16. The correlation coefficient between per capita income in thousands of dollars and the

number of medical doctors per 10, 000 residents is r=0.934.

(a) Find the coefficient of determination.

(b) What does this tell you about the explained variation of the data about the re-

gression line?

17. Determine wether the points in a scatter plot for the two variables are likely to have

a positive slope, negative slope, or not follow a straight - line pattern.

(a) The number of hours you study for an exam and the score you make on that

exam.

(b) The price of a used car and the number of miles on the odometer.

(c) The pressure on a gas pedal and the speed of the car.

(d) Shoe size and IQ for adults.

18. A prediction should NOT be made with a regression model if . . .

(a) The data do not fall in a linear pattern when graphed on a scatter plot.

(b) The correlation coefficient is not statistically significant (|r|> critical value.

(c) You wish to make a prediction about a value outside the range of the sample data.

(d) The population is different than that from which the sample data were drawn.

(e) All of the above.

19. If the correlation coefficient for the relationship between the number of cups of hot

chocolate sold at an outdoor skating rink and the average temperature outside for that

evening is r= -0.65, how much of the variation in number of cups of hot chocolate sold can be associated with the variation in the temperature.

20. The following data depicts the amount forest burned in forest fires, measured in thousands of hectares, in the western U.S. and the number of days in which there was significant rainfall, called "wetting rain days," that year for the last 8 years.

Wetting Rain Days x 31 30 18 20 22 24 26 27

Hectares Burned y 85 40 475 325 450 180 95 98

(a) Find a linear regression model for predicting the amount of Forrest burned based on the number of wetting rain days.

(b) Using the model, what would be the result on number of hectares burned for each additional wetting rain day?

(c) What would be the number of hectares burned if there were no wetting rain days for that year?

(d) What would be the number of hectares burned if there were 35 wetting rain days for that year?

21. The number of hours 9 students spent studying for a test and their scores on that test is given below.

Hours spent x 0 2 4 5 5 5 6 7 8

Test scores y 40 51 64 69 73 75 93 90 95

(a) Find the equation of the least squared regression line for the data.

(b) What does x=0 represent in the model?

(c) What average grade does the model predict for students who have spent 6 hours studying for the test?

(d) What average grade does the model predict for students who have spent 10 hours studying for the test?

(e) Use the model to determine the average grade for students who never studied for the test.

(f) What is the slope of the regression line? Interpret the slope.

22. The data below are the final exam scores of 10 randomly selected history students and the number of hours they slept the night before the exam. Find the equation of the regression line for the given data. What would be the predicted score for a history student who slept 7 hours the previous night? Is this a reasonable question? Round the regression line values to the nearest hundredth, and round the predicted score to the nearest whole number.

Hours x 3 5 2 8 2 4 4 5 6 3

Scores y 65 80 60 88 66 78 85 90 90 71

(a)y= -5.04x + 56.11; 21; No, it is not reasonable. 7 hours is well outside the scope of the model.

(b)y= -5.04x + 56.11; 21; Yes, it is reasonable.

(c)y=5.04x + 56.11; 91; Yes, it is reasonable.

(d)y=5.04x + 56.11; 91; No, it is not reasonable. 7 hours is well outside the scope of the model.

23. The local school board wants to evaluate the relationship between class size and performance on the state achievement test. It decides to collect data from various schools in the district, and the data from a sample of eight classes are shown in the following table. Each pair of data represents the class size and corresponding average score on the achievement test for 1 class.

Class Size x 15 17 18 20 21 24 26 29 30 31

Average Test Score y 85.5 86.2 85 82.7 81.9 78.8 75.3 71.1 69 66.4

(a) Determine if there is a sufficient linear relationship between class size and average test score.

(b) If the relationship is significant, find the least-square regression line for these data.

(c) Predict the average achievement test score for class size of 19 at a school in the district.

(d) Predict the average achievement test score for class size of 16 at a school in the district.

(e) Predict the average achievement test score for class size of 25 at a school in the neighboring district.

(f) Predict the average achievement test score for class size of 50 at a school in the district.