Statistics is one of the most challenging, and most valuable, fields of mathematics because it is a tool for directly understanding some of the most complicated problems that the world can throw at us. In this case, when the question asks you what the trend 'means,' it's not asking for a mathematical formula or rule; it's asking for you to describe a real-world relationship that appears to be represented mathematically.
The correlation in the graph is negative. That means that as one axis increases in value, the value on other axis tends to decrease. And what are the axes? Well, the x-axis represents the students' current weight, and the y-axis represents their desired weight change--positive for gain, negative for loss.
So what we need to do is translate that relation into plain English. What does it mean that, as students initial weight increases, their desired weight change becomes more and more negative? It means something that's actually quite intuitive: that heavier people want to lose more weight.
The negative trend in this scatterplot indicates that the two variables, weight and desired weight change, are negatively correlated. That means as a student's weight goes up, his or her desired weight change goes down (meaning that it is a negative number). If you draw a line of best fit through the data (meaning a straight line that approximately goes through the center of the data), students who weight 100 pounds will want to gain about 10 pounds (positive ten), while students who weigh about 130 will not want to lose any weight (meaning a value of 0). As students' weights increase, their desired weights become negative because they want to lose weight. For example, a student who weighs 180 pounds will have a desired weight change of approximately negative 40. Therefore, as a student's weight increases, the desired weight change becomes increasingly negative, meaning that the variables are negatively correlated and there is a negative trend in the data.
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