TwoVariable Statistics CHAPTER 11 Correlation Direction Positive Negative

Two-Variable Statistics CHAPTER 11

Correlation

Direction Positive Negative None

Linearity

Strength

Outliers

*Correlation does not necessarily imply causation.

Measuring Correlation

Pearson’s Product-Moment Correlation Coefficient (r) https: //www. youtube. com/watch? v=HK-gy. Kw. NR 6 M • Gives us a more precise measure of the strength of a linear correlation • Values of r range from -1 to 1 • Sign indicates direction and size indicates strength of correlation

Line of Best Fit To draw the line of best fit…

Interpolation & Extrapolation • The lowest and highest data points are called poles. • Interpolation – predicting y for x between the poles • Extrapolation – predicting y for x outside the poles

Linear Regression

The Least Squares Regression Line • The sums of the squares of the distances from each point in a data set to that line is the smallest. • More reliable than drawing a line of best fit by eye • https: //www. youtube. com/watch? v=s. Ve. Nr. DLhgn. I

9/12/18 Bell-Ringer

9/13/18 Bell-Ringer: Starting Salaries for Engineers with BS vs. Ph. Ds (strict time: 7 min) 1. What is the value of the correlation coefficient for this data set? 2. Describe the correlation. 3. Write the linear regression equation. 4. If the starting salary for a mechanical engineer with a Ph. D is $83, 000, use the equation to predict the starting salary for a mechanical engineer with a BS. 5. Comment on the reliability of your prediction from #4.

USED TO DETERMINE WHETHER TWO VARIABLES FROM THE SAMPLE ARE INDEPENDENT BY EXAMINING THE DIFFERENCE BETWEEN OBSERVED AND EXPECTED VALUES

• Complete an expected frequency table. • Square the difference between observed & expected values, and divide it by the expected value. • Find the sum of these values. • Smaller than critical value = independent • Larger than critical value = not independent

P-value

9/14/18 Bell-Ringer: (strict time: 8 min)

https: //www. youtube. com/watch? v=MNkfv. YD 4 uk 0

(rows or columns)

Yates’ Continuity Correction

9/17/18 Bell-Ringer: Using your notes and textbook, work within your groups to complete the task below. Remember to state the null and alternative hypotheses and the rejection inequality.