A public health researcher wants to use regression to predict the sun safety kno
ID: 3294782 • Letter: A
Question
A public health researcher wants to use regression to predict the sun safety knowledge of pre-school children. The researcher randomly sampled 35 pre-schoolers, assigned them to one of two groups, and then measured the following three variables:
SUNSCORE: y = Score on sun-safety comprehension test
READING: x1= Reading comprehension score
GROUP: x2= 1 if child received a Be Sun Safe demonstration, 0 if not
Use the following information to answer the multiple regression questions.
Printout C: UNWEIGHTED LEAST SQUARES LINEAR REGRESSION OF SUNSCORE
PREDICTOR
VARIABLES COEFFICIENT STD ERROR STUDENT'S T P
CONSTANT 4.23186 0.82079 5.16 0.0000
READING 0.00631 0.00194 3.25 0.0027
READSQ .00000425 .00000087 4.87 0.0000
GROUP 2.04026 0.45579 4.48 0.0001
RSQUARED 0.7757 RESID. MEAN SQUARE (MSE) 1.79234
ADJUSTED RSQUARED 0.7546 STANDARD DEVIATION 1.33878
SOURCE DF SS MS F P
REGRESSION 3 198.310 66.1033 36.88 0.0000
RESIDUAL 32 57.3548 1.79234
TOTAL 35 255.665
Notice that the interaction term(s) of the complete 2nd-order model is/are not on Printout C above. You can assume that I tested this/these term(s) and deemed it/them as not providing useful information predicting SUNSCORE. What type of test did I need to conduct to determine whether to drop the interaction term(s)?
A t-test.Explanation / Answer
The partial F-test assesses whether the improvement in model fit (as assessed by a reduction in prediction error) using the full model is too large to be ascribed to chance alone. First we would have done it without the interaction terma dn then with the interaction term.
Therefore a Partial F-test ( or best subset test ) would have been used here.
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