Fundamentals of Statistics (5th Edition)
5th Edition
ISBN: 9780134508306
Author: Michael Sullivan III
Publisher: PEARSON
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Textbook Question
Chapter 4.1, Problem 20AYU
In Problems 17–20, (a) draw a
20.
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Fill in the following table and calculate the correlation coefficient.
Consider a two-dimensional scatterplot representing the relationship between two continuous variables. If the correlation coefficient is -1, then:
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b. All points lie in a straight line with an unknown negative slope.
c. All points do not lie in a straight line but the best fitting regression line has a slope of -1
d. There is a strong positive relationship between the two variables.
If x and y are two uncorrelated variables and u=x+y,
v =x - y, find the coefficient of correlation between u and v in terms of
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Chapter 4 Solutions
Fundamentals of Statistics (5th Edition)
Ch. 4.1 - What is the difference between univariate data and...Ch. 4.1 - The _____ variable is the variable whose value can...Ch. 4.1 - A _____ _____ is a graph that shows the relation...Ch. 4.1 - What does it mean to say two variables are...Ch. 4.1 - If r = _____, then a perfect negative linear...Ch. 4.1 - True or False: If the linear correlation...Ch. 4.1 - A _____ variable is a variable that is related to...Ch. 4.1 - True or False: Correlation implies causation.Ch. 4.1 - In Problems 912, determine whether the scatter...Ch. 4.1 - In Problems 912, determine whether the scatter...
Ch. 4.1 - In Problems 912, determine whether the scatter...Ch. 4.1 - In Problems 912, determine whether the scatter...Ch. 4.1 - NW Match the linear correlation coefficient to the...Ch. 4.1 - Match the linear correlation coefficient to the...Ch. 4.1 - Prob. 15AYUCh. 4.1 - Relation between Education and Birthrate? The...Ch. 4.1 - In Problems 1720, (a) draw a scatter diagram of...Ch. 4.1 - In Problems 1720, (a) draw a scatter diagram of...Ch. 4.1 - In Problems 1720, (a) draw a scatter diagram of...Ch. 4.1 - In Problems 1720, (a) draw a scatter diagram of...Ch. 4.1 - Name the Relation, Part I For each of the...Ch. 4.1 - Prob. 22AYUCh. 4.1 - The TIMMS Exam The Trends in International...Ch. 4.1 - Prob. 24AYUCh. 4.1 - NW An Unhealthy Commute The Gallup Organization...Ch. 4.1 - Credit Scores Your Fair Isaacs Corporation (FICO)...Ch. 4.1 - Height versus Head Circumference A pediatrician...Ch. 4.1 - American Black Bears The American black bear...Ch. 4.1 - Weight of a Car versus Miles per Gallon An...Ch. 4.1 - Hurricanes The data in the next column represent...Ch. 4.1 - CEO Performance The following data represent the...Ch. 4.1 - Bear Markets A bear market in the stock market is...Ch. 4.1 - Does Size Matter? Researchers wondered whether the...Ch. 4.1 - Prob. 34AYUCh. 4.1 - Weight of a Car versus Miles per Gallon Suppose...Ch. 4.1 - American Black Bears The website that contained...Ch. 4.1 - Draw Your Data! Consider the four data sets shown...Ch. 4.1 - Predicting Winning Percentage The ultimate goal in...Ch. 4.1 - Prob. 39AYUCh. 4.1 - Lyme Disease versus Drownings Lyme disease is an...Ch. 4.1 - Prob. 41AYUCh. 4.1 - Prob. 42AYUCh. 4.1 - Crime Rate and Cell Phones The linear correlation...Ch. 4.1 - Prob. 44AYUCh. 4.1 - Influential Consider the following set of data: a....Ch. 4.1 - Prob. 46AYUCh. 4.1 - Prob. 47AYUCh. 4.1 - Prob. 48AYUCh. 4.1 - What does it mean to say that the linear...Ch. 4.1 - What does it mean if r = 0?Ch. 4.1 - Prob. 51AYUCh. 4.1 - Prob. 52AYUCh. 4.1 - Explain the difference between correlation and...Ch. 4.1 - Suppose that two variables, x and y, are...Ch. 4.2 - The difference between the observed and predicted...Ch. 4.2 - If the linear correlation between two variables is...Ch. 4.2 - Prob. 3AYUCh. 4.2 - Prob. 4AYUCh. 4.2 - For the data set a. Draw a scatter diagram....Ch. 4.2 - For the data set a. Draw a scatter diagram....Ch. 4.2 - In Problems 712: a. By hand, draw a scatter...Ch. 4.2 - In Problems 712: a. By hand, draw a scatter...Ch. 4.2 - Prob. 9AYUCh. 4.2 - In Problems 712: a. By hand, draw a scatter...Ch. 4.2 - In Problems 712: a. By hand, draw a scatter...Ch. 4.2 - In Problems 712: a. By hand, draw a scatter...Ch. 4.2 - NW Income and Education In Problem 15 from Section...Ch. 4.2 - You Explain It! Study Time and Exam Scores After...Ch. 4.2 - Age Gap at Marriage Is there a relation between...Ch. 4.2 - You Explain It! CO2 and Energy Production The...Ch. 4.2 - NW An Unhealthy Commute (Refer to Problem 25,...Ch. 4.2 - Credit Scores (Refer to Problem 26, Section 4.1.)...Ch. 4.2 - Height versus Head Circumference (Refer to Problem...Ch. 4.2 - Prob. 20AYUCh. 4.2 - Weight of a Car versus Miles per Gallon (Refer to...Ch. 4.2 - Hurricanes (Refer to Problem 30, Section 4.1) The...Ch. 4.2 - Cola Consumption vs. Bone Density Example 5 in...Ch. 4.2 - Attending Class The following data represent the...Ch. 4.2 - CEO Performance (Refer to Problem 31 in Section...Ch. 4.2 - Bear Markets (Refer to Problem 32, Section 4.1) A...Ch. 4.2 - Male vs. Female Drivers (Refer to Problem 34,...Ch. 4.2 - Graduation Rates Go to...Ch. 4.2 - Putting It Together: Housing Prices One of the...Ch. 4.2 - Putting It Together: Smoking and Birth Weight It...Ch. 4.2 - What is a residual? What does it mean when a...Ch. 4.2 - Explain the phrase outside the scope of the model....Ch. 4.2 - Explain what each point on the least-squares...Ch. 4.3 - The _____ _____ _____, R2, measures the proportion...Ch. 4.3 - Total deviation = _____ deviation + _____...Ch. 4.3 - Match each coefficient of determination to a...Ch. 4.3 - NW The Other Old Faithful Perhaps you are familiar...Ch. 4.3 - Concrete As concrete cures, it gains strength. The...Ch. 4.3 - Prob. 7AYUCh. 4.3 - Problems 712 use the results from Problems 2530 in...Ch. 4.3 - Prob. 9AYUCh. 4.3 - Problems 712 use the results from Problems 2530 in...Ch. 4.3 - Problems 712 use the results from Problems 2530 in...Ch. 4.3 - Prob. 12AYUCh. 4.3 - Weight of a Car versus Miles per Gallon Suppose...Ch. 4.3 - American Black Bears Suppose that we find a bear...Ch. 4.3 - Putting It Together: Exam Scores The data below...Ch. 4.3 - Sullivan Survey II Go to...Ch. 4.4 - What is meant by a marginal distribution? What is...Ch. 4.4 - Refer to Table 8. Is constructing a conditional...Ch. 4.4 - Prob. 3AYUCh. 4.4 - Explain the idea behind Simpsons Paradox.Ch. 4.4 - In Problems 5 and 6, a. Construct a frequency...Ch. 4.4 - In Problems 5 and 6, a. Construct a frequency...Ch. 4.4 - Made in America In a recent Harris Poll, a random...Ch. 4.4 - Desirability Traits In a recent Harris Poll, a...Ch. 4.4 - NW Party Affiliation Is there an association...Ch. 4.4 - Prob. 10AYUCh. 4.4 - Health and Happiness The General Social Survey...Ch. 4.4 - Happy in Your Marriage? The General Social Survey...Ch. 4.4 - Prob. 13AYUCh. 4.4 - Treating Kidney Stones Researchers conducted a...Ch. 4.4 - Sullivan Survey II Go to...Ch. 4 - Basketball Spreads In sports betting, Las Vegas...Ch. 4 - Fat and Calories in Cheeseburgers A nutritionist...Ch. 4 - Prob. 3RECh. 4 - Prob. 4RECh. 4 - Prob. 5RECh. 4 - a. Draw a scatter diagram treating x as the...Ch. 4 - Use the results from Problems 2 and 4 to compute...Ch. 4 - Prob. 8RECh. 4 - Prob. 9RECh. 4 - New versus Used Car Satisfaction Are you more...Ch. 4 - Unemployment Rates Recessions are an economic...Ch. 4 - Prob. 12RECh. 4 - Prob. 13RECh. 4 - Prob. 1CTCh. 4 - Use the data from Problem 1. a. Find the...Ch. 4 - Use the results from Problems 1 and 2 to compute...Ch. 4 - The following data represent the speed of a car...Ch. 4 - Prob. 5CTCh. 4 - Prob. 6CTCh. 4 - Consider the following contingency table, which...Ch. 4 - What would you say about a set of quantitative...Ch. 4 - If the slope of a least-squares regression line is...Ch. 4 - What does it mean if a linear correlation...
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- Find the equation of the regression line for the following data set. x 1 2 3 y 0 3 4arrow_forwardThere is a negative correlation between the number of flu cases reported each week throughout the year (call this variable X) and the amount of ice cream (call this variable Y) sold that week. The most plausible explanation for this association is: Group of answer choices c. changes in X and Y are due to a common response to other variables: winter months see low ice cream sales and simultaneously high numbers of flu cases. Vice versa for summer months. a. X causes Y: Sick people don’t eat ice cream. Thus, more flu cases results in less ice cream consumption. b. Y causes X: Eating a lot of ice cream causes people to get sick. Thus, the more ice cream consumed the more flu cases. d. the association between X and Y is purely coincidental: It is a complete fluke.arrow_forwardSuppose that the correlation r between two quantitative variables was found to be r = 0. This means that: (a) there is a strong linear relationship between the two variables. (b) there is no linear relationship between the two variables. (c) there is a strong relationship between the two variables. (d) there is no relationship between the two variables. (e) none of the above.arrow_forward
- If the correlation coefficient obtained from data pairs of variables X and Y is 0.98 the strength and direction of the relationship between X and Y is which of the following: (i) very strong positive (ii) moderate positive (iii) moderate negative (iv) very weak negativearrow_forward1. If someone owns an electric car it is represented by a one and if they don’t it is represented by a zero. If someone owns an electric car and their yearly salary in pounds for four people are (0,80000), (0, 17000), (0, 37000) and (1, 58000) calculate the correlation coefficient.arrow_forwardA housing developer in a certain subdivision wants to determine if the number of family members and the number of bedrooms are linearly related. A sample of 10 families in a certain subdivision revealed the following observations. Number of Family Members (X) 3 1 3 7 4 5 2 5 6 3 Number of Bedrooms (Y) 1 2 3 4 2 1 5 4 6 2 Determine the strength of the relationship of variable x and y by finding the value of correlation coefficient and coefficient of determination. Then, Interpret the results.arrow_forward
- 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.arrow_forward2)arrow_forwardA study conducted by students in an AP Psychologyclass at South Kent School in Connecticut discovereda correlation of –0.38 between hours of sleep (x) andGPA (y). If we change the variable on the horizontal axisto hours awake (24 - x), but make no change to theGPA data, which of the following would be true aboutthe new scatterplot?A) It slopes down, and the correlation is -0.38.B) It slopes down, and the correlation is +0.38.C) It slopes up, and the correlation is -0.38.D) It slopes up, and the correlation is +0.38.E) None of the above choices is correct.(Source: http://www.cardinalnewsnetwork.org/south-kent-community/sleep-study-sks-style/)arrow_forward
- 1) You compare the height and weight of 5 adult women. You get the following results: height 60 67 62 70 66weight 119 143 131 155 136(a) Construct a scatter plot of height (x) vs. weight (y) (b) Calculate the following (show your work for SScp): SSx SSy SScp ̄x ̄y(c) Calculate the correlation coefficient (r)arrow_forwardChild Mortality vs CO2 Emissions 2.5 1 0.5arrow_forward1.) You compare the height and weight of 5 adult women. You get the following results: height 60 67 62 70 66 weight 119 143 131 155 136 1A.) Construct a scatter plot of height (x) vs. weight (y) 1B.) Calculate the following (show your work for SScp): SSx SSy SScp ̄x ̄y 1C.) Calculate the correlation coefficient (r) 2.) Use the information from problem 1. Perform a complete test of the hypothesis that the population correlation coefficient (ρ) is 0. Show all steps (note - obviously this should be a one sided test! Make sure you know why!). 3.) Now let's assume you wanted to predict weights from heights. In other words, now let's use the same data from problem (1) and do a regression instead. 3A.) Calculate b0 and b1. 3B.) Carefully draw your least square regression line on the plot you made in 1(a). (Don't just “sketch”, be a little careful). 4(a) Now do a significance test of H0: β1 = 0. Show all your…arrow_forward
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