has largest R^2
model 1 is unreduced ,
model 2 is reduced
TS = ((SSR_r - SSR_ur)/q) / (SSR_ur / (n-k-1))
= (396 - 388)/2)/(388/(200-5-1))

=2

q = 2 , n = 200 , k = 5

df1 = q , df2 = n-k-1
df1 = 2 , df2 = 194

p-value = P(F > TS) = 1- 0.86 = 0.14

0.1 < p-value < 0.25

b)

ho: b3 =0

unreduced model - 2 reduced model - 4
df1 = 1 , df2 = 200-3-1=196

Ts = ((412-396)/1)/(396/(196)

= 7.9191919

p-value = 1-0.995 = 0.005

0.001 < p-value <0.01

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