The correlation coefficient, R, measures a) whether or not a scatterplot shows an interesting pattern. b) whether or not a cause-and-effect relation exists between two variables. c) the strength and direction of the linear relation between two variables.
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- A statistical program is recommended. A study of emergency service facilities investigated the relationship between the number of facilities and the average distance traveled to provide the emergency service. The following table gives the data collected. Number of Facilities Average Distance (miles) 9 1.67 11 1.11 16 0.84 21 0.62 27 0.50 30 0.47 (a) Develop a scatter diagram for these data, treating average distance traveled as the dependent variable. 35 1.8T 1.8 1.8 1.6 1.6 1.6- 30 1.4 1.4 1.4 25 1.2 1.2 1.2 1. 1. 1. 20 0.8 0.8 0.8 15 0.6 0.6 0.6 .. 0.4 0.4 0.4 10 0.2 0.2 0.2 0. 0. 0. 0. 0.2 0.4 0.6 0.8 1. 1.2 1.4 1.6 1.8 10 15 20 25 30 35 5 10 15 20 25 30 35 5 10 15 20 25 30 35 Distance Number Number Number (b) Does a simple linear regression model appear to be appropriate? Explain. O No, the scatter diagram suggests that there is a curvilinear relationship. O No, the scatter diagram suggests that there is no relationship. O Yes, the scatter diagram suggests that there is a linear…A researcher found that sales of televisions and lawn fertilizer have been increasing over the past 12 years. The sales had a strong positive linear correlation, but no evidence could be found to support a cause-and-effect relationship. Rather, this would have been purely coincidental. This is an example of a) an accidental cause-and-effect relationship b) a cause-and-effect relationship O c a reverse cause-and-effect relationship O a presumed cause-and-effect d) relationshipA data set includes weights of garbage discarded in one week from 62 different households. The paired weights of paper and glass were used to obtain the results shown to the right. Is there sufficient evidence to support the claim that there is a linear correlation between weights of discarded paper and glass? Use a significance level of α=0.05. Click here to view a table of critical values for the correlation coefficient. LOADING... Correlation matrix: Variables Paper Glass Paper 1 0.3098 Glass 0.3098 1 Determine the null and alternative hypotheses. H0: ρ ▼ greater than> less than< equals= not equals≠ nothing H1: ρ ▼ less than< equals= greater than> not equals≠ nothing (Type integers or decimals. Do not round.) Identify the test statistic, r. r=nothing (Round to three decimal places as needed.) Identify the critical value(s). (Round to three decimal places as needed.)…
- A statistical program is recommended. A study of emergency service facilities investigated the relationship between the number of facilities and the average distance traveled to provide the emergency service. The following table gives the data collected. Average Number of Facilities Distance (miles) 1.67 11 1.11 16 0.82 21 0.62 27 0.50 30 0.47 (a) Develop a scatter diagram for these data, treating average distance traveled as the dependent variable. 1.8 1.8 35 1.8- 1.6 1.6 1.6 1.4 30 1.4 1.4 a 1.2 1.2 25 1.2 1. 1. E 1. 0.8 20 0.8 0.8- 0.6 0.6- 15 0.6- 0.4- 0.4- 0.4 0.2 10 0.2- 0. 5 0.2 10 15 20 25 30 35 0. 5 0. 10 15 20 25 30 35 0. 0.2 0.4 0.6 0.8 1. 1.2 1.4 1.6 1.8 10 15 20 25 30 35 Number Number Distance Number (b) Does a simple linear regression model appear to be appropriate? Explain. O Yes, the scatter diagram suggests that there is a linear relationship. O No, the scatter diagram suggests that there is a curvilinear relationship. O No, the scatter diagram suggests that there is…(4) An emergency service wishes to see whether a relationship exists between the outside temperature and the number of emergency calls it receives for a 7-hour period temperature and y = number of calls. 68 74 82 88 93 99 101 7 4 8. 10 11 11 13 a) Draw a scatter diagram b) Based on the diagram estimate the correlation coefficient, positive, negative, and explain in words this relation.C. Give an example for each of the following: a. Two variables in which you have enough reasons to explain their cause-and-effect relationship. State the independent (x) and dependent variable (y). Provide also description of the cause-and-effect relationship. b. Two variables from which a considerable possible nature of linear correlation may exist. Explain briefly the possible nature of the relationship. State both variables and give a short description of their relationship.
- The data provides information on life expectancy and the number of televisions per thousand people in a sample of 22 countries, as reported by the world almanac and book of facts 2006 A. Describe the Direction and strength of the correlation between the two variables B. Because of the association between the variables, someone might mistakenly conclude that simply sending televisions to the countries with the lower life expectancies would cause their inhabitants to live longer. Comment on this argument and the reason televisions are likely associated with longer life expectancies C. In general, if two variables are strongly associated, does it follow there must be a cause and effect relationship between them? ExplainTable of critical values shown to the right. Is there sufficient evidence to A data set includes weights of garbage discarded in one week from 62 different hou support the claim that there is a linear correlation between weights of discarded pa Correlation matrix: Variables Paper Glass Click here to view a table of critical values for the correlation coefficient. |Раper 10.3890 Glass 0.3890 1 a = .05 a = 01 4 .950 .990 .878 .959 Determine the null and alternative hypotheses. 6 .811 .917 7 .754 .875 Ho: P 8. .707 .834 9. .666 .798 (Type integers or decimals. Do not round.) 10 .632 .765 11 .602 .735 Identify the test statistic, r. 12 .576 .708 13 .553 .684 r = (Round to three decimal places as needed.) 14 .532 .661 15 .514 .641 Identify the critical value(s). (Round to three decimal places as needed.) 16 .497 .623 17 .482 .606 O A. There is one critical value at r= 18 .468 .590 19 .456 .575 B. There are two critical values at r = ± 20 .444 .561 25 .396 .505 State the conclusion. 30 .361…Jim and Larry run a soup stand. The data below represents the sales of soup that they had on 8 randomly selected days, along with the high temperature on that day. a) Create a scatter diagram for this data set and comment on whether there is a positive or negative relationship between these variables.b) Calculate the correlation coefficient between temperature and sales.c) Does a linear relationship exist between these variables? Explain to me why or why not this is the case.d) Using excel, calculate the least squares regression equation for this data set. e) Using your equation, predict the soup sales on a day where the temperature is 29 degrees.f) Interpret the slope of this equation.g) Can we use this data set and regression equation to predict the sales on a day when the average temperature is 102 degrees? Why or why not?h) What is the R-squared for this equation? How do you interpret that R-squared?
- Does a major league baseball team's record during spring training indicate how the team will play during the regular season? Over a six-year period, the correlation coefficient between a team's winning percentage in spring training and its winning percentage in the regular season is . Shown are the winning percentages for the American League teams during a season. Team SpringTraining RegularSeason Team SpringTraining RegularSeason Baltimore Orioles 0.409 0.424 Minnesota Twins 0.492 0.542 Boston Red Sox 0.426 0.588 New York Yankees 0.579 0.559 Chicago White Sox 0.411 0.535 Oakland A's 0.690 0.468 Cleveland Indians 0.578 0.492 Seattle Mariners 0.492 0.379 Detroit Tigers 0.578 0.459 Tampa Bay Rays 0.722 0.601 Kansas City Royals 0.540 0.461 Texas Rangers 0.640 0.491 Los Angeles Angels 0.724 0.619 Toronto Blue Jays 0.442 0.533 a. What is the correlation coefficient between the spring training and the regular season winning percentages…Online clothes An online clothing retailer keeps trackof its customers’ purchases. For those customers who signed up for the company’s credit card, the com-pany also has information on the customer’s Age and Income. A random sample of 500 of these customers shows the following scatterplot of Total Yearly Pur-chases by Age:The correlation between Total Yearly Purchases and Age isr = 0.037. Summary statistics for the two variables are: a) What is the linear regression equation for predictingTotal Yearly Purchase from Age?b) Do the assumptions and conditions for regressionappear to be met?c) What is the predicted average Total Yearly Purchasefor an 18-year-old? For a 50-year-old? d) What percent of the variability in Total Yearly Pur-chases is accounted for by this model? e) Do you think the regression might be a useful one forthe company? Explain.A sample of 548 ethnically diverse students from Massachusetts were followed over a 19-month period from 1995 and 1997 in a study of the relationship between TV viewing and eating habits. For each additional hour of television viewed per day, the number of fruit and vegetable servings per day was found to decrease on average by 0.14 serving. (a) For this study, what is the dependent variable? O location of students O number of fruit and vegetable servings per day O number of non fruit or vegetable servings per day O number of hours of television viewed per day year What is the independent variable? O location of students O number of fruit and vegetable servings per day O number of non fruit or vegetable servings per day O number of hours of television viewed per day O year (b) Would the least-squares line for predicting number of servings of fruits and vegetables using number of hours spent watching TV as a predictor have a positive or negative slope? Explain. O The slope of the least…
