STAT CHAP 4

Will the following variables have positive​ correlation, negative​ correlation, or no​ correlation? YEARS OF EDUCATION AND ANNUAL SALARY

POSITIVE

Match the linear correlation coefficient to the scatter diagram. r= -0.546

B

If r is close to​ 0, then little or no evidence exists of a relation between the two quantitative variables.

FALSE

Match the linear correlation coefficient to the scatter diagram. The scales on the​ x- and​ y-axis are the same for each scatter diagram. (a) r=−0.049​, (b) r=−1​,

I,III,II

Match the linear correlation coefficient to the scatter diagram. The scales on the​ x- and​ y-axis are the same for each scatter diagram. (a) r=0.787​, (b) r=0.523​,

II,I,III

scatter diagram

In a scatter​ diagram, the explanatory variable is plotted on the horizontal axis and the response variable is plotted on the vertical axis.

A pediatrician wants to determine the relation that may exist between a​ child's height and head circumference. She randomly selects 8​ children, measures their height and head​ circumference, and obtains the data shown in the table. The pediatrician wants to use height to predict head circumference.

STAT--> REGRESSION--> LINEAR--> COMPUTE

The closer r is to +​1, the stronger weaker the evidence is of positive negative association between the two variables.

STRONGER POSITIVE

1. number of adminitrators on staff and the square footage of a hospital 2. the number of rats at a resturant and the size of the tip

1. scatter plot goes up 2. scatter plot is going down

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

D r=0.952 Because the correlation coefficient is positive and the absolute value of the correlation​ coefficient, 0.952 is greater than the critical value for this data​ set, 0.878​, a positive linear relation exists between x and y.

A pediatrician wants to determine the relation that may exist between a​ child's height and head circumference. She randomly selects 8​ children, measures their height and head​ circumference, and obtains the data shown in the table. (d) Determine if a linear relation exists between height and head circumference.​ (Note that the linear correlation coefficient between the height and head circumference of a child is r=0.886​.) Find the critical value. Does a linear relation exist between height and head​ circumference?

N=8 SO... 0.707 Yes, there appears to be a positive linear association because r is positive and is greater than the critical value.

What does it mean if r=​0?

No linear relationship exists between the variables.

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

The data points have a linear relationship because they lie mainly in a straight line. The two variables have a positive association.

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

The data points have a linear relationship because they lie mainly in a straight line. The two variables have a positive association.

Use the given data to complete parts​ (a) and​ (b) below. (a) Draw a scatter diagram of the data. Choose the correct answer below. Compute the linear correlation coefficient. The linear correlation coefficient for the four pieces of data is nothing (b) Draw a scatter diagram of the data with the additional data point (10.4,9.2). Choose the correct answer below. Explain why correlations should always be reported with scatter diagrams.

A R=0.094 C R= 0.871 The additional data point strengthens the appearence of a linear association between the data points. The scatter diagram is needed to see if the correlation coefficient is being affected by the presence of outliers.

Lyme disease is an inflammatory disease that results in a skin rash and flulike symptoms. It is transmitted through the bite of an infected deer tick. The following data represent the number of reported cases of Lyme disease and the number of drowning deaths for a rural county. Complete parts ​(a) through ​(c) below. (a) Draw a scatter diagram of the data. Choose the correct graph below. (b) Determine the linear correlation coefficient between Lyme disease and drowning deaths. c) Does a linear relation exist between the number of reported cases of Lyme disease and the number of drowning​ deaths? Do you believe that an increase of Lyme disease causes an increase in drowning​ deaths? What is a likely lurking variable between cases of Lyme disease and drowning​ deaths?

A R=965 The variables Lyme disease and drowning deaths are positively associated because r is positive and the absolute value of the correlation​ coefficient, 0.965​, is greater than the critical​ value, 0.576. An increase in Lyme disease does not cause an increase in drowning deaths. The temperature and time of year are likely lurking variables.

\Lyme disease is an inflammatory disease that results in a skin rash and flulike symptoms. It is transmitted through the bite of an infected deer tick. The following data represent the number of reported cases of Lyme disease and the number of drowning deaths for a rural county. Complete parts ​(a) through ​(c) below. (a) Draw a scatter diagram of the data. Choose the correct graph below. (b) Determine the linear correlation coefficient between Lyme disease and drowning deaths. (c) Does a linear relation exist between the number of reported cases of Lyme disease and the number of drowning​ deaths? Do you believe that an increase of Lyme disease causes an increase in drowning​ deaths? What is a likely lurking variable between cases of Lyme disease and drowning​ deaths?

B The linear correlation coefficient between Lyme disease and drowning deaths is r=0.965 The variables Lyme disease and drowning deaths are positively associated because r is positive and the absolute value of the correlation​ coefficient, 0.965​, is greater than the critical​ value, 0.576. An increase in Lyme disease does not cause an increase in drowning deaths. The temperature and time of year are likely lurking variables.

For the following data​ set, (a) Draw a scatter​ diagram, (b) compute the correlation​ coefficient, and​ (c) comment on the type of relation that appears to exist between x and y. (b) Compute the correlation coefficient. (c) What type of relation appears to exist between x and​ y?

B GO TO STAT--> REGREGESSION--> LINEAR--> COMPUTE AND FIND R The linear correlation coefficient is close to 1 so a positive linear relation exists between x and y.

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

NO THE ECONOMY

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?

R THAT IS CLOSEST TO 0 IS THE ANSWER A AND B If your goal is to have one stock go up when the other goes​ down, you should select Stock B and Stock C, since the linear correlation coefficient for these two stocks is closest to - 1.

A pediatrician wants to determine the relation that may exist between a​ child's height and head circumference. She randomly selects 8 children from her​ practice, measures their height and head​ circumference, and obtains the data shown in the table. Complete parts​ (a) through​ (e) below. a) If the pediatrician wants to use height to predict head​ circumference, determine which variable is the explanatory variable and which is the response variable. Choose the correct answer below. (b) Draw a scatter diagram. Choose the correct graph below. (c) Compute the linear correlation coefficient between the height and head circumference of a child. (d) Does a linear relation exist between height and head​ circumference? Select the correct choice below and fill in the answer box to complete your choice. (e) Convert the data to centimeters​ (1 inch=2.54 ​cm), and recompute the linear correlation coefficient. What effect did the conversion have on the linear correlation​ coefficient? Convert the first four data values to centimeters.

The explanatory variable is height and the response variable is head circumference. D R=0.973 Yes, the variables height and head circumference are positively associated because r is positive and the absolute value of the correlation coefficient is greater than the critical​ value, 0.707 MULTIPLY ALL NUMBERS BY 2.54 R=0.973 HAS NO EFFECT

A pediatrician wants to determine the relation that may exist between a​ child's height and head circumference. She randomly selects 8​ children, measures their height and head​ circumference, and obtains the data shown in the table. ​(a) If the pediatrician wants to use height to predict head​ circumference, determine which variable is the explanatory variable and which is the response variable. (b) Draw a scatter diagram. Which of the following represents the​ data?

The explanatory variable is height and the response variable is head circumference. d

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

There is a linear relationship between the​ variables, and whenever the value of one variable​ increases, the value of the other variable increases. There is a linear relationship between the​ variables, and whenever the value of one variable​ increases, the value of the other variable decreases.

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 0.813. 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. What does this result​ mean?

Yes, since 0.813 is greater than the critical value for 30. Countries in which students answered a greater percentage of items in the background questionnaire tended to have higher mean scores on the exam.