The initial visual impact of a scatter diagram depends on the scales used on the x and y axes. Consider the following data. x 1 2 3 4 5 6 y 1 4 6 3 6 7 (a) Make a scatter diagram using the same scale on both the x and y axes (i.e., make sure the unit lengths on the two axes are equal). Draw the straight line that best fits the data points. Choose one (b) Make a scatter diagram using a scale on the y axis that is twice as long as that on the x axis. Draw the straight line that best fits the data points. Choose one (c) Make a scatter diagram using a scale on the y axis that is half as long as that on the x axis. Draw the straight line that best fits the data points. Choose one (d) How do the slopes (or directions) of the three lines appear to change? Choose one Stretching the scale on the y-axis makes the line appear steeper. Shrinking the scale on the y-axis makes the line appear flatter. The slopes change in actual value. Stretching the scale on the y-axis makes the line appear flatter. Shrinking the scale on the y-axis makes the line appear steeper. The slopes change in actual value. Stretching the scale on the y-axis makes the line appear steeper. Shrinking the scale on the y-axis makes the line appear flatter. The slopes do not change in actual value . Stretching the scale on the y-axis makes the line appear flatter. Shrinking the scale on the y-axis makes the line appear steeper. The slopes do not change in actual value. The correlation coefficient r is a sample statistic. What does it tell us about the value of the population correlation coefficient (Greek letter rho)? You do not know how to build the formal structure of hypothesis tests of yet. However, there is a quick way to determine if the sample evidence based on is strong enough to conclude that there is some population correlation between the variables. In other words, we can use the value of r to determine if 0. We do this by comparing the value |r| to an entry in the correlation table. The value of in the table gives us the probability of concluding that 0 when, in fact, = 0 and there is no population correlation. We have two choices for : = 0.05 or = 0.01. (a) Look at the data below regarding the variables x = age of a Shetland pony and y = weight of that pony. Is the value of |r| large enough to conclude that weight and age of Shetland ponies are correlated? Use = 0.05. (Use 3 decimal places.) x 3 6 12 26 16 y 60 95 140 178 172 r critical r Conclusion choose one Reject the null hypothesis, there is sufficient evidence to show that age and weight of Shetland ponies are correlated. Reject the null hypothesis, there is insufficient evidence to show that age and weight of Shetland ponies are correlated. Fail to reject the null hypothesis, there is insufficient evidence to show that age and weight of Shetland ponies are correlated . Fail to reject the null hypothesis, there is sufficient evidence to show that age and weight of Shetland ponies are correlated. (b) Look at the data below regarding the variables x = lowest barometric pressure as a cyclone approaches and y = maximum wind speed of the cyclone. Is the value of |r| large enough to conclude that lowest barometric pressure and wind speed of a cyclone are correlated? Use = 0.01. (Use 3 decimal places.) x 1004 975 992 935 970 938 y 40 100 65 145 70 148 r critical r Conclusion choose one Reject the null hypothesis, there is sufficient evidence to show that lowest barometric pressure and maximum wind speed for cyclones are correlated. Reject the null hypothesis, there is insufficient evidence to show that lowest barometric pressure and maximum wind speed for cyclones are correlated. Fail to reject the null hypothesis, there is insufficient evidence to show that lowest barometric pressure and maximum wind speed for cyclones are correlated. Fail to reject the null hypothesis, there is sufficient evidence to show that lowest barometric pressure and maximum wind speed for cyclones are correlated. We use the form = a + bx for the least-squares line. In some computer printouts, the least-squares equation is not given directly. Instead, the value of the constant a is given, and the coefficient b of the explanatory or predictor variable is displayed. Sometimes a is referred to as the constant, and sometimes as the intercept. Data from Climatology Report No. 77-3 of the Department of Atmospheric Science, Colorado State University, showed the following relationship between elevation (in thousands of feet) and average number of frost-free days per year in Colorado locations. A Minitab printout provides the following information. Predictor Coef SE Coef T P Constant 317.43 28.31 11.24 0.002 Elevation -32.190 3.511 -8.79 0.003 S = 11.8603 R-Sq = 97.2% Notice that "Elevation" is listed under "Predictor." This means that elevation is the explanatory variable x. Its coefficient is the slope b. "Constant" refers to a in the equation (a) Use the printout to write the least-squares equation. = + = a + bx. x (b) For each 1000-foot increase in elevation, how many fewer frost-free days are predicted? (Use 3 decimal places.) (c) The printout gives the value of the coefficient of determination r2. What is the value of r? Be sure to give the correct sign for r based on the sign of b. (Use 3 decimal places.) x 1 2 3 4 5 Sum y 3 6 12 26 16 63 Correlation Correlation x^2 60 95 140 178 172 645 y^2 9 36 144 676 256 1121 xy 3600 9025 19600 31684 29584 93493 180 570 1680 4628 2752 9810 0.917 (Using Excel formula) 0.917 (Using manual computation formula) x 1 2 3 4 5 Sum y 3 6 12 26 16 63 Correlation Correlation x^2 60 95 140 178 172 645 y^2 9 36 144 676 256 1121 xy 3600 9025 19600 31684 29584 93493 180 570 1680 4628 2752 9810 0.917 (Using Excel formula) 0.917 (Using manual computation formula)