EBook Problems GLM Corr

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.

Answer

 (b)

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.

Answer

 (b) , (c)

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.

Answer

 (a)

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.

Answer

 (c)

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.

Answer

 (c)

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.

Answer(e)

 {{{2}}}

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.

Answer

 (c)

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.

Answer

 (a)

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.

Answer

 (b) , (d)

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.

Answer

 (c)

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.

Answer

 (d)

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.

Answer

 (c)

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.

Answer

 (b)

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.

Answer

 (b)

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