Linear Regression and Correlation

1. Linear Regression and Correlation Eight backpackers were asked their age (in years) and the number of days they backpacked on their last backpacking trip. Is there a linear relationship between the age of a backpacker and the number of days they backpack on one trip? Age # Days 20 17 40 8 34 8 40 10 58 7 50 7 26 12 70 3

2. Linear Regression and Correlation Age # Days 20 17 40 8 34 8 40 10 58 7 50 7 26 12 70 3 • First, do a scatterplot of the data. • Then do Linear Regression.

3. Linear Regression and Correlation • Line of Best Fit or Least Squares Line • yhat = a + bx: • yhat = 18.5286 – 0.2255x • Correlation: r = - 0.9011

4. Linear Regression and Correlation • Is the correlation, r, significant? • Compare r = - 0.9011 to the value in the 95% Critical Values of the Sample Correlation Coefficient Table at the end of chapter 12. • Since n – 2 = 8 – 2 = 6, the table critical value is – 0.707 • Because -0.9011 < -0.707, r is significant. • We will plot the line and use use the line for prediction.

5. Linear Regression and Correlation • If age of backpacker = 45 years, how many days, on average, would he or she backpack? • If age of backpacker = 32 years, how many days, on average, would he or she backpack? • If age of backpacker = 90 years, how many days, on average, would he or she backpack? • (Reminder: 20  x  70)