# EBook Problems GLM Corr

### From Socr

Line 458: | Line 458: | ||

:''(d) 93.52% | :''(d) 93.52% | ||

{{hidden|Answer|(d)}} | {{hidden|Answer|(d)}} | ||

+ | |||

+ | ===Problem 32=== | ||

+ | In the early 1900's when Francis Galton and Karl Pearson measured 1078 pairs of fathers and their grown-up sons, they calculated that the mean height for fathers was 68 inches with deviation of 3 inches. For their sons, the mean height was 69 inches with deviation of 3 inches. (The actual deviations a bit smaller, but we will work with these values to keep the calculations simple.) The correlation coefficient was 0.50. Use the information to calculate the slope of the linear model that predicts the height of the son from the height of the fathers. | ||

+ | |||

+ | *Choose one answer. | ||

+ | |||

+ | :''(a) 35.00 | ||

+ | |||

+ | :''(b) 0.50 | ||

+ | |||

+ | :''(c) The slope cannot be determined without the actual data | ||

+ | |||

+ | :''(d) 3/3 = 1.00 | ||

+ | {{hidden|Answer|(b)}} | ||

+ | |||

+ | ===Problem 33=== | ||

+ | Use the information from the Heights of Fathers and Sons to write the linear model that best predicts the height of the son from the height of the father. | ||

+ | |||

+ | *Choose one answer. | ||

+ | |||

+ | :''(a) Son's height = 1.00 + 1.00* Father's height | ||

+ | |||

+ | :''(b) Son's height = 0.5 + 35*Father's height | ||

+ | |||

+ | :''(c) Son's height = 35 + 0.5*Father's height | ||

+ | |||

+ | :''(d) The model cannot be determined without the actual data | ||

+ | {{hidden|Answer|(c)}} | ||

+ | |||

+ | ===Problem 34=== | ||

+ | Use the linear model to predict the height of a son whose father's height is 6 feet. | ||

+ | |||

+ | *Choose one answer. | ||

+ | |||

+ | :''(a) The son's height = 35 + 0.5(6) inches | ||

+ | |||

+ | :''(b) The son's height = 35 + 0.5(72) inches | ||

+ | |||

+ | :''(c) The "Regression Effect" states that the son will be a bit taller than his father | ||

+ | |||

+ | :''(d) Cannot be determined without the data | ||

+ | {{hidden|Answer|(b)}} | ||

+ | |||

<hr> | <hr> |

## Current revision as of 07:27, 6 January 2009

## EBook Problems Set - Correlation

### Problem 1

A positive correlation between two variables X and Y means that if X increases, this will cause the value of Y to increase.

*(a) This is always true.*

*(b) This is sometimes true.*

*(c) This is never true.*

### Problem 2

The correlation between high school algebra and geometry scores was found to be + 0.8. Which of the following statements is not true?

*(a) Most of the students who have above average scores in algebra also have above average scores in geometry.*

*(b) Most people who have above average scores in algebra will have below average scores in geometry*

*(c) If we increase a student's score in algebra (ie. with extra tutoring in algebra), then the student's geometry scores will always increase accordingly.*

*(d) Most students who have below average scores in algebra also have below average scores in geometry.*

### Problem 3

Researchers discover that the correlation between miles ran per week and cardiovascular endurance is +0.75. They also discover that the correlation between hours spent watching television per week and cardiovascular endurance is -0.75. What is the conclusion that best characterizes the result of this study?

- Choose one answer.

*(a) Most people who spend a lot of hours watching television have low cardiovascular endurance.*

*(b) Most people who have good cardiovascular endurance spend a lot of time running and little time watching television.*

*(c) Based on the correlation, if you increase your running hours per week, your cardiovascular endurance will decrease.*

*(d) Based on the correlation, if you increases your television watching time, your cardiovascular endurance will decrease.*

*(e) Most people with a lot of miles ran per week have high cardiovascular endurance.*

((hidden|Answer|(b)}}

### Problem 4

The correlation between working out and body fat was found to be exactly -1.0. Which of the following would not be true about the corresponding scatterplot?

- Choose one answer.

*(a) The slope of the best line of fit should be -1.0.*

*(b) All the points would lie along a perfect straight line, with no deviation at all.*

*(c) The best fitting line would have a downhill (negative) slope.*

*(d) 100% of the variance in body fat can be predicted from workout.*

### Problem 5

Suppose that the correlation between working out and body fat was found to be exactly -1.0. Which of the following would NOT be true, about the corresponding scatterplot?

- Choose one answer.

*(a) All points would lie along a straight line, with no deviation at all.*

*(b) 100% of the variance in body fat can be predicted from the workout.*

*(c) The slope of the linear model is -1.0.*

*(d) The best fitting line would have a negative slope.*

### Problem 6

A recent article in an educational research journal reports a correlation of +0.8 between math achievement and overall math aptitude. It also reports a correlation of -0.8 between math achievement and a math anxiety test. Which of the following interpretations is the most correct?

- Choose one answer

*(a) You cannot compare a positive and a negative correlation.*

*(b) The correlation of +0.8 indicates a stronger relationship than the correlation of -0.8.*

*(c) The correlation of +0.8 is just as strong as the correlation of -0.8.*

*(d) It is impossible to tell which correlation is stronger.*

### Problem 7

Psychologists have shown that there is a relationship between stress levels and productivity. As stress levels increase, productivity also increases up to a certain point, and after that productivity decreases as stress levels increase. Suppose you were given this data for a random sample of 200 adults. If you calculated the Pearson coefficient of correlation, what would you expect to find?

- Choose one answer.

*(a) I would expect r to be between -0.50 to -0.70.*

*(b) I would expect r to be -1.*

*(c) I would expect r to be between 0.50 and 0.70.*

*(d) I would expect r to be +1.*

*(e) I would expect r to be zero.*

### Problem 8

If the correlation coefficient is 0.80, then:

- Choose one answer.

*(a) The explanatory variable is usually less than the response variable.*

*(b) The explanatory variable is usually more than the response variable.*

*(c) None of the statements are correct.*

*(d) Below-average values of the explanatory variable are more often associated with below-average values of the response variable.*

*(e) Below-average values of the explanatory variable are more often associated with above-average values of the response variable.*

### Problem 9

Given the following data, what is the best estimate for the coefficient of correlation between the ages of the husbands and wives?

There are 50 couples (husband and wife). The age range for men is from 50 to 70 years old. The age range for women is from 48 to 68 years old. For all of the couples, the husband is two years older than the wife. For instance, in one couple the husband is 50 years old and the wife is 48 years old.

- Choose one answer.

*(a) The coefficient of correlation between the age of husband and wife is equal to +1.*

*(b) We need the actual data to compute the coefficient of correlatin between the age of the husband and wife.*

*(c) The coefficient of correlation between the age of husband and wife is equal to zero.*

*(d) The coefficient of correlation between the age of husband and wife is equal to +0.50.*

*(e) The coefficient of correlation between the age of husband and wife is equal to -1.*

### Problem 10

The correlation between high school algebra and geometry scores was found to be + 0.8. Which of the following statements is not true?

- Choose at least one answer.

*(a) Most students who have below average scores in algebra also have below average scores in geometry.*

*(b) If we increase a student's score in algebra (ie. with extra tutoring in algebra), then the student's geometry scores will always increase accordingly.*

*(c) Most of the students who have above average scores in algebra also have above average scores in geometry.*

*(d) Most people who have above average scores in algebra will have below average scores in geometry.*

### Problem 11

Two different researchers wanted to study the relationship between math anxiety and taking exams. Researcher A measured anxiety with a scale that had a minimum score of 0 and a maximum score of 20, and a final exam that had a minimum score of 0 and a maximum score of 50. He tested 120 students. Researcher B measured anxiety with a scale that had a minimum of 0 and a maximum of 30, and a final exam that had a minimum score of 0 and a maximum score of 35. He tested 60 students. Researcher A found that the coefficient of correlation between a student's math anxiety and his or her score on the final was -0.60. Researcher B found the correlation between a student's math anxiety and his or her score on the final was -0.30.

- Choose one answer.

*(a) The coefficient of correlation for researcher A is twice as strong as the coefficient of correlation for researcher B.*

*(b) Based on the study by researcher A one can conclude that high math anxiety is the reason that a lot of the students do not do well in math.*

*(c) Given that coefficient of correlation shows the association between standardized scores, one can conclude that for researcher A a greater precentage of the students who have above average anxiety are likely to have below average score on the final.*

*(d) Given that the minimum and the maximum values for math and anxiety are so different for the two researchers one cannot compare the coefficient of correlation found by these two researchers.*

### Problem 12

Suppose the correlation between two variables, math achievement and math attitude was found to be 0.78. What does this tell us about the correlation between math attitude and math achievement?

- Choose one answer.

*(a) The correlation is 1 - 0.78 = 0.22.*

*(b) The correlation is -0.78.*

*(c) Not enough information is given to answer the question.*

*(d) The correlation is still 0.78.*

### Problem 13

A spokesperson for the Bureau of Economic Research reported to the Council of Economic Advisers the following information:

"We found that the correlation between the duration (in months) of business cycles expansions and the duration (in months) of business cycles contractions was 0.25 years."

This statement contains a mistake. Can you tell which?

- Choose one answer.

*(a) The correlation coefficient measures only direction and strength, not duration.*

*(b) the two variables compared are not both quantitative.*

*(c) The correlation coefficient doesn't have units.*

*(d) The correlation coefficient can not be that small.*

### Problem 14

If females of a certain species of lizard always mate with males that are 0.75 years younger than they are, what is the correlation between the ages of these male and female lizards?

- Choose one answer.

*(a) Not enough information to tell.*

*(b) -0.75*

*(c) -1*

*(d) 1*

*(e) 0.75*

{{hidden|Answer|(d)

### Problem 15

A researcher finds that the coefficient of correlation between the height and the weight of newborn babies is +0.70. What is the best answer?

- Choose one answer.

*(a) Most babies with above average weight have below average height.*

*(b) Most babies with above average height will also have above average weight.*

*(c) Based to the result of this study, increasing a baby's weight will cause its height to increase.*

*(d) None of the other answers.*

*(e) Most babies with above average height have below average weight.*

### Problem 16

A student is hired by the Registrar's Office to conduct a statistical analysis on the data collected on students' grades. He finds that the relationship between GPA in major and overall GPA is linear and that the coefficient of correlation is +0.76. Given the magnitude of the coefficient of correlation between GPA in major and overall GPA, and given that there are no major outliers or influencial points, one can conclude that

- Choose one answer.

*(a) Studying hard for courses in one's major and getting high grades leads to high grades in all other courses.*

*(b) Students whose overall GPA is above average are highly unlikely to have below average GPA in their major.*

*(c) Besides the coefficient of correlation, one needs to know the mean and the standard deviation to decide whether high GPA in major leads to high overall GPA.*

*(d) Besides the coefficient of correlation, one needs the sample size to decide whether high overall GPA leads to high GPA in major.*

### Problem 17

Without doing the calculations, what is the correlation between these four points: (-1, 1), (1, 1), (-1, -1), and (1, -1)?

- Choose one answer.

*(a) The correlation is -1.*

*(b) Can't tell from the information given.*

*(c) The correlation is 0.*

*(d) The correlation is 1 because there is a perfect pattern here.*

### Problem 18

A correlation of r=0 between two quantitative variables X and Y means

- Choose one answer.

*(a) There is a positive relationship between the two variables.*

*(b) There is no linear relationship between the two variables.*

*(c) There is a negative relationship between the two variables.*

*(d) There is no relationship between the two variables.*

### Problem 19

In a plot of bivariate data, an outlier appears outside the general pattern of data points and far from a fitted regression line. How will this outlier affect the correlation coefficient?

- Choose one answer.

*(a) It will increase the correlation coefficient by making a stronger pattern appear in the data that was unknown before.*

*(b) There is not enough information to tell.*

*(c) It will make the correlation coefficient smaller because it pulls the best fitting line toward it, and away from the rest of the data.*

*(d) It will not affect the correlation coefficient at all. An outlier is not representative of the actual relationship so it should be disregarded.*

### Problem 20

The statement below contains some mistakes or bad uses of the correlation coefficient. How many?

Statement: "We found a high correlation (r= -3) between delivery time and type of firm in charge of the delivery"

- Choose one answer.

*(a) One mistake.*

*(b) Three mistakes.*

*(c) Two mistakes.*

### Problem 21

Two different researchers are working on studying the relationship between penmanship and creative writing anxiety. Researcher A tested 150 students using an anxiety scale that had a minimum of 0 and a maximum of 100, and a penmanship test that had a minimum of 10 and a maximum of 60. He found a correlation of 0.54 between creative writing anxiety and penmanship. Researcher B tested 120 students using an anxiety scale that had a minimum of 0 and a maximum of 50, and a penmanship test that had a minimum of 0 and a maximum of 10. She found a correlation of -0.27 between creative writing anxiety and penmanship. Choose the best answer.

- Choose one answer.

*(a) Given that the coefficient of correlation shows the association between standardized scores, one can conclude that for researcher A a greater percentage of the students who have above average anxiety are likely to have above average penmanship.*

*(b) The coefficient of correlation for researcher A is twice as strong as the coefficient of correlation for researcher B.*

*(c) Given that coefficient of correlation shows the association between standardized scores, one can conclude that for researcher A a greater precentage of the students who have above average anxiety are likely to have below average penmanship.*

*(d) Based on the study by researcher A one can conclude that high creative writing anxiety is the reason that a lot of the students have bad penmanship.*

### Problem 22

A study in a recent sociology journal shows a correlation of 0.6 between politicians and corruption, as well as a correlation of -0.6 between politicians and intelligence. Which of the following interpretations is the most correct?

- Choose one answer.

*(a) It is impossible to tell which correlation is stronger.*

*(b) The correlation of 0.6 indicates a stronger relationship than the correlation of -0.6.*

*(c) You cannot compare a positive and a negative correlation.*

*(d) The correlation of 0.6 is just as strong as the correlation of -0.6.*

### Problem 23

Which of the following correlation values represents a perfect linear relationship between two quantitative variables?

- Choose at least one answer.

*(a) -1*

*(b) 0*

*(c) 1*

*(d) 0.5*

*(e) 0.9*

### Problem 24

Physicists have shown that there is a relationship between entropy and the quantum state of a quark. As the state decreases, the entropy increases up to a certain point. After that point, entropy decreases as the state increases. If you calculated the Pearson coefficient of correlation between entropy and quark state, what would you expect to find?

- Choose one answer.

*(a) -0.4*

*(b) -1.0*

*(c) 1.0*

*(d) 0*

*(e) 0.4 to 0.6*

### Problem 25

If yellow-bellied sharks always hunt prey that are 0.25 times as large as they are, what would the correlation between the sizes of sharks and their prey be?

- Choose one answer.

*(a) 1.0*

*(b) -0.25*

*(c) -0.75*

*(d) 0.75*

*(e) 0.25*

### Problem 26

A study of 4,500 subjects finds a correlation of +0.06 between two measures of scholastic aptitude to be statistically significant at the .001 level. What do these results mean?

- Choose one answer.

*(a) For practical reasons, there is no important relationship between the two measures*

*(b) There is less than a 0.1% probability that their relationship is not important*

*(c) There is evidence of a positive relationship between these two measures in the population*

*(d) The relationship between the two measures is important.*

### Problem 27

Which of these statements are false?

- Choose one answer.

*(a) Since the correlation between X and Y is 0, this means there is no relationship whatsoever between these two variables*

*(b) All*

*(c) None*

*(d) There is a strong relationship between gender and height because we found a correlation of 0.65*

*(e) Plant height and leaf height were found to be negatively correlated because the correlation coefficient is -1.41*

### Problem 28

Use the linear model to predict the height for a son whose father is 6 feet. Son's height = 35 + 0.5*Father's height.

- Choose one answer.

*(a) The "Regression Effect" states that the son will be a bit taller than his father*

*(b) The son's height = 35 + 0.5(72) inches*

*(c) Cannot be determined without the data*

*(d) The son's height = 35 + 0.5(6) inches*

### Problem 29

Suppose we are trying to predict the amount of ice cream sold from the temperature at noon on the same day. Given that the coefficient of correlation is 0.6, which of the following conclusions is right?

- Choose at least one answer.

*(a) 60 % of the variance in the amount of ice cream sold can be explained by the temperature.*

*(b) 36 % of the variance in the amount of ice cream sold can be explained by the temperature.*

*(c) 60% of the variance in the temperature can be explained by the amount of ice cream sold.*

*(d) 36 % of the variance in the temperature can be explained by the amount of ice cream sold.*

### Problem 30

If the correlation between two data sets was found to be approximately zero, which of the conclusions can be made about the scatterplot?

- Choose at least one answer.

*(a) The scatterplot could be a horizontal line*

*(b) The slope of the regression line will be positive but the points will not be so close to the line*

*(c) The scatterplot could be non-linear*

*(d) The slope of the regression line will be negative*

### Problem 31

The correlation between tree diameter and volume in a data set is 0.9671. How much of the variability of volume is explained by diameter?

- Choose one answer.

*(a) 96.71%*

*(b) 98.34%*

*(c) we need to know the regression line to tell*

*(d) 93.52%*

### Problem 32

In the early 1900's when Francis Galton and Karl Pearson measured 1078 pairs of fathers and their grown-up sons, they calculated that the mean height for fathers was 68 inches with deviation of 3 inches. For their sons, the mean height was 69 inches with deviation of 3 inches. (The actual deviations a bit smaller, but we will work with these values to keep the calculations simple.) The correlation coefficient was 0.50. Use the information to calculate the slope of the linear model that predicts the height of the son from the height of the fathers.

- Choose one answer.

*(a) 35.00*

*(b) 0.50*

*(c) The slope cannot be determined without the actual data*

*(d) 3/3 = 1.00*

### Problem 33

Use the information from the Heights of Fathers and Sons to write the linear model that best predicts the height of the son from the height of the father.

- Choose one answer.

*(a) Son's height = 1.00 + 1.00* Father's height*

*(b) Son's height = 0.5 + 35*Father's height*

*(c) Son's height = 35 + 0.5*Father's height*

*(d) The model cannot be determined without the actual data*

### Problem 34

Use the linear model to predict the height of a son whose father's height is 6 feet.

- Choose one answer.

*(a) The son's height = 35 + 0.5(6) inches*

*(b) The son's height = 35 + 0.5(72) inches*

*(c) The "Regression Effect" states that the son will be a bit taller than his father*

*(d) Cannot be determined without the data*

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