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.
[pic] [pic]
[pic] [pic]
[pic]
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.
[pic] or [pic]
[pic]
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
[pic] where [pic] and [pic]
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 = | | | |
[pic] where [pic] and [pic]
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