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

question 95

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: $\quad \mathrm { y } =$ Score on sun-safety comprehension test
READING: $\quad \mathrm { x } _ { 1 } =$ Reading comprehension score
GROUP: $\quad\quad x _ { 2 } = 1$ if child received a Be Sun Safe demonstration, 0 if not

The following two models were hypothesized:
Model 1: $E ( y ) = \beta _ { 0 } + \beta _ { 1 } x _ { 1 } + \beta _ { 2 } x _ { 1 } ^ { 2 } + \beta _ { 3 } x _ { 2 } + \beta _ { 4 } x _ { 1 } x _ { 2 } + \beta _ { 5 } x _ { 1 } ^ { 2 } x _ { 2 }$
Model 2: $E ( y ) = \beta _ { 0 } + \beta _ { 1 } x _ { 1 } + \beta _ { 3 } x _ { 2 } + \beta _ { 4 } x _ { 1 } x _ { 2 }$

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 _____ $\text { (at } \alpha = 0.05 )$

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

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Definitions:

School-Aged Children

Children in the age group that typically attend school, usually considered to be between the ages of 6 and 18.

Second Grade

An educational level following first grade, typically involving students aged 7 to 8, focusing on developing basic math, reading, and writing skills.

Third Grade

A year or level of education in primary schools in various education systems, typically involving children ages 8 to 9.

Treisman's Attenuation Theory

A theory proposed by Anne Treisman that suggests information is processed at varying levels of attention, where some stimuli are attended to less intensely but not completely filtered out.