Describe the association’s Form, Direction, and Strength CORRELATION = r Is there a relationship between student quiz grades and their test grade? Quiz Avg. 75 86 92 95 80 Test Avg. 79 100 90 Describe the association’s Form, Direction, and Strength

Quiz Avg. 75 86 92 95 80 Test Avg. 79 100 90 r = ¼ [1.7449 + -0.0239 + 0.9577 + 0.7033 + 0] r = ¼ (3.382) = 0.8455

Just put these data points into List 1,2,3,& 4 WARM-UP Just put these data points into List 1,2,3,& 4 Describe the Form, Direction, and Strength of each. A. B. X Y 1 5 2 11 3 20 4 32 58 6 120 7 200 X Y 50 1 48 2 30 3 40 4 20 5 35 6 10 7 12 r = -0.87 r = 0.88

FACTS ABOUT CORRELATION Chapter 7 (continued) FACTS ABOUT CORRELATION Positive r refers to positively associated variables while negative r refers to negatively associated variables. (The Pos./Neg. sign of ‘r’ matches the slope’s sign.) 2. Correlation is ALWAYS between -1 ≤ r ≤ 1. The correlation is strong when r is close to 1 or -1 but weak when r is close to zero. 3. r has NO UNITS. 4. Correlation is only valuable for LINEAR relationships. Like the Mean and Std. Dev., Correlation is non-resistant and is very influenced by outliers.

CHAPTER 8 - Interpreting the Least Squares Regression Model is: The is called y-hat and represents the Predicted y values. The is the Slope of the linear equation: Interpreted as: For each unit increase in x the y-variable is predicted to change b amount on average. The is the y-intercept of the linear equation: Interpreted as: ”a” is the average amount of the y variable when x = 0.

R-Squared –Coefficient of Determination R-Squared –Coefficient of Determination. the percent or fraction of variation in the values of y that is explained by the least squares regression of y on x. R-Squared – Identifies what percent of the variation in the predicted values of y that are attributed by x. Thus (100% - R2) of the variation in y is attributed to by other factors. Does temperature outside affect the number of ice cream treats a store sells. R2 = 88.5% R2: 88.5% of the variation is the predicted amount of ice cream sales is attributed by the temperature outside.

Fat (g) 19 31 34 35 39 26 43 Calories 920 1300 1310 960 1180 1100 1260 Regression model: Calories = 785.94 + 11.14(Fat) Regression model: Slope: For every additional gram of fat the model predicts approximately an additional 11.14 Calories in the food. Slope: y-intercept: If the food product contained NO fat it would still predict 785.936 calories on average. y-intercept: Correlation: Correlation: r = 0.562 Moderate strong positive linear relationship. R2: 31.5% of the variation in the predicted amount of calories is attributed by the amount of fat. R2:

Homework: Page 189: 7, 8, 9, 10, [13, 14 omit c]

Fast food is often considered unhealthy because of the amount of fat and calories in it. Does the amount of Fat content contribute to the number of calories a food product contains? Fat (g) 19 31 34 35 39 26 43 Calories 920 1300 1310 960 1180 1100 1260 Construct and Describe the Scatterplot for this data. Find the Regression model and interpret the slope, y-intercept, correlation, residual plot, and R2.