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Question

# A local university is keeping track of the number of art students who use the pottery studio each day. Day $1$ $2$ $3$ $4$ $5$ $6$ $7$ Students $10$ $15$ $18$ $15$ $13$ $19$ $20$ a. Write an equation of the regression line and find and interpret the correlation coefficient.b. Graph the residual plot and determine if the regression line models the data well.

Solution

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Step 1
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a) If you have a TI-83 or TI-84 graphing calculator, use the steps shown in Real-World Example 1 in the lesson to input the values in the table. Input the number of days under the $L_1$ list and the number of students under the $L_2$ list. Then use the LinReg feature on your calculator to find the linear regression equation and correlation coefficient. The steps to do this are also shown in the Real-World Example 1. The calculator gives $a\approx1.18$, $b=11$, and $r\approx0.718$. The equation of the regression line is then $y=ax+b\rightarrow y=1.18x+11$. The correlation coefficient of $r\approx0.718$ is close to 1 so the regression fits the data fairly well.

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