A Public Health Researcher Wants to Use Regression to Predict $\quad y =$

Multiple Choice

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: $\quad y =$ Score on sun-safety comprehension test
READING: $\quad \mathrm { x } _ { 1 } =$ Reading comprehension score
GROUP: $\quad x _ { 2 } = 1$ if child received a Be Sun Safe demonstration, 0 if not
The following two models were hypothesized:
$$\begin{array} { l } \text { Model 1: } E ( y ) = \beta _ { 0 } + \beta _ { 1 } x _ { 1 } + \beta _ { 2 } x _ { 1 } ^ { 2 } + \beta _ { 3 } x _ { 2 } + \beta _ { 4 } x _ { 1 } x _ { 2 } + \beta _ { 5 } x _ { 1 } ^ { 2 } x _ { 2 } \\\text { Model 2: } E ( y ) = \beta _ { 0 } + \beta _ { 1 } x _ { 1 } + \beta _ { 3 } x _ { 2 } + \beta _ { 4 } x _ { 1 } x _ { 2 }\end{array}$$
A 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 $\alpha = 0.05$ ) .

A) sufficient evidence of interaction between sun-safety score and reading score.
B) insufficient evidence of quadratic relationship between sun-safety score to reading score.
C) sufficient evidence of a quadratic relationship between sun-safety score to reading score.
D) sufficient evidence of a statistically useful model for sun-safety score.