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Review for the chapter 6 test 6. 1 Scatter plots & Correlation 6

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1 Review for the chapter 6 test 6. 1 Scatter plots & Correlation 6
Review for the chapter 6 test Scatter plots & Correlation 6.2 Regression, Prediction, and Causation

2 1. Which could be the least squares regression equation for the graph?
A) y= a B) y= a + bx C) y=a – bx D) not enough information to tell C

3 2. Which could be the least squares regression equation for the graph?
A) y= a B) y= a + bx C) y=a – bx D) not enough information to tell A

4 3. The correlation between the heights of fathers and the heights of their (grownup) sons is r=0.52. This tells us that, A) taller than average fathers tend to have taller then average sons B) taller than average fathers tend to have shorter then average sons C) sons are, on the average, taller then their fathers D) there is a moderate to weak correlation between heights of fathers and sons D

5 4. There is a positive correlation between the size of a hospital (measured by number of beds) and the median number of days that patients remain in the hospital. Does this mean that you can shorten a hospital stay by choosing to go to a small hospital? (a) No -- a negative correlation would allow that conclusion, but this correlation is positive. (b) Yes -- the data show that stays are shorter in smaller hospitals. (c) No -- the positive correlation is probably explained by the fact that seriously ill people go to large hospitals (d) Yes -- the correlation can't just be an accident. C

6 A 5. Assuming this is true from the previous question that the positive correlation is probably explained by the fact that seriously ill people go to large hospitals, this would be an example of, A) Common Response B) Voluntary Response C) Confounding D) Causation

7 6. You compute the correlation coefficient between hours of TV watched and grade point average for a sample of college undergraduates and obtain r = This means that A) you made an arithmetic mistake B) students who watch more TV tend to get lower grades C) students who watch more TV tend to get higher grades D) you can conclude that radiation from TV screens causes gradual brain damage. E) you can conclude that students who get good grades gradually lose their ability to appreciate TV. A

8 7. The correlation r=0.52 in the previous question shows that the fact that fathers have different heights, A) explains about 27% of the observed variation in their sons’ heights B) explains about 52% of the observed variation in their sons’ heights C) explains about 73% of the observed variation in their sons’ heights D) explains about 95% of the observed variation in their sons’ heights E) explains why some sons look a lot like their fathers A

9 8. Suppose that the least squares regression line for predicting y from x is y = 100 - 1.3x.
Which of the following is a possible value for the correlation between y and x? (a) 0.3 (b) -1.3 (c) 0 (d) -0.5 (e) 0.5 D

10 9. The equation of the regression line for son's height in inches y versus father's height in inches x is y = 0.5x For 72 inch tall fathers, what is the mean height of their sons? (a) 69 inches (b) 71 inches (c) 72 inches (d) 74 inches (e) None of the above. B

11 10. If fathers' heights were measured in feet (one foot equals 12 inches), and sons' heights were measured in furlongs (one furlong equals 7920 inches), the correlation between heights of fathers and heights of sons would be (a) much smaller that 0.52 (b) slightly smaller than 0.52 (c) unchanged: equal to 0.52 (d) slightly larger than 0.52 (e) much larger that 0.52 C

12 D 11. Perfect correlation means all of the following except
(a) r = -1 or r = +1. (b) all points on the scatter plot lie on a straight line (c) all variation in one variable is explained by variation in the other variable. (d) there is a causal relationship between the variables. (e) each variable is a perfect predictor of the other. D

13 12. Which of the following are most likely to be negatively correlated?
(a) The total floor space and the price of an apartment in New York. (b) The percentage of lean body mass and the time it takes to run a mile for male college students. (c) The heights and yearly earnings of 35 year old U.S. adults. (d) Gender and yearly earnings among 35 year old U.S. adults. B

14 13. The correlation between average monthly temperature x and monthly natural gas consumption y over a period of months at Lincoln High School is Which of the following operations would change the value of the correlation? (a) Measure gas consumption in cubic meters instead of cubic feet. (b) Remove two outliers from the data before doing the calculation. (c) Measure temperature in degrees Kelvin instead of in degrees Fahrenheit. (d) All of (a), (b), and (c) would change the value of the correlation. B

15 14. Here is a scatter plot of the percent of games won by 11 basketball teams versus the percent of their shots that they made. What is the correlation between these two variables? (a) about -0.7 (b) about -0.3 (c) close to (d) about 0.3 (e) about 0.7 E

16 15. Suppose that the correlation between the scores of students on Exam 1 and Exam 2 in a statistics class is r = 0.7. One way to interpret r is to say what percent of the variation in Exam 2 scores can be explained by the straight line relationship between Exam 2 scores and Exam 1 scores. This percent is about (a) 84% (b) 70% (c) 49% (d) 30% C

17 16. A study of home heating costs collects data on the size of houses and the monthly cost to heat the houses with natural gas. Here are the data. Just by looking at the data (don't do a calculation) you can see that the correlation between house size and heating cost is B (a) close to zero. (b) clearly positive. (c) clearly negative. (d) not close to zero, but could be either positive or negative. (e) makes no sense for these data.

18 17. A study gathers data on the outside temperature during the winter, in degrees Fahrenheit, and the amount of natural gas a household consumes, in cubic feet per day. Call the temperature x and gas consumption y. The house is heated with gas, so x helps explain y. The least-squares regression line for predicting y from x is y = x. The next four questions concern this line. On a day when the temperature is 20F, the regression line predicts that gas used will be about (a) 1724 cubic feet (b) 1383 cubic feet (c) 1325 cubic feet (d) 964 cubic feet (e) None of these. D

19 D 18. We can see from the equation of the line that
A study gathers data on the outside temperature during the winter, in degrees Fahrenheit, and the amount of natural gas a household consumes, in cubic feet per day. Call the temperature x and gas consumption y. The house is heated with gas, so x helps explain y. The least-squares regression line for predicting y from x is y = x. The next three questions concern this line. 18. We can see from the equation of the line that (a) as the temperature x goes up, gas used y goes up, because the slope 1344 is positive (b) as the temperature x goes up, gas used y goes up, because the slope 19 is positive (c) as the temperature x goes up, gas used y goes down because the slope 1344 is bigger than 19. (d) as the temperature x goes up, gas used y goes down, because the slope -19 is negative D

20 A study gathers data on the outside temperature during the winter, in degrees Fahrenheit, and the amount of natural gas a household consumes, in cubic feet per day. Call the temperature x and gas consumption y. The house is heated with gas, so x helps explain y. The least-squares regression line for predicting y from x is y = x. The next two questions concern this line. 19. When the temperature goes up 1 degree, what happens to the gas usage predicted by the regression line? (a) It goes up 1 cubic foot (b) It goes down 1 cubic foot (c) It goes up 19 cubic feet (d) It goes down 19 cubic feet (e) Can’t tell without seeing the data D

21 A study gathers data on the outside temperature during the winter, in degrees Fahrenheit, and the amount of natural gas a household consumes, in cubic feet per day. Call the temperature x and gas consumption y. The house is heated with gas, so x helps explain y. The least-squares regression line for predicting y from x is y = x. This is the last question that concerns this line. 20. The correlation between temperature x and gas usage y is r = Which of the following would not change r? (a) measuring temperature in degrees Celsius instead of degrees Fahrenheit (b) removing two outliers from the data used to calculate r. (c) measuring gas usage in hundreds of cubic feet, so that all values of y are divided by 100. (d) Both a and c (e) All of a, b, and c. D


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