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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 11 22 33 44 55 66 77
Students 1010 1515 1818 1515 1313 1919 2020

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 L1L_1 list and the number of students under the L2L_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 a1.18a\approx1.18, b=11b=11, and r0.718r\approx0.718. The equation of the regression line is then y=ax+by=1.18x+11y=ax+b\rightarrow y=1.18x+11. The correlation coefficient of r0.718r\approx0.718 is close to 1 so the regression fits the data fairly well.

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