Registered Nurse Salaries In Exercises 2730, use the table, which shows the years of

What is a residual? Explain when a residual is positive, negative, and zero.

Two variables have a positive linear correlation. Is the slope of the regression line for the variables positive or negative?

Explain how to predict y@values using the equation of a regression line.

For a set of data and a corresponding regression line, describe all values of x that provide meaningful predictions for y.

In order to predict y@values using the equation of a regression line, what must be true about the correlation coefficient of the variables?

. Why is it not appropriate to use a regression line to predict y@values for x@values that are not in (or close to) the range of x@values found in the data?

In Exercises 712, match the description in the left column with its symbol(s) in the right column.The y@value of a data point corresponding to xi a. yni

In Exercises 712, match the description in the left column with its symbol(s) in the right column.The y@value for a point on the regression line corresponding to xi

In Exercises 712, match the description in the left column with its symbol(s) in the right column.. Slope

In Exercises 712, match the description in the left column with its symbol(s) in the right column.y@intercept

In Exercises 712, match the description in the left column with its symbol(s) in the right column.The mean of the y@values

In Exercises 712, match the description in the left column with its symbol(s) in the right column.The point a regression line always passes through

Graphical Analysis In Exercises 1316, match the regression equation with the appropriate graph. (Note that the x- and y-axes are broken.)yn = -1.04x + 50.3

Graphical Analysis In Exercises 1316, match the regression equation with the appropriate graph. (Note that the x- and y-axes are broken.)yn = 1.662x + 83.34

Graphical Analysis In Exercises 1316, match the regression equation with the appropriate graph. (Note that the x- and y-axes are broken.)yn = 0.00114x + 2.53

Graphical Analysis In Exercises 1316, match the regression equation with the appropriate graph. (Note that the x- and y-axes are broken.)yn = -0.667x + 52.6

Finding the Equation of a Regression Line In Exercises 1726, find the equation of the regression line for the data. Then construct a scatter plot of the data and draw the regression line. (Each pair of variables has a significant correlation.) Then use the regression equation to predict the value of y for each of the x-values, if meaningful. If the x-value is not meaningful to predict the value of y, explain why not. If convenient, use technology.Height and Number of Stories The heights (in feet) and the numbers of stories of nine notable buildings in Atlanta (Source: Emporis Corporation) Height, x 869 820 771 696 692 676 656 492 486 Stories, y 60 50 50 52 40 47 41 39 26 (a) x = 800 feet (b) x = 750 feet (c) x = 400 feet (d) x = 625 feet

Finding the Equation of a Regression Line In Exercises 1726, find the equation of the regression line for the data. Then construct a scatter plot of the data and draw the regression line. (Each pair of variables has a significant correlation.) Then use the regression equation to predict the value of y for each of the x-values, if meaningful. If the x-value is not meaningful to predict the value of y, explain why not. If convenient, use technology.Square Footage and Home Sale Price The square footages and sale prices (in thousands of dollars) of seven homes are shown in the table at the left. (Source: Howard Hanna) (a) x = 1450 square feet (b) x = 2720 square feet (c) x = 2175 square feet (d) x = 1890 square feet

Finding the Equation of a Regression Line In Exercises 1726, find the equation of the regression line for the data. Then construct a scatter plot of the data and draw the regression line. (Each pair of variables has a significant correlation.) Then use the regression equation to predict the value of y for each of the x-values, if meaningful. If the x-value is not meaningful to predict the value of y, explain why not. If convenient, use technology.Hours Studying and Test Scores The number of hours 9 students spent studying for a test and their scores on that test Hours spent studying, x 0 2 4 5 5 5 6 7 8 Test scores, y 40 51 64 69 73 75 93 90 95 (a) x = 3 hours (b) x = 6.5 hours (c) x = 13 hours (d) x = 4.5 hours

Finding the Equation of a Regression Line In Exercises 1726, find the equation of the regression line for the data. Then construct a scatter plot of the data and draw the regression line. (Each pair of variables has a significant correlation.) Then use the regression equation to predict the value of y for each of the x-values, if meaningful. If the x-value is not meaningful to predict the value of y, explain why not. If convenient, use technology.Wins and Earned Run Averages The numbers of wins and the earned run averages (mean number of earned runs allowed per nine innings pitched) for eight professional baseball pitchers in the 2012 regular season (Source: Major League Baseball) Wins, x 20 18 17 16 14 12 11 9 Earned run average, y 2.73 3.29 2.64 3.74 3.85 4.33 3.81 5.11 (a) x = 5 wins (b) x = 10 wins (c) x = 21 wins (d) x = 15 wins

Finding the Equation of a Regression Line In Exercises 1726, find the equation of the regression line for the data. Then construct a scatter plot of the data and draw the regression line. (Each pair of variables has a significant correlation.) Then use the regression equation to predict the value of y for each of the x-values, if meaningful. If the x-value is not meaningful to predict the value of y, explain why not. If convenient, use technology.21. Heart Rate and QT Interval The heart rates (in beats per minute) and QT intervals (in milliseconds) for 13 males (the figure at the left shows the QT interval of a heartbeat in an electrocardiogram) (Adapted from Chest) Heart rate, x 60 75 62 68 84 97 66 QT interval, y 403 363 381 367 341 317 401 Heart rate, x 65 86 78 93 75 88 QT interval, y 384 342 377 329 377 349 (a) x = 120 beats per minute (b) x = 67 beats per minute (c) x = 90 beats per minute (d) x = 83 beats per minute

Finding the Equation of a Regression Line In Exercises 1726, find the equation of the regression line for the data. Then construct a scatter plot of the data and draw the regression line. (Each pair of variables has a significant correlation.) Then use the regression equation to predict the value of y for each of the x-values, if meaningful. If the x-value is not meaningful to predict the value of y, explain why not. If convenient, use technology.Length and Girth of Harbor Seals The lengths (in centimeters) and girths (in centimeters) of 12 harbor seals (Adapted from Moss Landing Marine Laboratories) Length, x 137 168 152 145 159 159 Girth, y 106 130 116 106 125 119 Length, x 124 137 155 148 147 146 Girth, y 103 104 120 110 107 109 (a) x = 140 centimeters (b) x = 172 centimeters (c) x = 164 centimeters (d) x = 158 centimeters

Finding the Equation of a Regression Line In Exercises 1726, find the equation of the regression line for the data. Then construct a scatter plot of the data and draw the regression line. (Each pair of variables has a significant correlation.) Then use the regression equation to predict the value of y for each of the x-values, if meaningful. If the x-value is not meaningful to predict the value of y, explain why not. If convenient, use technology. Hot Dogs: Caloric and Sodium Content The caloric contents and the sodium contents (in milligrams) of 10 beef hot dogs (Source: Consumer Reports) Calories, x 150 170 120 120 90 Sodium, y 420 470 350 360 270 Calories, x 180 170 140 90 110 Sodium, y 550 530 460 380 330 (a) x = 170 calories (b) x = 100 calories (c) x = 140 calories (d) x = 210 calories

Finding the Equation of a Regression Line In Exercises 1726, find the equation of the regression line for the data. Then construct a scatter plot of the data and draw the regression line. (Each pair of variables has a significant correlation.) Then use the regression equation to predict the value of y for each of the x-values, if meaningful. If the x-value is not meaningful to predict the value of y, explain why not. If convenient, use technology.High-Fiber Cereals: Caloric and Sugar Content The caloric contents and the sugar contents (in grams) of 11 high-fiber breakfast cereals (Source: Consumer Reports) Calories, x 140 200 160 170 170 190 Sugar, y 6 9 6 9 10 17 Calories, x 190 210 190 170 160 Sugar, y 13 18 19 10 10 (a) x = 150 calories (b) x = 90 calories (c) x = 175 calories (d) x = 208 calories

Finding the Equation of a Regression Line In Exercises 1726, find the equation of the regression line for the data. Then construct a scatter plot of the data and draw the regression line. (Each pair of variables has a significant correlation.) Then use the regression equation to predict the value of y for each of the x-values, if meaningful. If the x-value is not meaningful to predict the value of y, explain why not. If convenient, use technology.Shoe Size and Height The shoe sizes and heights (in inches) of 14 men Shoe size, x 8.5 9.0 9.0 9.5 10.0 10.0 10.5 Height, y 66.0 68.5 67.5 70.0 70.0 72.0 71.5 Shoe size, x 10.5 11.0 11.0 11.0 12.0 12.0 12.5 Height, y 69.5 71.5 72.0 73.0 73.5 74.0 74.0 (a) x = size 11.5 (b) x = size 8.0 (c) x = size 15.5 (d) x = size 10.0

Finding the Equation of a Regression Line In Exercises 1726, find the equation of the regression line for the data. Then construct a scatter plot of the data and draw the regression line. (Each pair of variables has a significant correlation.) Then use the regression equation to predict the value of y for each of the x-values, if meaningful. If the x-value is not meaningful to predict the value of y, explain why not. If convenient, use technology.Age and Hours Slept The ages (in years) of 10 infants and the numbers of hours each slept in a day Age, x 0.1 0.2 0.4 0.7 0.6 0.9 Hours slept, y 14.9 14.5 13.9 14.1 13.9 13.7 Age, x 0.1 0.2 0.4 0.9 Hours slept, y 14.3 13.9 14.0 14.1 (a) x = 0.3 year (b) x = 3.9 years (c) x = 0.6 year (d) x = 0.8 year

Registered Nurse Salaries In Exercises 2730, use the table, which shows the years of experience of 14 registered nurses and their annual salaries (in thousands of dollars). (Source: Payscale, Inc.)Correlation Using the scatter plot of the registered nurse salary data shown below, what type of correlation, if any, do you think the data have? Explain. Years of experience Annual salary (in thousands of dollars) y Registered Nurses 2 4 6 8 10 12 14 16

Registered Nurse Salaries In Exercises 2730, use the table, which shows the years of experience of 14 registered nurses and their annual salaries (in thousands of dollars). (Source: Payscale, Inc.)Regression Line Find an equation of the regression line for the data. Sketch a scatter plot of the data and draw the regression line.

Registered Nurse Salaries In Exercises 2730, use the table, which shows the years of experience of 14 registered nurses and their annual salaries (in thousands of dollars). (Source: Payscale, Inc.)Using the Regression Line The analyst used the regression line you found in Exercise 28 to predict the annual salary for a registered nurse with 28 years of experience. Is this a valid prediction? Explain your reasoning.

Registered Nurse Salaries In Exercises 2730, use the table, which shows the years of experience of 14 registered nurses and their annual salaries (in thousands of dollars). (Source: Payscale, Inc.)Significant Correlation? A salary analyst claims that the population has a significant correlation for a = 0.01. Test this claim.

Interchanging x and y In Exercises 31 and 32, do the following. (a) Find the equation of the regression line for the data, letting Row 1 represent the x-values and Row 2 the y-values. Sketch a scatter plot of the data and draw the regression line. (b) Find the equation of the regression line for the data, letting Row 2 represent the x-values and Row 1 the y-values. Sketch a scatter plot of the data and draw the regression line. (c) What effect does switching the explanatory and response variables have on the regression line?. Row 1 0 1 2 3 3 5 5 5 6 7 Row 2 96 85 82 74 95 68 76 84 58 65

Interchanging x and y In Exercises 31 and 32, do the following. (a) Find the equation of the regression line for the data, letting Row 1 represent the x-values and Row 2 the y-values. Sketch a scatter plot of the data and draw the regression line. (b) Find the equation of the regression line for the data, letting Row 2 represent the x-values and Row 1 the y-values. Sketch a scatter plot of the data and draw the regression line. (c) What effect does switching the explanatory and response variables have on the regression line?Row 1 16 25 39 45 49 64 70 Row 2 109 122 143 132 199 185 199

In Exercises 33 and 34, (a) find the equation of the regression line, (b) construct a scatter plot of the data and draw the regression line, (c) construct a residual plot, and (d) determine whether there are any patterns in the residual plot and explain what they suggest about the relationship between the variables.x 38 34 40 46 43 48 60 55 52 y 24 22 27 32 30 31 27 26 28

In Exercises 33 and 34, (a) find the equation of the regression line, (b) construct a scatter plot of the data and draw the regression line, (c) construct a residual plot, and (d) determine whether there are any patterns in the residual plot and explain what they suggest about the relationship between the variables.x 8 4 15 7 6 3 12 10 5 y 18 11 29 18 14 8 25 20 12

In Exercises 35 and 36, (a) construct a scatter plot of the data, (b) identify any possible outliers, and (c) determine whether the point is influential. Explain your reasoning.x 5 6 9 10 14 17 19 44 y 32 33 28 26 25 23 23 8

In Exercises 35 and 36, (a) construct a scatter plot of the data, (b) identify any possible outliers, and (c) determine whether the point is influential. Explain your reasoning.x 1 3 6 8 12 14 y 4 7 10 9 15 3

In Exercises 3740, use the data shown in the table at the left, which shows the number of bacteria present after a certain number of hoursFind the equation of the regression line for the data. Then construct a scatter plot of 1x, y2 and sketch the regression line with it.

In Exercises 3740, use the data shown in the table at the left, which shows the number of bacteria present after a certain number of hoursReplace each y@value in the table with its logarithm, log y. Find the equation of the regression line for the transformed data. Then construct a scatter plot of 1x, log y2 and sketch the regression line with it. What do you notice?

In Exercises 3740, use the data shown in the table at the left, which shows the number of bacteria present after a certain number of hoursAn exponential equation is a nonlinear regression equation of the form y = abx . Use technology to find and graph the exponential equation for the original data. Include the original data in your graph. Note that you can also find this model by solving the equation log y = mx + b from Exercise 38 for y.

In Exercises 3740, use the data shown in the table at the left, which shows the number of bacteria present after a certain number of hours Compare your results in Exercise 39 with the equation of the regression line and its graph in Exercise 37. Which equation is a better model for the data? Explain.

In Exercises 41 44, use the data shown in the table at the left.Find the equation of the regression line for the data. Then construct a scatter plot of 1x, y2 and sketch the regression line with it.

In Exercises 41 44, use the data shown in the table at the left.Replace each x@value and y@value in the table with its logarithm. Find the equation of the regression line for the transformed data. Then construct a scatter plot of 1log x, log y2 and sketch the regression line with it. What do you notice?

In Exercises 41 44, use the data shown in the table at the left.A power equation is a nonlinear regression equation of the form y = axb . Use a technology tool to find and graph the power equation for the original data. Include a scatter plot in your graph. Note that you can also find this model by solving the equation log y = m1log x2 + b from Exercise 42 for y

In Exercises 41 44, use the data shown in the table at the left.Compare your results in Exercise 43 with the equation of the regression line and its graph in Exercise 41. Which equation is a better model for the data? Explain.

Logarithmic Equation In Exercises 45 48, use the following information and technology. The logarithmic equation is a nonlinear regression equation of the form y = a + b ln x.Find and graph the logarithmic equation for the data in Exercise 25.

Logarithmic Equation In Exercises 45 48, use the following information and technology. The logarithmic equation is a nonlinear regression equation of the form y = a + b ln x.Find and graph the logarithmic equation for the data in Exercise 26.

Logarithmic Equation In Exercises 45 48, use the following information and technology. The logarithmic equation is a nonlinear regression equation of the form y = a + b ln x.Compare your results in Exercise 45 with the equation of the regression line and its graph. Which equation is a better model for the data? Explain.

Logarithmic Equation In Exercises 45 48, use the following information and technology. The logarithmic equation is a nonlinear regression equation of the form y = a + b ln x.Compare your results in Exercise 46 with the equation of the regression line and its graph. Which equation is a better model for the data? Explain