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

Age # Days First, do a scatterplot of the data, where age is the independent variable and # Days is the dependent variable. Do the Linear Regression Hypothesis Test. H o : ρ = 0 H a : ρ ≠ 0

Calculator instructions: 1.Enter Age into L1 and # Days into L2. 2.Access LinRegTTest (STAT, TESTS, scroll to LinRegTTests) 3.Xlist is L1, Ylist is L2, Freq is 1, choose ≠, leave RegEQ blank, Calculate 4.The following will show on the calculator. y=a + bx t = p = df = 6 a = b = s = 1.94 r 2 = (this is the coefficient of determination) r =

Line of Best Fit or Least Squares Line yhat = a + bx: yhat = – x Correlation: r =

Is the correlation, r, significant? (this is Method 1) Because the pvalue = which is less than the assumed alpha of 0.05, we reject the Null Hypothesis. This means the correlation coefficient is significant and the line is a good fit. We can plot the line and can use the line for prediction.

Is the correlation, r, significant? (this is Method 2) Compare r = 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; negative r, use negative critical value. Because < , r is significant. We can plot the line and can use the line for prediction.

TABLE 95% CRITICAL VALUES OF THE SAMPLE CORRELATION COEFFICIENT Degrees of Freedom: n - 2Critical Values: (+ and -)

If age of backpacker = 45 years, how many days, on average, would he or she backpack? yhat = – (45) = 8.38 days If age of backpacker = 32 years, how many days, on average, would he or she backpack? yhat = – (32) = days If age of backpacker = 90 years, how many days, on average, would he or she backpack? yhat = – (90) = days This answer makes no sense since 90 is outside the domain of the equation. (Reminder: 20  x  70)