Section 4.1 HW

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 = −0.992​, (b) r = −0.049​, (c) r= -1 ​(a) Scatter diagram _____ ​(b) Scatter diagram _____ ​(c) Scatter diagram ______

(a) I: negative correlation with two or three dots (b) II: : plots are all scattered (c) III: negative correlative with only one dot

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. (a) Do the two variables have a linear​ relationship? A. The data points have a linear relationship because they do not lie mainly in a straight line. B. The data points have a linear relationship because they lie mainly in a straight line. C. The data points do not have a linear relationship because they lie mainly in a straight line. D. The data points do not have a linear relationship because they do not lie mainly in a straight line. (b) If the relationship is linear do the variables have a positive or negative​ association? A. The variables have a positive association. B. The variables have a negative association. C. The relationship is not linear.

(a) The data points do not have a linear relationship because they do not lie mainly in a straight line. (b) The relationship is not linear.

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. (a) Do the two variables have a linear​ relationship? A. The data points have a linear relationship because they do not lie mainly in a straight line. B. The data points do not have a linear relationship because they do not lie mainly in a straight line. C. The data points do not have a linear relationship because they lie mainly in a straight line. D. The data points have a linear relationship because they lie mainly in a straight line. (b) If the relationship is linear do the variables have a positive or negative​ association? A. The variables have a positive association. B. The variables have a negative association. C. The relationship is not linear.

(a) The data points have a linear relationship because they lie mainly in a straight line. (b) The variables have a negative association.

The data in the table to the right are based on the results of a survey comparing the commute time of adults to their score on a​ well-being test. Complete parts​ (a) through​ (d) below. (a) Which variable is likely the explanatory variable and which is the response​ variable? A. The explanatory variable is commute time and the response variable is the​ well-being score because commute time affects the​ well-being score. B. The explanatory variable is commute time and the response variable is the​ well-being score because​ well-being score affects the commute time score. C. The explanatory variable is the​ well-being score and the response variable is commute time because commute time affects the​ well-being score. D. The explanatory variable is the​ well-being score and the response variable is commute time because​ well-being score affects the commute time. ​(b) Draw a scatter diagram of the data. Which of the following represents the​ data? ​(c) Determine the linear correlation coefficient between commute time and​ well-being score. r = ______ (​(Round to three decimal places as​ needed.) ​(d) Does a linear relation exist between the commute time and​ well-being index​ score? A. ​Yes, there appears to be a positive linear association because r is positive and is greater than the critical value. B. ​Yes, there appears to be a positive linear association because r is positive and is less than the critical value. C. ​No, there is no linear association since r is positive and is less than the critical value. D. ​Yes, there appears to be a negative linear association because r is negative and is less than the negative of the critical value.

(a) The explanatory variable is commute time and the response variable is the​ well-being score because commute time affects the​ well-being score. (b) scatter plot A: negative correlation (c) -0.986 (d) ​Yes, there appears to be a negative linear association because r is negative and is less than the negative of the critical value.

(a) What does it mean to say that two variables are positively​ associated? A. There is a linear relationship between the​ variables, and whenever the value of one variable​ increases, the value of the other variable increases. B. There is a relationship between the variables that is not linear. C. There is a linear relationship between the​ variables, and whenever the value of one variable​ increases, the value of the other variable decreases. D. There is a linear relationship between the variables. (b) What does it mean to say that two variables are negatively​ associated? A. There is a linear relationship between the​ variables, and whenever the value of one variable​ increases, the value of the other variable decreases. B. There is a linear relationship between the​ variables, and whenever the value of one variable​ increases, the value of the other variable increases. C. There is a linear relationship between the variables. D. There is a relationship between the variables that is not linear.

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

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. Let the number of reported cases of Lyme disease be the explanatory variable. Choose the correct graph below. (b) Determine the linear correlation coefficient between Lyme disease and drowning deaths. - The linear correlation coefficient between Lyme disease and drowning deaths is r = ________. ​(Round to three decimal places as​ needed.) (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? The variables Lyme disease and drowning deaths are ____(1)_____ associated because r is ____(2)_____ and the absolute value of the correlation​ coefficient,___(3)____​, is ____(4)______ than the critical​ value, ____(5)_______. (Round to three decimal places as​ needed.) (c2) 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. An increase in Lyme disease does not cause an increase in drowning deaths. There are no lurking variables. B. An increase in Lyme disease does not cause an increase in drowning deaths. Pesticide control and life guards are likely lurking variables. C. An increase in Lyme disease causes an increase in drowning deaths. There are no lurking variables. D. An increase in Lyme disease does not cause an increase in drowning deaths. The temperature and time of year are likely lurking variables.

(a) scatter plot C: few dots low: one high (b) 0.955 (c1) positive; positive, 0.955, greater, 0.576 (c2) An increase in Lyme disease does not cause an increase in drowning deaths. The temperature and time of year are likely lurking variables.

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

-1

What does it mean if r = 0? A. No linear relationship exists between the variables. B. A relationship does exist between the variables. C. No relationship exists between the variables. D. A linear relationship does exist between the variables.

No linear relationship exists between the variables.

Match the linear correlation coefficient to the scatter diagram. r= -0.049

Scatter plot C: plots are all scattered

What does it mean to say that the linear correlation coefficient between two variables equals​ 1? What would the scatter diagram look​ like? A. When the linear correlation coefficient is​ 1, there is a perfect negative linear relation between the two variables. The scatter diagram would contain points that all lie on a line with a negative slope. B. When the linear correlation coefficient is​ 1, there is a perfect positive linear relation between the two variables. The scatter diagram would contain points that all lie on a line with a positive slope. C. When the linear correlation coefficient is​ 1, there is a perfect horizontal linear relation between the two variables. The scatter diagram would contain points that all lie on a horizontal line. D. When the linear correlation coefficient is​ 1, there is no linear relation between the variables. The scatter diagram would contain points that show no discernable relationship.

When the linear correlation coefficient is​ 1, there is a perfect positive linear relation between the two variables. The scatter diagram would contain points that all lie on a line with a positive slope.

True or​ false: Correlation implies causation.

false

Will the following variables have positive​ correlation, negative​ correlation, or no​ correlation? - years of education and annual salary

positive correlation