Question

practice comparing data sets.
enter values for x and y in the table to plot points in the graph. use the regression calculator to compare students sat scores based on their iq scores.
the trend line shows correlation.
the equation of the trend line is
y = 18.8x - 763
y = 18.8x + 763
y = -18.8x - 763

Explanation:

Step1: Analyze the correlation

As IQ (x - variable) increases, SAT (y - variable) also increases. So, there is a positive correlation.

Step2: Check the equation of the trend - line

We use the formula for the regression line \(y = mx + b\). When \(x = 115\), if \(y=18.8x - 763\), then \(y=18.8\times115-763=2162 - 763 = 1399\approx1440\) (approximate due to regression nature). If \(x = 84\), \(y=18.8\times84 - 763=1579.2-763 = 816.2\approx780\). For \(y = 18.8x+763\), when \(x = 84\), \(y=18.8\times84 + 763=1579.2 + 763=2342.2\) (not close to 780). For \(y=-18.8x - 763\), when \(x = 84\), \(y=-18.8\times84-763=-1579.2-763=-2342.2\) (negative, not relevant as SAT scores are positive).

Answer:

The trend line shows a positive correlation. The equation of the trend line is \(y = 18.8x-763\).