Section 2.7 Station Review DO NOT WRITE ON THIS!

1) Find the following for this data on average temperature and rainfall for eight months in Boston, MA. Average Temperature and Rainfall in Boston

Temp (℉) 29 30 39 48 58 68 73 72 Rainfall (mm) 95 91 100 93 84 79 73 92

A. What is the correlation coefficient, r? Is it a strong or weak correlation? Explain. B. What is the equation of the line of best fit? Let Temperature be the independent variable. C. Describe the relationship between temperature and rainfall in words. D. Predict the temperature when the rainfall is 86 mm. How accurate do you think your prediction is?

2) Here are the number of teachers and the number of students at a randomly selected sample of high schools in a city. Teachers and Students at Selected Schools

Teachers 92 52 114 49 110 62 76 84 Students 1050 653 753 381 1312 813 496 910

A. Find the correlation coefficient. Is it a strong or a weak correlation? B. What is the equation of the line of best fit? Let independent variable be teachers. C. Predict the number of teachers in a high school that has 600 students. How accurate do you think your prediction is?

3) Hummingbird wing beat rates are much higher than those in other birds. Estimates for various species are given in the table.

Hummingbird Wing Beats Mass (g) 3.1 2.0 3.2 4.0 3.7 1.9 4.5

Wing Beats (per sec) 60 85 50 45 55 90 40 A. What is the correlation coefficient? Is it a strong or a weak one? Explain B. What is the equation of the line of best fit? C. Using your equation, predict the wing beats rate for a Giant Hummingbird with a mass of 19g. How accurate do you think your prediction is? Section 2.7 Station Review DO NOT WRITE ON THIS! 1) Find the following for this data on average temperature and rainfall for eight months in Boston, MA.

Average Temperature and Rainfall in Boston Temp (℉) 29 30 39 48 58 68 73 72

Rainfall (mm) 95 91 100 93 84 79 73 92 A. What is the correlation coefficient, r? Is it a strong or weak correlation? Explain. B. What is the equation of the line of best fit? Let Temperature be the independent variable. C. Describe the relationship between temperature and rainfall in words. D. Predict the temperature when the rainfall is 86 mm. How accurate do you think your prediction is?

2) Here are the number of teachers and the number of students at a randomly selected sample of high schools in a city. Teachers and Students at Selected Schools

Teachers 92 52 114 49 110 62 76 84 Students 1050 653 753 381 1312 813 496 910

A. Find the correlation coefficient. Is it a strong or a weak correlation? B. What is the equation of the line of best fit? Let independent variable be teachers. C. Predict the number of teachers in a high school that has 600 students. How accurate do you think your prediction is?

3) Hummingbird wing beat rates are much higher than those in other birds. Estimates for various species are given in the table.

Hummingbird Wing Beats Mass (g) 3.1 2.0 3.2 4.0 3.7 1.9 4.5

Wing Beats (per sec) 60 85 50 45 55 90 40 A. What is the correlation coefficient? Is it a strong or a weak one? Explain B. What is the equation of the line of best fit? C. Using your equation, predict the wing beats rate for a Giant Hummingbird with a mass of 19g. How accurate do you think your prediction is?

Section 2.7 Station Review DO NOT WRITE ON THIS! 1) Find the following for this data on average temperature and rainfall for eight months in Boston, MA.

Average Temperature and Rainfall in Boston Temp (℉) 29 30 39 48 58 68 73 72

Rainfall (mm) 95 91 100 93 84 79 73 92 A. What is the correlation coefficient, r? Is it a strong or weak correlation? Explain. The correlation coefficient is ! ≈ −!.!" and it is not very strong but rather an okay correlation. The closer it is to 1 or -1, the stronger the correlation is and -0.70 shows that the line doesn’t represent strongly. B. What is the equation of the line of best fit? Let temperature be the independent variable. x = temperature and y = rainfall (mm) ! = −!.!"# + !"#.! C. Describe the relationship between temperature and rainfall in words. As the temperature increases, the rainfall decreases. D. Predict the temperature when the rainfall is 86 mm. How accurate do you think your prediction is? y = 86 ! = −!.!"# + !"#.! ! !" = −!.!"# + !"#.! ! −!".! = −!.!"# ! ! = !".!°! The temperature when the rainfall is 86mm is !".!°!. This prediction is not very accurate because the scatter plot and value of r (correlation coefficient) show that temperature is not necessarily an accurate predictor of rainfall.

2) Here are the number of teachers and the number of students at a randomly selected sample of high schools in a city.

Teachers and Students at Selected Schools Teachers 92 52 114 49 110 62 76 84 Students 1050 653 753 381 1312 813 496 910

A. Find the correlation coefficient. Is it a strong or a weak correlation? The correlation coefficient is ! ≈ !.!"#. This is a weaker correlation (not very strong). B. What is the equation of the line of best fit? Let independent variable be teachers. x = the number of teachers and y = the number of students ! = !.!! + !!".! C. Predict the number of teachers in a high school that has 600 students. How accurate do you think your prediction is? y = 600; find x ! = !.!! + !!!.! ! !"" = !.!! + !!".! ! !"#.! = !.!! ! ! = !".!" The number of teachers in a high school that has 600 students is approximately 56. This prediction is not very accurate because our correlation coefficient is not very close to 1 and our data is more scattered.

3) Hummingbird wing beat rates are much higher than those in other birds. Estimates for various species are given in the table.

A. What is the correlation coefficient? Is it a strong or a weak one? Explain. ! ≈ !.!"#. It is a strong correlation because it is close to 1. B. What is the equation of the line of best fit? x = mass (g) and y = wing beats per sec ! = −!".!"! + !"!.!" C. Using your equation, predict the wing beats rate for a Giant Hummingbird with a mass of 19g. How accurate do you think your prediction is? x = 19; solve for y. ! = −!".!"! + !"!.!" ! ! = −!".!" !" + !"!.!" ! !! = −!"#.!" The wing beats rate for a giant humming bird should be -241.69 beats/sec. This would be impossible despite our strong correlation coefficient. Therefore, our prediction is not accurate.

Hummingbird Wing Beats Mass (g) 3.1 2.0 3.2 4.0 3.7 1.9 4.5

Wing Beats (per sec) 60 85 50 45 55 90 40