Section 4.1 Homework

1.  What does it mean to say that two variables are positively​ associated? Negatively​ associated?  What does it mean to say that two variables are positively​ associated?

1. There is a linear relationship between the variables.
2. There is a linear relationship between the​ variables, and whenever the value of one variable​ increases, the value of the other variable decreases.
3. There is a relationship between the variables that is not linear.
4. There is a linear relationship between the​ variables, and whenever the value of one variable​ increases, the value of the other variable increases.

What does it mean to say that two variables are negatively​ associated?

1. There is a relationship between the variables that is not linear.
2. There is a linear relationship between the variables.
3. There is a linear relationship between the​ variables, and whenever the value of one variable​ increases, the value of the other variable decreases.
4. There is a linear relationship between the​ variables, and whenever the value of one variable​ increases, the value of the other variable increases.

2.   Fill in the blank below.

If r=​_______, then a perfect negative linear relation exists between the two quantitative variables.

3.   True or​ false: Correlation implies causation.  Choose the correct response.

1. False
2. True

4.  Determine whether the scatter diagram indicates that a linear relation may exist between the two variables. If the relation is​ linear, determine whether it indicates a positive or negative association between the variables.  Use this information to answer the following.

Do the two variables have a linear​ relationship?

1. The data points have a linear relationship because they lie mainly in a straight line.
2. The data points do not have a linear relationship because they do not lie mainly in a straight line.
3. The data points do not have a linear relationship because they lie mainly in a straight line.
4. The data points have a linear relationship because they do not lie mainly in a straight line.

Do the two variables have a positive or a negative​ association?

1. The two variables have a positive association.
2. The two variables have a negative association.
3. None of the above

5.  Match the linear correlation coefficient to the scatter diagram.  r=

Choose the correct graph below.

6.  For the accompanying data​ set, (a) draw a scatter diagram of the​ data, (b) by​ hand, compute the correlation​ coefficient, and​ (c) determine whether there is a linear relation between x and y.

​(a) Draw a scatter diagram of the data. Choose the correct graph below.

​(b) By​ hand, compute the correlation coefficient.

The correlation coefficient is _____  (Round to three decimal places as​ needed.)

​(c) Determine whether there is a linear relation between x and y.

Because the correlation coefficient is _______ and the absolute value of the correlation​ coefficient, _____

is _________ than the critical value for this data​ set, _______ _____________ linear relation exists between x and y.

7.  Will the following variables have positive​ correlation, negative​ correlation, or no​ correlation?  Number of doctors on staff at a hospital and number of administrators on staff

Will these variables have positive​ correlation, negative​ correlation, or no​ correlation?

1. No correlation
2. Positive
3. Negative

8.   On an international​ exam, students are asked to respond to a variety of background questions. For the 41 nations that participated in the​ exam, the correlation between the percentage of items answered in the background questionnaire​ (used as a proxy for student task​ persistence) and mean score on the exam was 0.834.   Does this suggest there is a linear relation between student task persistence and achievement​ score? Write a sentence that explains what this result might mean.

Does this suggest there is a linear relation between student task persistence and achievement​ score? Choose the best response below.

1. ​No, since 0.834 is less than the critical value for 30.
2. ​No, since 0.834 is greater than the critical value for 30.
3. ​Yes, since 0.834 is greater than the critical value for 30.
4. ​Yes, since 0.834 is less than the critical value for 30.

What does this result​ mean?

1. Countries in which students answered a greater percentage of items in the background questionnaire tended to have higher mean scores on the exam.
2. There is no linear relation between countries in which students answered a greater percentage of items in the background questionnaire and higher mean scores on the exam.
3. Countries in which students answered a lesser percentage of items in the background questionnaire tended to have higher mean scores on the exam.
4. Countries in which students cheated on the exam also cheated on the items in the background questionnaire.

9.   The data in the accompanying table represent the annual rates of return for various stocks. If you only wish to invest in two​ stocks, which two would you select if your goal is to have low correlation between the two​ investments? Which two would you select if your goal is to have one stock go up when the other goes​ down?

If your goal is to have low correlation between the two​ investments, which two should stocks should you​ select?

1. Stock B and Stock C
2. Stock A and Stock C
3. Stock A and Stock B

If your goal is to have one stock go up when the other goes​ down, you should select _________ since the linear correlation coefficient for these two stocks _______

10.  The linear correlation between violent crime rate and percentage of the population that has a cell phone is

−0.918 for years since 1995. Do you believe that increasing the percentage of the population that has a cell phone will decrease the violent crime​ rate? What might be a lurking variable between percentage of the population with a cell phone and violent crime​ rate?

Will increasing the percentage of the population that has a cell phone decrease the violent crime​ rate? Choose the best option below.

1. Yes
2. No

What might be a lurking variable between percentage of the population with a cell phone and violent crime​ rate?

1. the average cell​ phone’s effectiveness as a weapon
2. the economy
3. the police
4. overall cell phone signal strength

11.  What does it mean if r=​0?  Choose the correct answer below.

1. A relationship does exist between the variables.
2. A linear relationship does exist between the variables.
3. No linear relationship exists between the variables.
4. No relationship exists between the variables.

12.  Draw a scatter diagram that might represent each relation.

weight of car and its towing capacity

number of cars sold and the remaining cars on the lot

Choose the most accurate scatter diagram below for the first relation.

Choose the most accurate scatter diagram below for the second relation.