Quizzes 7, 8 & 9. Review. Cathy Poliak, Ph.D. (Department of Mathematics ReviewUniversity of Houston ) May 25, 2017

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1 Quizzes 7, 8 & 9 Review Cathy Poliak, Ph.D. cathy@math.uh.edu Department of Mathematics University of Houston May 25, 2017 May 25, / 19

2 Outline 1 Quiz 7 2 Quiz 8 3 Quiz 9 May 25, / 19

3 Example 1 Given the following data set give the scatterplot: x y May 25, / 19

4 Example 2 Given the following data set determine the correlation coefficient: x y May 25, / 19

5 Example 3 Which of the following is a true statement? a) The variable that is being predicted in regression analysis is the independent variable. b) If there is no correlation between the independent and dependent variables, then the value of the correlation coefficient must be -1. c) The correlation coefficient r is always between -1 and +1. d) The coefficient of determination can assume negative values. e) A negative correlation indicates that as values of x decrease, values of y will decrease. May 25, / 19

6 Example 4 The decline of salmon fisheries along the Columbia River in Oregon has caused great concern among commercial and recreational fishermen. The paper Feeding of Predaceous Fishes on Out-Migrating Juvenile Salmonids in John Day Reservoir, Columbia River (Trans. Amer. Fisheries Soc. (1991: )) gave the accompanying data on y = maximum size of salmonids consumed by a northern squaw fish (the most abundant salmonid predator) and x = squawfish length, both in mm. Use the following statistics to give the equation of the least squares regression line. x = , ȳ = , s x = , s y = , r = May 25, / 19

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8 Example 5 Suppose that you are given the following results. Find the correlation coefficient of the data. s x = 1.791, s y = , b = May 25, / 19

9 Example 6 Suppose you find that the correlation coefficient for a set of data is What is the coefficient of determination and what does it mean? a) 0.820; This means that we are 82.0% accurate with our prediction of the LSRL equation. b) 0.820; This means that 82.0% of the variation of y is explained by the LSRL of y on x. c) 0.672; This means that 67.2% of the variation of y is explained by the LSRL of y on x. d) 0.672; This means that we are 67.2% accurate with our prediction of the LSRL equation. May 25, / 19

10 Example 7 Suppose that the LSRL for the appraised value (in thousands of dollars) and number of rooms for houses in East Meadow, New York is ŷ = x Predict the price of a 10 room house (in thousands of dollars). a) b) c) d) e) May 25, / 19

11 Example 8 Determine the equation of the least squares line for the data: (51.00, 1.30), (48.75, 3.25), (52.50,.65), (46.50, 6.50), (45.00, 5.85), (41.25, 8.45), (43.50, 6.50). May 25, / 19

12 Example 9 Suppose you have the following data: a) Determine the LSRL. x y b) Find the residual value for x = 5. c) Give the residual plot. May 25, / 19

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15 Example 10 If the LSRL relating the independent variable x and the dependent variable y for a given problem is ŷ = 2x + 5, then an increase of 1 unit in x is associated with an increase of how many units in y? May 25, / 19

16 Example 11 The following two-way table describes the preferences in movies and fast food restaurants for a random sample of 100 people. McDonalds Taco Bell Wendy s Iron Man Dispicable Me Harry Potter a) What percent of people in the sample like the movie Dispicable Me? b) What percent of the Dispicable Me lovers also like McDonald s? May 25, / 19

17 Example 12 Identify the population of interest in the following situation: Ann Landers once asked her readers, "If you had it to do over again, would you have children?" About 10,000 readers responded and approximately 7,000 said no. a) The 10,000 people who responded. b) The population of the United States. c) People who read Ann Landers column. d) People who feel strongly about doing it over again. e) The 7,000 people who said no. May 25, / 19

18 Example 13 What are each defining? a) every possible sample of a given size has the same chance to be selected. b) the explanatory variable(s) in an experiment. c) gives each member of the population a known chance to be selected. d) successively smaller groups are selected within the population in stages. e) using extraneous factors to create similar groups. f) people who choose themselves for a sample by responding to a general appeal. g) choosing the individuals easiest to reach. h) directly holding extraneous factors constant. i) population is divided into similar groups and a SRS is chosen from each group. May 25, / 19

19 Example 14 Suppose you are interested in the effects on boys of different dosages of a new drug to treat ADHD. You set up an experiment to consider the factor of dosage with two levels (300 mg vs. 500 mg). Which would be the best choice for the different treatment groups of the experiment within each block? a) Three groups: no drug, 300 mg of new drug, 500 mg of new drug. b) Two groups: placebo drug and either 300 mg of new drug or 500 mg of new drug. c) Four groups: no drug, placebo drug, 300 mg of new drug, 500 mg of new drug. d) Three groups: placebo drug, 300 mg of new drug, 500 mg of new drug. e) Two groups: 300 mg of new drug and 500 mg of new drug. May 25, / 19

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21 Example 15 A game of chance is based on rolling a die two times in succession. The player wins if the larger of the two numbers is greater than 3. Which of the following situations would simulate 10 plays of this game? a) Choosing 60 digits from the random number table (discarding 0,7,8, and 9). b) Choosing 10 digits from the random number table (discarding 0,7,8, and 9). c) Choosing 10 pairs of single digits from the random number table (discarding 0,7,8, and 9). d) Choosing 2 single digits from the random number table (discarding 0,7,8, and 9). May 25, / 19