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Ch. 4: Correlation and Regression

Ch. 4: Correlation and Regression. Ma260notes_ch4_ppnotes.pptx. Intro-- review h.s . algebra, graphing, slope, y-intercept…. Correlation. r = 1,…. Calculation formula for Correlation. Calculation formula is an easier equivalent to theoretical formula in the book r = .

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Ch. 4: Correlation and Regression

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  1. Ch. 4: Correlation and Regression Ma260notes_ch4_ppnotes.pptx

  2. Intro-- review h.s. algebra, graphing, slope, y-intercept…

  3. Correlation • r = 1,…

  4. Calculation formula for Correlation Calculation formula is an easier equivalent to theoretical formula in the book r =

  5. Ex#1: x=hours sleep, y=typing speed

  6. Calculate r r=

  7. Regression- notes • Choice of variable names often differ in books.  In our book, the equation of the least-squares regression line is y=b1x+b0 • However, our calculators use y=ax+b. So we’ll use this. • a = slope • b = y-intercept

  8. Directions– correlation/ regression for ex#1 on the TI30XII 1.      After turning on, go to EXIT STAT (2nd STATVAR) to clear old work. (It will either clear it or give you an error if it was empty). 2.      Go to STAT (2nd DATA) 3.      Select 2-VAR  (Recall, earlier in the semester when we were doing standard deviations that we selected 1-VAR). 4.      Go to DATA and input 5.      Go to STATVAR. Scroll through to see mans, standard deviations, and summations for both x and y. At the end is a (the slope of the regression line, known as b1 in our book), b (the y-intercept in the regression line (b0 in our book), and r (the correlation coefficient). 6.      Go to EXIT STAT (2nd STATVAR) to clear your work before doing another example or before returning one of my calculators.  

  9. Calculator results • Calculator reads: 26 =    95         =  244                 =  3325 = 900 a = slope=4.107           b = -3.929        r = correlation = 0.9972 So regression line is   = 4.107x – 3.929

  10. Interpretation • y-intercept: If we get no sleep, my typing speed is -3.929 • slope: For every hour of sleep, my typing speed goes up 4.107 words per minute.

  11. Directions on the TI83 or 84: • To make sure r appears, go to CATALOG and select DIAGNOSTIC ON • Clear lists: Go to STAT/Edit: Pick 4. Type "CltList L1"  or ClList L1, L2" • Enter data: Go to STAT/Edit Pick 1. Edit.  Enter your list of numbers. • For regression: Go to STAT/CALC and pick 4. LinReg(ax+b) • Optional: If r still doesn't appear: Go to STAT/TESTS and pick E: LinRegTTest and go down to CALCULATE. It will tell you a, b, and r.

  12. Prediction • Ex #1 Regression equation: Y= 4.107x – 3.929 • Pick an appropriate x (hours of sleep) • Calculate the predicted y (typing speed)

  13. Ex #2– x=hours studied, y=test grade Plot points, and calculate r by hand and regression on the calculator Should get: • Correlation r=0.985 • Regression: y= 19x - 1

  14. r

  15. Example #3   (use a calculator) Predictor: x= snowfall in inches Response Variable: y= times snowplow plows x                      y          Oct                  5                      1 Nov                 18                    3 Dec                  25                    4 Jan                   18                    4 Feb                  60                    12 Mar                  12                    2 Apr                  10                    1

  16. Example #4 predictor   X=ave monthly temperature response  Y=gas bill x                      y          Jan                   32                    250 Feb                  25                    280 Mar                  39                    165 Apr                  45                    130 May                 59                    30 Jun                   70                    25 Jul                    80                    20 Aug                 85                    25 Sept                 70                    45 Oct                  50                    85 Nov                 40                    110 Dec                  25                    180

  17. Additional topics • Multiple regression– see Minitab demo… • Residual= observed y – predicted y For ex #1, x=4 hours of study gets a grade of y=70. Use the regression equation y= 19x – 1 to calculate the residual. • R 2 gives a percentage for the amount of y that can be predicted from the predictor x

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