Are good grades in high school associated with family togetherness? A random sample of 142 high school students was asked how many meals per week their families ate together. Their responses produced a mean of 3.78 meals per week, with a standard deviation of 2.2. Researchers then matched these responses against the students’ grade point averages (GPAs). The scatterplot appeared to be reasonably linear, so they created a line of regression. No apparent pattern emerged in the residuals plot. The equation of the line was
GPA
= 2.73 + 0.11 Meals.
a) Interpret they-intercept in this context. b) Interpret the slope in this context. c) What was the mean GPA for these students? d) If a student in this study had a negative residual, what did that mean? e) Upon hearing of this study, a counselor recommended that parents who want to improve the grades their children get should get the family to eat together more often. Do you agree with this interpretation? Explain.
Answer
a) If a student never ate with his family, his GPA is expected to be about 2.73.
b) GPA increases by about 0.11 for every meal per week
c) 3.1458
d) Student scored less on its GPA than expected
e) No
Explanation
a) The y=intercept is 2.73, which means that if a student never ate with his family, his GPA is expected to be about 2.73
b) The slope is 0.11, which means that the GPA increases by about 0.11 for every meal per week.
c) The mean GPA is:
Thus the GPA is expected to be 3.1458
d) The student scored less on its GPA than was expected (by model).
e) No, because it could be that families who eat more together are more interested in each other lives and are thus will motivate each other more to do better.
