Chapter 12 - The Pearson Product Moment Correlation ...



MTH 207 Elementary Statistics

Scatterplots, Correlation, and Regression by hand

Four different sets of data:

Fat Grams and Calories by Type of McDonalds Hamburgers

|Type |Grams of fat (X) |Calories (Y) |

|Hamburger |10 |270 |

|Cheeseburger |14 |320 |

|Quarter Pounder |21 |430 |

|Quarter Pounder |30 |530 |

|w/Cheese | | |

|Big Mac |28 |530 |

Percentage Taking SAT and Mean Math SAT for Western States

|State |Percentage Taking SAT|Mean Math SAT |

|Alaska |48 |517 |

|Arizona |29 |522 |

|California |45 |514 |

|Colorado |30 |539 |

|Hawaii |54 |512 |

|Idaho |15 |539 |

|Montana |22 |548 |

|Nevada |32 |509 |

|New Mexico |12 |545 |

|Oregon |50 |524 |

|Utah |4 |570 |

|Washington |46 |523 |

|Wyoming |12 |543 |

Value and Total Circulation of United States Currency

|Denomination |Total circulation ($) |

|$1 |6253758057 |

|$2 |548577377 |

|$5 |1468874833 |

|$10 |1338391336 |

|$20 |4093739605 |

|$50 |932552370 |

|$100 |2640194345 |

Year and Percentage of Twelfth Graders who have ever used Marijuana

|Year |Percent Used Marijuana |

|1987 |50.20 |

|1988 |47.20 |

|1990 |40.70 |

|1991 |36.70 |

|1992 |32.60 |

|1993 |35.30 |

|1994 |38.2 |

|1995 |41.70 |

|1996 |44.90 |

How can you see the relationship between the variables? Scatter plots can help us see the relationship between two quantitative variables.

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Chapter 12 - The Pearson Product Moment Correlation Coefficient – r – measures the strength of the linear relationship between the paired x and y values in a sample.

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Judging the strength of the linear relationship – according to Cohen (1988), the following can be concluded:

• r = +/- .50 are considered strong

• r = +/- .30 are considered moderate

• r = +/- .10 are considered weak

Find correlation of McDonald’s fat/calories using above formula’s

| Type |Grams of fat (X) |Calories (Y) | XY | X2 | Y2 |

|Hamburger |10 |270 | | | |

|Cheeseburger |14 |320 | | | |

|Quarter Pounder |21 |430 | | | |

|Quarter Pounder w/Cheese |30 |530 | | | |

|Big Mac |28 |530 | | | |

| |Mean = |Mean = | | | |

regression line – is a straight line that describes how a response variable y changes as an explanatory variable x changes. We often use a regression line to predict the value of y for a given value of x. Regression, unlike correlation, requires that we have an explanatory variable and a response variable.

Remember y = mx + b? Now we just call it something slightly different

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b is the slope, and a is the y-intercept (constant)

Regression Line for McDonald’s Data

If a new hamburger has 250 calories, it will have __________ grams of fat.

Correlation: [pic]

| |Father’s Education |Respondant’s | XY | X2 | Y2 |

|Respondant |(X) |Education (Y) | | | |

|1 |10 |10 | | | |

|2 |10 |11 | | | |

|3 |12 |12 | | | |

|4 |14 |13 | | | |

|5 |14 |14 | | | |

| |Mean = |Mean = | | | |

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