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**Linear Correlation and Regression**

Using the TI-83 or TI-84

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**Finding “r” and the trend line equation by using the calculator……**

Temp. Emergency Calls 68 7 74 4 82 8 88 10 93 11 99 9 101 13 Before we begin, make sure that your diagnostic is turned on: Press 2nd 0 Scroll down to diagnostic on Press Enter twice

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Calculator Steps: Put x’s in L1 and y’s in L2. Press Stat Calc 4:LinReg Vars Y-Vars 1:Function Enter Enter You should see all data.

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**Correlation Coefficient “r” is equal to .811.**

The trend line equation is y = .19x – 7.54

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**a. Explain the meaning of the y-intercept .**

Temp. Emergency Calls 68 7 74 4 82 8 88 10 93 11 99 9 101 13 In the equation y = .19x – 7.54 a. Explain the meaning of the y-intercept . b. Explain the meaning of the slope.

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Equation: y = .19x – 7.54 Temp. Emergency Calls 68 7 74 4 82 8 88 10 93 11 99 9 101 13 A. The number of emergency phone calls when the temp is 0. B. The number of emergency phone calls increases .19 for every degree increase in temperature. (The # of calls/degree temp increase)

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**You can also graph it…… The equation for the trend line is now in**

Press zoom 9 to see the scatter plot and the trend line.

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**You try…… Find: a. Correlation coefficient b. Trend line equation**

Graph on graphing calculator. Explain the meaning of the y-int and the slope. Absences Final Grade 6 82 2 86 15 43 9 74 12 58 5 90 8 78

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Absences Final Grade 6 82 2 86 15 43 9 74 12 58 5 90 8 78

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**Correlation Coefficient: -.944**

Equation: y = -3.62x

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**Equation: y = -3.62x + 102.5 Meaning of Y-Intercept:**

Absences Final Grade 6 82 2 86 15 43 9 74 12 58 5 90 8 78 Meaning of Y-Intercept: The final grade when a student has 0 absences. (102.5) Meaning of slope: Final grade/absence – the grade decreases (3.62) for every absence made

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Example…… Max used linear regression to help him understand the relationship between the temp and the number of ice cream cones sold. The line of best fit was y = 5x + 60, where x is the # of ice cream cones sold and y is the temp in degrees F. In terms of ice cream cones sold and temp answer the following.

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**Equation: y = 5x + 60 Explain the meaning of the y-intercept:**

The temperature (60 degree F) when no ice cream cones are sold. Explain the meaning of the slope: The temperature increases 5 degrees F for every ice cream cone sold. (Temp/# sold)

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Assignment…… Use ONLY the TI-83 or TI-84 to find the values on the HW assignment.

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AP Statistics HW: p. 165 #42, 44, 45 Obj: to understand the meaning of r 2 and to use residual plots Do Now: On your calculator select: 2 ND ; 0; DIAGNOSTIC.

AP Statistics HW: p. 165 #42, 44, 45 Obj: to understand the meaning of r 2 and to use residual plots Do Now: On your calculator select: 2 ND ; 0; DIAGNOSTIC.

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