Section 10-3 Chapter 10 Correlation and Regression Correlation Let’s work Exercise #19 from Section 5.1 Correlation

Section 10-3 Exercise #13 Chapter 10 Correlation and Regression Let’s work Exercise #19 from Section 5.1 Exercise #13

For the following exercise, complete these steps. Draw the scatter plot for the variables. Compute the value of the correlation coefficient. State the hypotheses. Test the significance of the correlation coefficient at  = 0.05, using Table I. Give a brief explanation of the type of relationship.

a. Draw the scatter plot for the variables. A researcher wishes to determine if a person’s age is related to the number of hours he or she exercises per week. The data for the sample are shown below. a. Draw the scatter plot for the variables. Age x 18 26 32 38 52 59 Hours y 10 5 2 3 1.5 1 2 4 6 8 10 20 30 40 50 60 Age Hours 70

b. Compute the value of the correlation coefficient. Age x 18 26 32 38 52 59 Hours y 10 5 2 3 1.5 1

c. State the hypotheses. Age x 18 26 32 38 52 59 Hours y 10 5 2 3 1.5

d. Test the significance of the correlation coefficient at  = 0 d. Test the significance of the correlation coefficient at  = 0.05, using Table I. Age x 18 26 32 38 52 59 Hours y 10 5 2 3 1.5 1

e. Give a brief explanation of the type of relationship. Age x 18 26 32 38 52 59 Hours y 10 5 2 3 1.5 1 There is a significant linear relationship between a person’s age and the number of hours he or she exercises per week.

Section 10-3 Exercise #15 Chapter 10 Correlation and Regression Let’s work Exercise #19 from Section 5.1 Exercise #15

For the following exercise, complete these steps. Draw the scatter plot for the variables. Compute the value of the correlation coefficient. State the hypotheses. Test the significance of the correlation coefficient at  = 0.05, using Table I. Give a brief explanation of the type of relationship.

relationship between the amount of an alumnus’s The director of an alumni association for a small college wants to determine whether there is any type of relationship between the amount of an alumnus’s contribution (in dollars) and the years the alumnus has been out of school. The data are shown here. Years x 1 5 3 10 7 6 Contribution y 500 100 300 50 75 80

a. Draw the scatter plot for the variables. Years x 1 5 3 10 7 6 Contribution y 500 100 300 50 75 80 100 200 300 400 500 2 4 8 6 10 20 Years Contribution 30

b. Compute the value of the correlation coefficient. Years x 1 5 3 10 7 6 Contribution y 500 100 300 50 75 80

b. Compute the value of the correlation coefficient.

b. Compute the value of the correlation coefficient.

c. State the hypotheses. Years x 1 5 3 10 7 6 Contribution y 500 100 300 50 75 80

d. Test the significance of the correlation coefficient at  = 0 d. Test the significance of the correlation coefficient at  = 0.05, using Table I. Years x 1 5 3 10 7 6 Contribution y 500 100 300 50 75 80

e. Give a brief explanation of the type of relationship. Years x 1 5 3 10 7 6 Contribution y 500 100 300 50 75 80 There is a significant linear relationship between a person’s age and his or her contribution.

Section 10-3 Exercise #17 Chapter 10 Correlation and Regression Let’s work Exercise #19 from Section 5.1 Exercise #17

For the following exercise, complete these steps. Draw the scatter plot for the variables. Compute the value of the correlation coefficient. State the hypotheses. Test the significance of the correlation coefficient at  = 0.05, using Table I. Give a brief explanation of the type of relationship.

Number of larceny crimes, x Number of vandalism crimes y A criminology student wishes to see if there is a relationship between the number of larceny crimes and the number of vandalism crimes on college campuses in Southwestern Pennsylvania. The data are shown. Is there a relationship between the two types of crimes? Number of larceny crimes, x 24 6 16 64 10 25 35 Number of vandalism crimes y 21 3 15 61 20

Number of larceny crimes, x Number of vandalism crimes y a. Draw the scatter plot for the variables. Number of larceny crimes, x 24 6 16 64 10 25 35 Number of vandalism crimes y 21 3 15 61 20 20 40 60 80 10 30 50 larceny crimes vandalism crimes 70

Number of larceny crimes, x Number of vandalism crimes y b. Compute the value of the correlation coefficient. Number of larceny crimes, x 24 6 16 64 10 25 35 Number of vandalism crimes y 21 3 15 61 20 Check the Math, specially n values.!

Number of larceny crimes, x Number of vandalism crimes y c. State the hypotheses. Number of larceny crimes, x 24 6 16 64 10 25 35 Number of vandalism crimes y 21 3 15 61 20

Number of larceny crimes, x Number of vandalism crimes y d. Test the significance of the correlation coefficient at  = 0.05, using Table I. Number of larceny crimes, x 24 6 16 64 10 25 35 Number of vandalism crimes y 21 3 15 61 20

Number of larceny crimes, x Number of vandalism crimes y e. Give a brief explanation of the type of relationship. Number of larceny crimes, x 24 6 16 64 10 25 35 Number of vandalism crimes y 21 3 15 61 20 There is not a significant linear relationship between the number of larceny crimes and the number of vandalism crimes.

Section 10-3 Exercise #23 Chapter 10 Correlation and Regression Let’s work Exercise #19 from Section 5.1 Exercise #23

For the following exercise, complete these steps. Draw the scatter plot for the variables. Compute the value of the correlation coefficient. State the hypotheses. Test the significance of the correlation coefficient at  = 0.05, using Table I. Give a brief explanation of the type of relationship.

Average daily temperature, x Average monthly precipitation, y The average daily temperature (in degrees Fahrenheit) and the corresponding average monthly precipitation (in inches) for the month of June are shown here for seven randomly selected cities in the United States. Determine if there is a relationship between the two variables. Average daily temperature, x 86 81 83 89 80 74 64 Average monthly precipitation, y 3.4 1.8 3.5 3.6 3.7 1.5 0.2

Average daily temperature, x Average monthly precipitation, y a. Draw the scatter plot for the variables. Average daily temperature, x 86 81 83 89 80 74 64 Average monthly precipitation, y 3.4 1.8 3.5 3.6 3.7 1.5 0.2 1 2 3 4 60 Temperature Precipitation 70 80 90 100 5

Average daily temperature, x Average monthly precipitation, y b. Compute the value of the correlation coefficient. Average daily temperature, x 86 81 83 89 80 74 64 Average monthly precipitation, y 3.4 1.8 3.5 3.6 3.7 1.5 0.2

Average daily temperature, x Average monthly precipitation, y c. State the hypotheses. Average daily temperature, x 86 81 83 89 80 74 64 Average monthly precipitation, y 3.4 1.8 3.5 3.6 3.7 1.5 0.2

Average daily temperature, x Average monthly precipitation, y d. Test the significance of the correlation coefficient at  = 0.05, using Table I. Average daily temperature, x 86 81 83 89 80 74 64 Average monthly precipitation, y 3.4 1.8 3.5 3.6 3.7 1.5 0.2

Average daily temperature, x Average monthly precipitation, y e. Give a brief explanation of the type of relationship. Average daily temperature, x 86 81 83 89 80 74 64 Average monthly precipitation, y 3.4 1.8 3.5 3.6 3.7 1.5 0.2 There is a significant linear relationship between temperature and precipitation.

Section 10-4 Chapter 10 Correlation and Regression Regression Let’s work Exercise #19 from Section 5.1 Regression

Section 10-4 Exercise #13 Chapter 10 Correlation and Regression Let’s work Exercise #19 from Section 5.1 Exercise #13

Find the equation of the regression line and find the y value for the specified x value. Remember that no regression should be done when r is not significant. Ages and Exercise 1 1.5 3 2 5 10 Hours y 59 52 38 32 26 18 Age x

Find y  when x = 35 years. Ages and Exercise 1 1.5 3 2 5 10 Hours y 59 52 38 32 26 18 Age x

Find y  when x = 35 years. Ages and Exercise 1 1.5 3 2 5 10 Hours y 59 52 38 32 26 18 Age x

Find y  when x = 35 years. Ages and Exercise 1 1.5 3 2 5 10 Hours y 59 52 38 32 26 18 Age x

Find y  when x = 35 years. Ages and Exercise 1 1.5 3 2 5 10 Hours y 59 52 38 32 26 18 Age x

Find y  when x = 35 years. Ages and Exercise 1 1.5 3 2 5 10 Hours y 59 52 38 32 26 18 Age x

Section 10-4 Exercise #15 Chapter 10 Correlation and Regression Let’s work Exercise #19 from Section 5.1 Exercise #15

Years and Contribution Find the equation of the regression line and find the y value for the specified x value. Remember that no regression should be done when r is not significant. Years and Contribution 80 75 50 300 100 500 Contribution y, $ 6 7 10 3 5 1 Years x

Years and Contribution Find y when x = 4 years. Years and Contribution 80 75 50 300 100 500 Contribution y, $ 6 7 10 3 5 1 Years x

Years and Contribution Find y when x = 4 years. Years and Contribution 80 75 50 300 100 500 Contribution y, $ 6 7 10 3 5 1 Years x

Years and Contribution Find y when x = 4 years. Years and Contribution 80 75 50 300 100 500 Contribution y, $ 6 7 10 3 5 1 Years x

Section 10-4 Exercise #23 Chapter 10 Correlation and Regression Let’s work Exercise #19 from Section 5.1 Exercise #23

Temperatures ( in. F ) and precipitation (in.) Find the equation of the regression line and find the y value when x = 70 ºF. Remember that no regression should be done when r is not significant. 0.2 64 1.5 3.7 3.6 3.5 1.8 3.4 Avg. mo. Precip. y 74 80 89 83 81 86 Avg. daily temp. x Temperatures ( in. F ) and precipitation (in.)

Section 10-5 Chapter 10 Correlation and Regression Let’s work Exercise #19 from Section 5.1 Coefficient of Determination and Standard Error of the Estimate

Section 10-5 Exercise #9 Chapter 10 Correlation and Regression Let’s work Exercise #19 from Section 5.1 Exercise #9

Find the coefficients of determination and non-determination when and explain the meaning 49% of the variation of y is due to the variation of x.

Find the coefficients of determination and non-determination when and explain the meaning 51% of the variation of y is due to chance.

Section 10-5 Exercise #15 Chapter 10 Correlation and Regression Let’s work Exercise #19 from Section 5.1 Exercise #15

Compute the standard error of the estimate. The regression line equation was found in Exercise 13 in Section 10-4.

Section 10-5 Exercise #19 Chapter 10 Correlation and Regression Let’s work Exercise #19 from Section 5.1 Exercise #19

Find the 90% prediction interval when x = 20 years. Age x 18 26 32 38 52 59 Hours y 10 5 2 3 1.5 1

Section 10-5 Exercise #21 Chapter 10 Correlation and Regression Let’s work Exercise #19 from Section 5.1 Exercise #21

Find the 90% prediction interval when x = 4 years. Years x 1 5 3 10 7 6 Contributions y, $ 500 100 300 50 75 80

Section 10-6 Chapter 10 Correlation and Regression Multiple Regression Let’s work Exercise #19 from Section 5.1 Multiple Regression

Section 10-6 Exercise #7 Chapter 10 Correlation and Regression Let’s work Exercise #19 from Section 5.1 Exercise #7

A manufacturer found that a significant relationship exists among the number of hours an assembly line employee works per shift x1, the total number of items produced x2, and the number of defective items produced y. The multiple regression equation is . Predict the number of defective items produced by an employee who has worked 9 hours and produced 24 items.

Section 10-6 Exercise #9 Chapter 10 Correlation and Regression Let’s work Exercise #19 from Section 5.1 Exercise #9

An educator has found a significant relationship among a college graduate’s IQ x1, score on the verbal section of the SAT x2, and income for the first year following graduation from college y. Predict the income of a college graduate whose IQ is 120 and verbal SAT score is 650. The regression equation is