Correlation and Linear Regression. YearPercent Used Marijuana 198750.20 198847.20 199040.70 199136.70 199232.60 199335.30 199438.2 199541.70 199644.90.

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Presentation transcript:

Correlation and Linear Regression

YearPercent Used Marijuana DenominationTotal circulation ($) $ $ $ $ $ $ $ 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

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

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

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

Find correlation of McDonald’s fat/calories using above formula. Type of Burger Calories (x) Fat (y) Hamburger27010 Cheeseburger32014 Quarter Pounder Quarter Pounder w/Cheese Big Mac53028 TypeGrams of fat (X) Calories (Y) XY X2 X2 Y2 Y2 Hamburger Cheeseburger Quarter Pounder Quarter Pounder w/Cheese Big Mac

Find correlation of McDonald’s fat/calories using above formula. Type of Burger Calories (x) Fat (y) Hamburger27010 Cheeseburger32014 Quarter Pounder Quarter Pounder w/Cheese Big Mac53028 TypeGrams of fat (X) Calories (Y) XY X2 X2 Y2 Y2 Hamburger Cheeseburger Quarter Pounder Quarter Pounder w/Cheese Big Mac Mean = 20.6 Mean= ,000 Let us take a closer look at these variables

Find correlation of McDonald’s fat/calories using above formula. Type of Burger Calories (x) Fat (y) Hamburger27010 Cheeseburger32014 Quarter Pounder Quarter Pounder w/Cheese Big Mac53028 TypeGrams of fat (X) Calories (Y) XY X2 X2 Y2 Y2 Hamburger Cheeseburger Quarter Pounder Quarter Pounder w/Cheese Big Mac Mean = 20.6 Mean= ,000

Find correlation of McDonald’s fat/calories using above formula. Type of Burger Calories (x) Fat (y) Hamburger27010 Cheeseburger32014 Quarter Pounder Quarter Pounder w/Cheese Big Mac53028 TypeGrams of fat (X) Calories (Y) XY X2 X2 Y2 Y2 Hamburger Cheeseburger Quarter Pounder Quarter Pounder w/Cheese Big Mac Mean = 20.6 Mean= ,000

Find correlation of McDonald’s fat/calories using above formula. Type of Burger Calories (x) Fat (y) Hamburger27010 Cheeseburger32014 Quarter Pounder Quarter Pounder w/Cheese Big Mac53028 TypeGrams of fat (X) Calories (Y) XY X2 X2 Y2 Y2 Hamburger Cheeseburger Quarter Pounder Quarter Pounder w/Cheese Big Mac Mean = 20.6 Mean= ,000

Find correlation of McDonald’s fat/calories using above formula. Type of Burger Calories (x) Fat (y) Hamburger27010 Cheeseburger32014 Quarter Pounder Quarter Pounder w/Cheese Big Mac53028 TypeC Grams of fat (X) Calories (Y) XY X2 X2 Y2 Y2 Hamburger Cheeseburger Quarter Pounder Quarter Pounder w/Cheese Big Mac Mean = 20.6 Mean= ,000

Find correlation of McDonald’s fat/calories using above formula. Type of Burger Calories (x) Fat (y) Hamburger27010 Cheeseburger32014 Quarter Pounder Quarter Pounder w/Cheese Big Mac53028 TypeGrams of fat (X) Calories (Y) XY X2 X2 Y2 Y2 Hamburger Cheeseburger Quarter Pounder Quarter Pounder w/Cheese Big Mac Mean = 20.6 Mean= ,000

Equation of a Line where and Regression Line for McDonald’s Data Equation of the line: y = x 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 Hamburger Cheeseburger Quarter Pounder Quarter Pounder w/Cheese Big Mac Mean = 20.6 Mean= ,000

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