## Related questions with answers

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

Verifieda) 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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