Question

Suppose you are trying to build a regression to predict how fast a state is growing economically from other factors. Below is a scatter plot relating the values of two variables you are considering using as independent variables: the average number of years of schooling that residents of the state have, and the number of families out of each 1000 that are low-income. 300.00 250.00- O o o Families per 1000 below.5 avg income 200.00- o оо O DOO 150.00 100.00 80.00 90.00 110.00 120.00 130.00 100.00 Avg. years of school x10 This scatter plot suggests that the best regression model: Would not include either years of school nor number of low-income families. Might include both years of school and number of low-income families. Might include either years of school or number of low-income families, but probably not both. Would definitely include the years of school, but never the number of low-income families.

Answer 1

We are given the scatter plot here between the two independent variables here. Just from this scatter plot, we can see that there is a clear negative correlation between the two variables. This means that as one independent variable increases, the other decreases while when one decreases, the other decreases. One of the main assumption of regression is that the independent variables cannot be correlated. Therefore we might include either years of school od number of low income families but probably not both.

(From just the given scatter plot, we cannot really know relation between the dependent variable and the independent variable but we know that they both cannot come in a single linear model as independent variables )