If the slope of the line predicting SAT score from family income is 6.25 points per $1000, what is the slope when predicting family income from SAT score?

To find the slope when predicting family income from SAT score, it's essential to understand the relationship between the two variables and how the slope of a regression line works. The slope of your initial relationship tells you how much the SAT score is predicted to change for a given increase in family income. Specifically, a slope of 6.25 means that for every additional $1000 of family income, the SAT score is predicted to increase by 6.25 points.

When flipping the predictors, the slope will also change in a way that relates to the reciprocal of the initial slope. To derive the new slope, we first express the original slope in terms of points per dollar. Since 6.25 points are gained for every $1000 of income, we convert this to a per dollar basis by dividing by 1000, which gives us 0.00625 points per dollar. This reflects how much the SAT score increases for each dollar increase in income.

Now, to predict family income from SAT score, we consider the inverse relationship. The slope for family income would be the reciprocal of the SAT score's increase per dollar of income. Thus, we take the inverse of 0.00625, resulting in a slope of 160 for income