Question

The relationship between between food insecurity and GPA is:

Food insecurity does not affect student GPA
Food insecure students report lower a lower GPA (2.0-2.49)
Food insecure students report a higher GPA (3.0-4.0)
There is no relationship between the two variables

Answer 1

The coefficient of determination between high school GPA and freshman college GPA is 0.1024, indicating that about 10% of the variance in freshman college GPA can be explained by high school GPA. The remaining 90% of the variance is not explained by high school GPA.

Step-by-step explanation:

The coefficient of determination is the square of the correlation coefficient. In this case, the correlation between high school GPA and freshman college GPA is 0.32. Therefore, the coefficient of determination is 0.32^2 = 0.1024, which represents the amount of variation in freshman college GPA explained by high school GPA.

The amount of variation in freshman college GPA that is not explained by high school GPA can be found by subtracting the coefficient of determination (0.1024) from 1. So, the amount that cannot be explained is 1 - 0.1024 = 0.8976, which is approximately 0.90.

Therefore, about 90 percent of the variance in freshman college GPA in this data is not explained by high school GPA.