 Describe the association between two quantitative variables using a scatterplot’s direction, form, and strength  If the scatterplot’s form is linear, use correlation to describe its direction and strength AP Statistics Objectives Ch7

 Scatterplot  Association  Direction  Outlier  Explanatory/Predictor Variable  Response variable Vocabulary  Form  Strength

 Correlation  Quantitative Condition  Straight Enough Condition  Outlier Condition Vocabulary

Scatterplot Example Correlation Info Vocabulary Chp 7 Assignment Practice Direction, Form, Strength Quick Review of Association for Categorical Data Calculator Skills

Chapter 7 Assignment Pages: Problems: #6,12,24,29&30

Scatterplot Example

Chp 7 – Scatterplots, Association, and Correlation Correlation Facts 1)Quantitative Condition – Data must be quantitative. 2)Straight Enough Condition - Form of scatterplot needs to be fairly linear 3) Outlier condition - r-value is influenced by outliers -outliers should be investigated and regression should be done w/ and w/o outliers Must meet the following conditions in order to use correlation:

Chp 7 – Scatterplots, Association, and Correlation More Correlation Facts: 2) -1 ≤ r ≤ 1 3) Sign of the r-value indicates direction 4) r = -1 indicates a perfect negative linear association 5) r = 1 indicates a perfect positive linear association 6) r = 0 indicates no linear association 1)It is your responsibility to check the conditions first

Chp 7 – Scatterplots, Association, and Correlation More Correlation Facts: 2) -1 ≤ r ≤ 1 3) Sign of the r-value indicates direction 4) r = -1 indicates a perfect negative linear association 5) r = 1 indicates a perfect positive linear association 6) r = 0 indicates no linear association 1)It is your responsibility to check the conditions first 7) Correlation has no units, therefore it is not affected by rescaling or shifting the data. 8) Correlation treats x and y symmetrically. The correlation of x with y is the same as the correlation of y with x.

Chp 7 – Scatterplots, Association, and Correlation Correlation Non-facts: NOTE: These are NOT exact values. Only gauges to help you start. The following general categories indicate a quick way of interpreting a calculated r value: r-valueLinear Strength -0.2 to 00 OR 0.0 to 0.2 None to virtually none -0.5 to -0.2 OR 0.2 to 0.5 Weak -0.8 to -0.5 OR 0.5 to 0.8 Moderate -0.9 to -0.8 OR 0.8 to 0.9 Strong -1.0 to -0.9 OR 0.9 to 1.0 Very strong Exactly -1 OR Exactly +1 Perfect

Describe the association shown (1) FORM: CURVED DIRECTION: NOT APPARENT STRENGTH: STRONG (2) FORM: LINEAR DIRECTION: POSITIVE STRENGTH: MODERATE

Describe the association shown (3) FORM: LINEAR DIRECTION: NEGATIVE STRENGTH: VERY STRONG (4) FORM: LINEAR DIRECTION: NEGATIVE STRENGTH: WEAK

Describe the association shown (1) NO ASSOCIATION FORM: NONE DIRECTION: NONE STRENGTH: NONE (2) FORM: LINEAR DIRECTION: POSITIVE STRENGTH: STRONG

Describe the association shown (3) FORM: CURVED DIRECTION: POSITIVE STRENGTH: MODERATE (4) FORM: LINEAR DIRECTION: NEGATIVE STRENGTH: STRONG

Describe the association shown (3) FORM: CURVED DIRECTION: POSITIVE STRENGTH: MODERATE (4) FORM: LINEAR DIRECTION: NEGATIVE STRENGTH: STRONG

Chapter 7 Calculator Steps Naming a List in TI-84 1) STAT - Edit - Arrow up to Highlight L1 - Arrow just past L6 2) Type Name of Column - Name the column “YR”; ENTER 3) Type Name of Next Column - Arrow Right - Name the column “TUIT”; ENTER

ENTER DATA YR TUIT YR 2000? Use 10 TUIT 9800

Making a Scatterplot 1) 2 nd Y= 2) ENTER to choose ‘Plot1’ 3) Choose ‘On’ 4) Choose 1 st icon for scatterplot 5) 2 nd STAT to choose ‘YR’ for ‘Xlist’ 6) 2 nd STAT to choose ‘TUIT’ for ‘Ylist’ 7) Zoom 9

Find Correlation 1) 2 nd CATALOG 2) ENTER ‘D’ 3) Arrow down and Choose ‘DiagnosticOn’ 4) ENTER twice 5) STAT ‘CALC’ Choose ‘8: LinReg(a+bx)’ 6) ‘YR’, ‘TUIT’, 7) VARS Choose ‘Y-VARS’ ENTER x3

ENTER DATA YR TUIT YR 2000? Use 10 TUIT 9800 What is the resulting linear regression? Predicted Tuition = (Year) Would predict 2004 tuition to be $

ENTER DATA YR TUIT YR 2000? Use 10 TUIT 9800 What is the resulting linear regression? Predicted Tuition = (Year) Would predict 2004 tuition to be $

Quick Review Association of two Categorical Variables 28.6% 8.2% 16.6% 11.2% 25.0% 35.4% 29.8% 45.2% 1)Use pie chart or segmented bar chart to do visual comparison 2) Compare the proportions (%) If nearly the same - The variables are independent If not nearly the same – The variables are not independent Variables? Survival & Ticket Class Association? Do not appear independent, ticket class & survival may be associated.

Quick Review Association of two Categorical Variables 28.6% 8.2% 16.6% 11.2% 25.0% 35.4% 29.8% 45.2% 1)Use pie chart or segmented bar chart to do visual comparison 2) Compare the proportions (%) If nearly the same - The variables are independent If not nearly the same – The variables are not independent Variables? Survival & Ticket Class Association? Do not appear independent, ticket class & survival may be associated.

Chp 7 – Scatterplots, Association, and Correlation Vocabulary 1. Scatterplot – Graph which shows the relationship between two quantitative variables 2. Explanatory variable – the quantitative variable which is plotted on the horizontal axis (aka x-axis) of a scatterplot. It is used as the “predictor” of the other variable, but should not be interpreted as the cause of the other variable. 3. Response variable – the variable which is plotted on the vertical axis (aka y-axis) of a scatterplot. Be careful not to interpret the effect of the other.

Chp 7 – Scatterplots, Association, and Correlation Vocabulary 4.Form – what type of pattern is seen? Is it LINEAR? Is it CURVED? 6.Strength – How tight is the scatter around the underlying form? Is it VERY STRONG? STRONG? MODERATE? WEAK? Maybe even PERFECT or NONE. 5. Direction – If it is POSITIVE, as one variable increases so does the other. If it is NEGATIVE, as one variable increases the other decreases 7. Outliers – They need to be identified

Chp 7 – Scatterplots, Association, and Correlation Vocabulary 8. Correlation – a numerical measure of direction and strength of a linear association (also referred to as the r-value) -----BEFORE using you must meet the following CONDITIONS:

Chp 7 – Scatterplots, Association, and Correlation Vocabulary 8. Correlation – a numerical measure of direction and strength of a linear association (also referred to as the r-value) -----BEFORE using you must meet the following CONDITIONS: 1)Quanitative Variables Condition – both variables must be quantitative 2)Straight Enough Condition – the form of the scatterplot must be basically linear, not curved 3)Outlier Condition – no apparent outliers exist

Chp 7 – Scatterplots, Association, and Correlation 9. Lurking Variable – A variable other than the explanatory and response variables recorded that affects both variables, accounting for the correlation between the two variables recorded. Example– The r-value for “average number of televisions sets per home” for a country and “average life span” for the country is very high. Does this mean we should ship tv’s to third world countries? The lurking variable here is “average income per household”. It affects both the number of tv’s and ability to increase life span through medical care.

Chp 7 – Scatterplots, Association, and Correlation 9. Lurking Variable – A variable other than the explanatory and response variables recorded that affects both variables, accounting for the correlation between the two variables recorded. Example– The r-value for “average number of televisions sets per home” for a country and “average life span” for the country is very high. Does this mean we should ship tv’s to third world countries? The lurking variable here is “average income per household”. It affects both the number of tv’s and ability to increase life span through medical care.