Question

enter values for x and y in the table to plot points in the graph. the table contains data for five students: homework scores, x, and corresponding test scores, y. the regression line shows a: negative trend line with a strong relationship. negative trend line with a weak relationship. positive trend line with a strong relationship. positive trend line with a weak relationship.

Explanation:

Step1: Analyze the trend

As \(x\) (homework scores) increases, \(y\) (test scores) generally increases. For example, when \(x = 65,y = 68\); when \(x=72,y = 78\); when \(x = 92,y=91\). So it is a positive - trend line.

Step2: Analyze the strength of the relationship

Calculate the correlation coefficient \(r\) (formula \(r=\frac{n\sum xy-\sum x\sum y}{\sqrt{[n\sum x^{2}-(\sum x)^{2}][n\sum y^{2}-(\sum y)^{2}]}}\)).
\(n = 6\), \(\sum x=65 + 72+75+88+92+96=488\), \(\sum y=68 + 78+75+82+91+90=484\), \(\sum xy=65\times68+72\times78 + 75\times75+88\times82+92\times91+96\times90=65\times68+72\times78+75\times75+88\times82+92\times91+96\times90 = 4420+5616+5625+7216+8372+8640=39889\), \(\sum x^{2}=65^{2}+72^{2}+75^{2}+88^{2}+92^{2}+96^{2}=4225+5184+5625+7744+8464+9216=40458\), \(\sum y^{2}=68^{2}+78^{2}+75^{2}+82^{2}+91^{2}+90^{2}=4624+6084+5625+6724+8281+8100=39438\).

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Since \(|r|\approx0.93\) which is close to \(1\), the relationship is strong.

Answer:

positive trend line with a strong relationship.