Exam 4: Describing the Relation Between Two Variables

Choose the one alternative that best completes the statement or answers the question. -The following data represent the infection rate for a particular disease in a third world country x years after a vaccine became widely available. Determine the "best" model to describe the relationship between years past and infection rate. Years After Vaccine, x Infection Rate (\%), y 1 32 2 11 3 5 4 2 5 0.5

Provide an appropriate response. -The following data represent the living situation of newlyweds in a large metropolitan area and their annual household income. Find the marginal frequency for newlyweds who make between $\$ 35,000$ and $\$ 50,000$ per year. <\ 20,000 \ 20-35,000 \ 35-50,000 \ 50-75,000 >\ 75,000 Own home 31 52 202 355 524 Rent home 67 66 52 23 11 Live w/family 89 69 30 4 2

Write the word or phrase that best completes each statement or answers the question. Provide an appropriate response. -An agricultural business wants to determine if the rainfall in inches can be used to predict the yield per acre on a wheat farm. Identify the predictor variable and the response variable.

Choose the one alternative that best completes the statement or answers the question. -For a given data set, the equation of the least squares regression line will always pass through

Write the word or phrase that best completes each statement or answers the question. Construct a scatter diagram for the data. -Five brands of cigarettes were tested for the amounts of tar and nicotine they contained. All measurements are in milligrams per cigarette. Cigarette Tar Nicotine Brand A 16 1.2 Brand B 13 1.1 Brand C 16 1.3 Brand D 18 1.4 Brand E 6 0.6

Write the expression as a sum of logs. Express powers as factors. - $10^{0.7743}$

Choose the one alternative that best completes the statement or answers the question. -The coefficient of correlation between $\mathrm { x }$ and $\mathrm { y }$ is $\mathrm { r } = 0.59$ . Calculate the coefficient of determination $\mathrm { R } ^ { 2 }$ .

Write the word or phrase that best completes each statement or answers the question. Provide an appropriate response. -Construct a scatter diagram for the given data. Determine whether there is a positive linear correlation, negative linear correlation, or no linear correlation. -5 -3 4 1 -1 -2 0 2 3 -4 11 6 -6 -1 3 4 1 -4 -5 8

Change the exponential expression to an equivalent expression involving a logarithm. - $9 ^ { 2 } = y$

Choose the one alternative that best completes the statement or answers the question. Use the scatter diagrams shown, labeled a through f to solve the problem. -An instructor wishes to determine if there is a relationship between the number of absences from his class and a studentʹs final grade in the course. What is the predictor variable

Provide an appropriate response. -The following data represent the bacteria population in a laboratory experiment. The researchers suspect that the population is growing exponentially. Determine the logarithm of the $\mathrm { y }$ -values so that $\mathrm { Y } = \log \mathrm { y }$ . Day, x Population, y 0 1787 1 4871 2 13,191 3 35,959 4 97,813 5 266,048

Compute the Sum of Squared Residuals -The regression line for the given data is $\hat { y } = 6.91 x + 46.26$ . Determine the residual of a data point for which $x = 3$ and $\mathrm { y } = 61$ . Number of years, 3 4 4 5 3 6 2 7 3 Grades on test, 61 68 75 82 73 90 58 93 72

Change the exponential expression to an equivalent expression involving a logarithm. - $\log _ { 5 } x = 3$

Compute the linear correlation coefficient between the two variables and determine whether a linear relation exists. -The table below shows the ages and weights (in pounds) of 9 randomly selected tennis coaches. Age, 33 36 40 43 46 48 52 56 60 Weight (pounds), 117 121 124 132 143 146 149 151 153

Choose the one alternative that best completes the statement or answers the question. -In order for a company's employees to work for the foreign office, they must take a test in the language of the country where they plan to work. The data below show the relationship between the number of years that employees have studied a particular language and the grades they received on the proficiency exam. What is the best predicted value for $y$ given $x = 5.5$ ? Number of years, 3 4 4 5 3 6 2 7 3 Grades on test, 61 68 75 82 73 90 58 93 72

Write the word or phrase that best completes each statement or answers the question. -A calculus instructor is interested in finding the strength of a relationship between the final exam grades of students enrolled in Calculus I and Calculus II at his college. The data (in percentages) are listed below. Calculus I 88 78 62 75 95 91 83 86 98 Calculus II 81 80 55 78 90 90 81 80 100 a) Graph a scatter diagram of the data. b) Find an equation of the regression line. c) Predict a Calculus II exam score for a student who receives an 80 in Calculus I.

Change the exponential expression to an equivalent expression involving a logarithm. - $6 ^ { 2 } = 36$

Provide an appropriate response. -Calculate the linear correlation coefficient for the data below.

Compute the Sum of Squared Residuals -Compute the sum of the squared residuals of the least-squares line for the given data. -5 -3 4 1 -1 -2 0 2 3 -4 -10 -8 9 1 -2 -6 -1 3 6 -8

Write the word or phrase that best completes each statement or answers the question. Construct a scatter diagram for the data. -In an area of the Great Plains, records were kept on the relationship between the rainfall (in inches) and the yield of wheat (bushels per acre). Rainfall (in inches), 10.5 8.8 13.4 12.5 18.8 10.3 7.0 15.6 16.0 Yield (bushels per acre), 50.5 46.2 58.8 59.0 82.4 49.2 31.9 76.0 78.8