1. Correlation and Linear Regression

2. YearPercent Used Marijuana 198750.20 198847.20 199040.70 199136.70 199232.60 199335.30 199438.2 199541.70 199644.90 DenominationTotal circulation ($) $16253758057 $2548577377 $51468874833 $101338391336 $204093739605 $50932552370 $1002640194345 StatePercentage Taking SATMean Math SAT Alaska48517 Arizona29522 California45514 Colorado30539 Hawaii54512 Idaho15539 Montana22548 Nevada32509 New Mexico12545 Oregon50524 Utah4570 Washington46523 Wyoming12543 TypeGrams of fat (X)Calories (Y) Hamburger10270 Cheeseburger14320 Quarter Pounder21430 Quarter Pounder w/Cheese30530 Big Mac28530

4. How do we measure the strength of a linear relationship? Correlation (r) Correlation is a value between no correlation weak correlation moderate correlation strong correlation

6. Find correlation of McDonald’s fat/calories using above formula. Type of Burger Calories (x) Fat (y) Hamburger27010 Cheeseburger32014 Quarter Pounder 43021 Quarter Pounder w/Cheese 53030 Big Mac53028 TypeGrams of fat (X) Calories (Y) XY X2 X2 Y2 Y2 Hamburger10270 Cheeseburger14320 Quarter Pounder21430 Quarter Pounder w/Cheese 30530 Big Mac28530

7. Find correlation of McDonald’s fat/calories using above formula. Type of Burger CaloriesFat Hamburger27010 Cheeseburger32014 Quarter Pounder 43021 Quarter Pounder w/Cheese 53030 Big Mac53028 TypeGrams of fat (X) Calories (Y) XY X2 X2 Y2 Y2 Hamburger10270 270010072900 Cheeseburger14320 Quarter Pounder21430 Quarter Pounder w/Cheese 30530 Big Mac28530

8. Find correlation of McDonald’s fat/calories using above formula. Type of Burger Calories (x) Fat (y) Hamburger27010 Cheeseburger32014 Quarter Pounder 43021 Quarter Pounder w/Cheese 53030 Big Mac53028 TypeGrams of fat (X) Calories (Y) XY X2 X2 Y2 Y2 Hamburger10270 270010072900 Cheeseburger14320 4480196102400 Quarter Pounder21430 9030441184900 Quarter Pounder w/Cheese 30530 15900900280900 Big Mac28530 14840784280900

9. Find correlation of McDonald’s fat/calories using above formula. Type of Burger Calories (x) Fat (y) Hamburger27010 Cheeseburger32014 Quarter Pounder 43021 Quarter Pounder w/Cheese 53030 Big Mac53028 TypeGrams of fat (X) Calories (Y) XY X2 X2 Y2 Y2 Hamburger10270 270010072900 Cheeseburger14320 4480196102400 Quarter Pounder21430 9030441184900 Quarter Pounder w/Cheese 30530 15900900280900 Big Mac28530 14840784280900 Mean = 20.6 Mean= 416 469502421922,000 Let us take a closer look at these variables

10. Find correlation of McDonald’s fat/calories using above formula. Type of Burger Calories (x) Fat (y) Hamburger27010 Cheeseburger32014 Quarter Pounder 43021 Quarter Pounder w/Cheese 53030 Big Mac53028 TypeGrams of fat (X) Calories (Y) XY X2 X2 Y2 Y2 Hamburger10270 270010072900 Cheeseburger14320 4480196102400 Quarter Pounder21430 9030441184900 Quarter Pounder w/Cheese 30530 15900900280900 Big Mac28530 14840784280900 Mean = 20.6 Mean= 416 469502421922,000

11. Find correlation of McDonald’s fat/calories using above formula. Type of Burger Calories (x) Fat (y) Hamburger27010 Cheeseburger32014 Quarter Pounder 43021 Quarter Pounder w/Cheese 53030 Big Mac53028 TypeGrams of fat (X) Calories (Y) XY X2 X2 Y2 Y2 Hamburger10270 270010072900 Cheeseburger14320 4480196102400 Quarter Pounder21430 9030441184900 Quarter Pounder w/Cheese 30530 15900900280900 Big Mac28530 14840784280900 Mean = 20.6 Mean= 416 469502421922,000

12. Find correlation of McDonald’s fat/calories using above formula. Type of Burger Calories (x) Fat (y) Hamburger27010 Cheeseburger32014 Quarter Pounder 43021 Quarter Pounder w/Cheese 53030 Big Mac53028 TypeGrams of fat (X) Calories (Y) XY X2 X2 Y2 Y2 Hamburger10270 270010072900 Cheeseburger14320 4480196102400 Quarter Pounder21430 9030441184900 Quarter Pounder w/Cheese 30530 15900900280900 Big Mac28530 14840784280900 Mean = 20.6 Mean= 416 469502421922,000

13. Find correlation of McDonald’s fat/calories using above formula. Type of Burger Calories (x) Fat (y) Hamburger27010 Cheeseburger32014 Quarter Pounder 43021 Quarter Pounder w/Cheese 53030 Big Mac53028 TypeC Grams of fat (X) Calories (Y) XY X2 X2 Y2 Y2 Hamburger10270 270010072900 Cheeseburger14320 4480196102400 Quarter Pounder21430 9030441184900 Quarter Pounder w/Cheese 30530 15900900280900 Big Mac28530 14840784280900 Mean = 20.6 Mean= 416 469502421922,000

14. Find correlation of McDonald’s fat/calories using above formula. Type of Burger Calories (x) Fat (y) Hamburger27010 Cheeseburger32014 Quarter Pounder 43021 Quarter Pounder w/Cheese 53030 Big Mac53028 TypeGrams of fat (X) Calories (Y) XY X2 X2 Y2 Y2 Hamburger10270 270010072900 Cheeseburger14320 4480196102400 Quarter Pounder21430 9030441184900 Quarter Pounder w/Cheese 30530 15900900280900 Big Mac28530 14840784280900 Mean = 20.6 Mean= 416 469502421922,000

15. Equation of a Line where and Regression Line for McDonald’s Data Equation of the line: y = 133.57 + 13.71x If a new hamburger has 250 calories then it would have ______grams of fat. TypeGrams of fat (X) Calories (Y) XY X2 X2 Y2 Y2 Hamburger10270 270010072900 Cheeseburger14320 4480196102400 Quarter Pounder21430 9030441184900 Quarter Pounder w/Cheese 30530 15900900280900 Big Mac28530 14840784280900 Mean = 20.6 Mean= 416 469502421922,000

16. Equation of a Line where and Regression Line for McDonald’s Data Equation of the line: y = 133.57 + 13.71x If a new hamburger has 250 calories then it would have 8.49 grams of fat.