Fundamentals of Statistics (5th Edition)
5th Edition
ISBN: 9780134508306
Author: Michael Sullivan III
Publisher: PEARSON
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Chapter 4.1, Problem 20AYU
In Problems 17–20, (a) draw a
20. 
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Suppose that the index model for two Canadian stocks HD and ML is estimated with the following results:
RHD =-0.03+2.10RM+eHD
R-squared =0.7
RML =0.06+1.60RM+eML
R-squared =0.6
σM =0.15
where M is S&P/TSX Comp Index and RX is the excess return of stock X.
What is the covariance and the correlation coefficient between HD and ML?
If a sample of 25 pairs of data yields a correlation coefficient, r, of 0.390 and the scatterplot displays a linear trend, can you use the regression equation to make predictions, assuming your x-values are within the domain of the data set? Choose your answer from the multiple choice answers below
A.) Yes, because rcrit = 0.396 and the regression coefficient, r, is less than this value.
B.) Yes, because rcrit = 0.381 and the regression coefficient, r, is greater than this value.
C.) No, because rcrit = 0.381 and the regression coefficient, r, is greater than this value.
D.) No, because rcrit = 0.396 and the regression coefficient, r, is less than this value.
Suppose that the index model for two Canadian stocks HD and ML is estimated with the following results:
RHD =-0.03+2.10RM+eHD
R-squared =0.7
RML =0.06+1.60RM+eML
R-squared =0.6
σM =0.15
where M is S&P/TSX Comp Index and RX is the excess return of stock X.
What is the covariance and the correlation coefficient between HD and ML?
For portfolio P with investment proportion of 0.4 in HD and 0.6 in ML, calculate the systematic risk, non-systematic risk, and total risk of P.
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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Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.Similar questions
- If the value of the Pearson correlation is r = 0, then all data points on a scatterplot would fall on a straight line with an intercept of zero. True Falsearrow_forward1. If the number of COVID 19 cases in various states of a country are strongly negatively correlated with the literacy rates, then what should be a likely value of the correlation coefficient? A. 2.11 B. 1.12 C. -5.09 D. -0.92 In problem 1, what should not be a possible line of best fit? A. y = -10 - 7x B. y = 10 - 7x C. y = -5 + 4x D. y = 5 - 4xarrow_forwardSuppose that X and Y are unknowns with E(X) = 10, Var (X) = 4, E(Y)=12 and Var (Y) = 100. In addition, suppose that the correlation coefficient of X and Y is .6. Then what is the variance of X-Y?arrow_forward
- Question 2. In a study on television violence and aggression, researchers measured the TV viewing habits of 3rd grade males (preference for violent TV shows) and their levels of aggression; and then revisited the men 10 years later and measured the same variables. They found these zero-order correlations: Aggression G3 TV G3 Aggression Y18 Aggression G3 1.0 .65 .45 TV G3 1.0 .5 Aggression Y18 1.0 What is going on if the partial correlation of TV G3 and AGG G3 with AGG Y18 held constant is .02?arrow_forwardCalculate the linear correlation coefficient for the data below. X -14 -12 -5 -8 -10 -11 -9 -7 -6 -13 Y -7 -5 12 4 1 -3 2 6 9 -5arrow_forwardWhat would be an example of an impossible correlation coefficient? In other words, give a value of r that would lead you to suspect that the researcher made a mistake.arrow_forward
- If there is a very strong correlation between two variables, then the correlation coefficient must beA. any value greater than 1.B. much smaller than 0, if the correlation is negative.C. much larger than 0, regardless of whether the correlation is negative or positive.D. None of these.arrow_forwardIf the correlation coefficient for a set of paired variables X and Y is negative, then there exists ____________________ between X and Y.arrow_forwardQuestion 7 Identify the most likely type of causal relationship between each of the following pairs of variables. Assume that a strong positive correlation has been observed between the two variables, with the first one being the independent variable. DDDD reverse cause and effect accidental relationship presumed relationship cause and effect 1. 2. 3. 4. the number of police officers, the number of crimes the UV index rating, the rate of developing a sunburn without any sunscreen protection on the skin sales of ice cream cones at Cold Stone Creamery, revenue at Wild Waterworks swimming pool at Confederation Park ticket sales for the school play, "Broadway Titans 2" revenue fromarrow_forward
- Imagine a study where all our data (x, y) falls perfectly on a flat and straight horizontal line. If we calculated the correlation coefficient r for this data, what would it be? What would that mean for our hypotheses?arrow_forwardSuppose you are given the following data involving weekly sales and test scores supposedly designed to pick out the "best" salespersons. Salesperson Test Score (x) Weekly Sales (y)-in thou. of dollars 1. Mr. Amber 4 $6 2. Mr. Archer 2 $12 3. Ms. Smith 3 $4 4. Mr. Malcolm 6 $8 5. Ms. Goodwin 10 $11 Calculate the correlation coefficient, r. Calculate the coefficient of determination, r2; of non determination. Interpret them. Suppose you wish to test for the significance of r, the correlation coefficient, in problem 2a, given that n=5. Using the .01 level of significance, test the hypothesis that r is not different from 0 versusthe hypothesis that r is different from 0 (remember r can be between -1 and +1) in the population. Do you accept or reject the null hypothesis?arrow_forwardQuestion 1For the following give:• Description of the correlation (negative or positive).• The appropriate critical value for ? identified from ?-table.• The comparison of the linear correlation coefficient to that identified in (b).• Decision on the null hypothesis (H0) and the conclusion based on the decision.a) ? = 10, ? = 0.149b) ? = 60, ? = −0.765arrow_forward
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