 # 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.

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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 2017 408 348 4010 587 507 2612 703

Age # Days 2017 408 348 4010 587 507 2612 703 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 = -5.09 p = 0.022 df = 6 a = 18.5286 b = -0.2255 s = 1.94 r 2 = 0.8112 (this is the coefficient of determination) r = -0.901

Line of Best Fit or Least Squares Line yhat = a + bx: yhat = 18.5286 – 0.2255x Correlation: r = - 0.9011

Is the correlation, r, significant? (this is Method 1) Because the pvalue = 0.0022 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 = - 0.901 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 -0.9011 < -0.707, 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 -) 10.997 20.950 30.878 40.811 50.754 60.707 70.666 80.632 90.602 100.576

If age of backpacker = 45 years, how many days, on average, would he or she backpack? yhat = 18.5286 – 0.2255(45) = 8.38 days If age of backpacker = 32 years, how many days, on average, would he or she backpack? yhat = 18.5286 – 0.2255(32) = 11.31 days If age of backpacker = 90 years, how many days, on average, would he or she backpack? yhat = 18.5286 – 0.2255(90) = -1.77 days This answer makes no sense since 90 is outside the domain of the equation. (Reminder: 20  x  70)

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