A public health researcher wants to use regression to predict the sun safety knowledge of pre-school children. The researcher randomly sampled 35 preschoolers, assigned them to one of two groups, and then measured the following three variables:
SUNSCORE:
y = Score on sun-safety comprehension test
READING:
x
1 = Reading comprehension score
GROUP:
x
2 = 1 if child received a Be Sun Safe demonstration, 0 if not
The following two models were hypothesized:
Model 1: E(y) = β
0 + β
1x
1 + β
2x
12 + β
3x
2 + β
4x
1 x
2 + β
5x
12x
2 Model 2: E(y) = β
0 + β
1x
1 + β
3x
2 + β
4x
1x
2A partial f-test was conducted to compare the two models and the resulting p-value was found to be 0.0023. Fill in the blank. The results lead us to conclude that there is
(at
).
◦ sufficient evidence of interaction between sun-safety score and reading score.
◦ sufficient evidence of a statistically useful model for sun-safety score.
◦ sufficient evidence of a quadratic relationship between sun-safety score to reading score.
◦ insufficient evidence of quadratic relationship between sun-safety score to reading score.
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