1. Ch. 12– part 2 Sec 12.6: Correlation and Regression

2. Intro-- review h.s. algebra, graphing, slope, y-intercept… Before we get started, let's review algebra: Plot the following lines and discuss the slope and y-intercept: y=2x-4 y= -2x +4 y= -3x +6 y = (1/2)x -4

3. Correlation r = 1,…

4. Calculation formula for Correlation Calculation formula for Correlation (pg 125) r =

5. Ex#1: x=hours sleep, y=typing speed XYX 2 Y 2Y 2 xy 830 620 1245

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=a+bx 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 (2 nd STATVAR) to clear old work. (It will either clear it or give you an error if it was empty). 2. Go to STAT (2 nd 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 b 1 in our book), b (the y-intercept in the regression line (b 0 in our book), and r (the correlation coefficient). 6. Go to EXIT STAT (2 nd 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 I 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. Prediction Y= 4.107x – 3.929

12. Directions on the TI83 or 84: 1.To make sure r appears, go to CATALOG and select DIAGNOSTIC ON 2.Clear lists: Go to STAT/Edit: Pick 4. Type "ClrList L1" or ClrList L1, L2" 3.Enter data: Go to STAT/Edit Pick 1. Edit. Enter your list of numbers. 4.For regression: Go to STAT/CALC and pick 4. LinReg(ax+b) 5.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.

13. Ex #2

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

17. 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

18. Multiple regression– see Minitab demo…

19. R-Sq R 2 gives a percentage for the amount of y that can be predicted from the predictor x Ex: