Scatterplots, Association and Correlation Chapter 7 Scatterplots, Association and Correlation

Examining Relationships Relationship between 2 quantitative variables. Ex. ___________________________________

Two Types of Variables ________________________ Example Measures an outcome of a study Used to explain the response variable. Example _____________________= Response variable. _____________________= Explanatory variable.

Two Types of Variables If there is a time factor, explanatory variable usually comes first. Example __________________________________________ Sometimes, no true response or explanatory variables. Ex. _______________________________

NOT Looking at Causation. Does not mean that changes in _______________ variable _____________ changes in _______________ variable.

Graphing Two Quant. Variables - Scatterplot Explanatory variable: __________________ Response variable: ___________________

Ex. Degree Days vs. Gas Usage Response = Amount of gas usage in a home Explanatory = Degree Days Measure of temperature for month High Temperature means low Degree Days.

Ex. – Degree Days vs. Gas Usage Month Degree Gas Month Degree Gas Nov. 24 6.3 July 0 1.2 Dec. 51 10.9 Aug. 1 1.2 Jan. 43 8.9 Sept. 6 2.1 Feb. 33 7.5 Oct. 12 3.1 March 26 5.3 Nov. 30 6.4 April 13 4.0 Dec. 32 7.2 May 4 1.7 Jan. 52 11.0 June 0 1.2 Feb. 30 6.9 Plot this by hand first, then show them splus graph.

Interpreting Scatterplots. Overall Pattern Form Direction Strength Deviations from the Pattern Outliers.

Interpreting Scatterplots Form Is the plot linear? Is the plot curved? Is there a distinct pattern in the plot? Strength Does the plot follow the form very closely? Or is there a lot of variation?

Interpreting Scatterplots Direction Is the plot increasing? Is the plot decreasing? Positively Associated Above (below) average in one variable tends to be associated with above (below) average in another variable. Negatively Associated Above (below) average in one variable tends to be associated with below (above) average in another variable.

Ex. – Degree Days vs. Gas Usage Form – ___________________ Strength – ____________________ Direction –__________________________ Outliers? – _____________

% Taking SAT vs. Average Score Form – _____________________________ ___________________________________ Strength – __________________________ Direction – __________________________ Outliers – ______________

Correlation Measures strength of ________________ relationship between two quantitative variables.

What is r? Change axes of plot to

Example Degree Days vs. Gas Usage Percent taking SAT vs. Average Verbal Score.

Properties of r r has no units, just a number. For ____________ association between two ____________________ variables ONLY. Affected by _____________.

Properties of r r ranges in value from –1 to 1. ________ indicates a straight increasing line. ________ indicates a straight decreasing line. ________ indicates no _________ relationship. As r moves away from 0, the linear relationship between variables gets ___________. Changing the scale of x or y will not change the value of r. Do graphs on board. (r = -1, r = -0.5, r = 0, r = 0.5, r = 1)

Calculating r. Femur (x) 38 56 59 63 74 Humerus (y) 41 63 70 72 84

Calculating r.

Calculating r.

Examples Degree Days vs. Gas Usage % Taking SAT vs. Average Verbal Score