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C955 - Module 6: Correlation &
Regression Questions and Answers.
A researcher wants to know if there was a relationship between student age and desire to complete a college degree. To answer this question, the researcher used a local community college as the sampling frame and then used stratified sampling to get a sample of students from 18 to 80 years old. Based on the information given, is there any potential bias in this study? a Yes, because the sampling frame does not match the intended population of the question. b Yes, because the sampling method will not give a representative sample. c Yes, because a voluntary sample should have been used. d No, there will likely be no bias in this study. - Correct answer Yes, because the sampling frame does not match the intended population of the question. A researcher conducts an observational study and finds a correlation between managers' income and the number of college credits earned. The correlation coefficient was r=.85 with a regression equation of y=515x+12000. What can you say about the relationship between these variables? a There is an association between these variables b There is a causation between these variables. c There is no relationship between these variables. d There is not enough information to determine the relationship between the variables. - Correct answer There is an association between these variables What technique is used to estimate the profit margin for a production level of 25 thousand units, if a line of best fit is created to estimate profit margin for production levels between 20 to 39 thousand units? a Interpolation b Linearization
c Extrapolation d Internalization - Correct answer Interpolation What is the most appropriate definition of a scatterplot? a A graph that uses dots to demonstrate relationships between two categorical variables. b A graph where lines are shown to represent positive or negative trends. c A graph where the explanatory and response variables are plotted as ordered pairs. d A graph where a positive causation is always represented with dots forming a straight line. - Correct answer A graph where the explanatory and response variables are plotted as ordered pairs. What does a strong positive correlation between two variables suggest? a The explanatory variable is increasing and the response variable is decreasing b There is an association between the variables c There is a causation between the variables d Cannot determine - Correct answer There is an association between the variables {{ Scatterplot of distance from city center vs. rent. The linear equation for this scatterplot is y equals negative one hundred five ten thousandths times x plus ten and three hundred eighty one thousandths. }} Using the scatterplot Distance from City Center vs. Monthly Rent, how far can we expect an apartment to be from the city center if the monthly rent is $ 980? Round your answer to the nearest mile. a Around 54 miles b Around 55 miles c Around 56 miles d Around 57 miles - Correct answer Around 55 miles Which correlation coefficient suggests the weakest correlation? a −0. b −0. c 0.
When linear regression is used to show there is a linear association between two variables, we know the relationship is: a A causation b A correlation c Neither A nor B d Both A and B - Correct answer A correlation A restaurant owner wants to see if she can use low temperatures to boost soup sales at her restaurant. To study a possible relationship between temperature and soup sales, she collects data throughout the year on the temperature of a given day (ranging between 20 degrees F and 90 degrees F) and the amount of soup sold that day. She performs a linear regression and comes up with a least squares regression line of y=−1.64x+176.6 with r=−0.89 where x is the temperature (in degrees F) and y is the number of daily soup sales. How much soup should she expect to sell on a day that is 50 degrees F? Round to the nearest integer. a 177 orders of soup b 95 orders of soup c 259 orders of soup d 101 orders of soup - Correct answer 95 orders of soup The line of best fit is also known as: a The extrapolation line b The regression line c The interpolation line d None of the above - Correct answer The regression line If a trend appears in a large sample of data, the trend may not be replicated if the sample is broken up into smaller subsets. What is this effect known as? a Foster's Theorem b Bayes' Theorem c Simpson's Paradox d Consistency Construct - Correct answer Simpson's Paradox
A variable not included in the study that is related to the measured variables in a study is called a ____________. a Independent variable b Confounding variable c Dependent variable d Lurking variable - Correct answer Lurking variable Using the scatterplot below, what type of correlation is suggested? Scatterplot displaying data points distributed from lower left to upper right. Points are relatively close to one another. a No correlation b Weak negative positive c Moderate positive d Strong negative - Correct answer Moderate positive What must be true about the dots on a scatterplot if there is no correlation? a The dots are far away from the line of best fit. b The dots form no recognizable linear pattern. c The dots are evenly spaced around the graph. d The dots form a non-linear pattern. - Correct answer The dots form no recognizable linear pattern. What is (are) a potential problem(s) that can occur when attempting to use regression analysis? a Extrapolation b Lurking variables c Inappropriate sampling d A, B, and C - Correct answer A, B, and C A researcher conducts an experimental study and finds a correlation between salary and levels of experience. The correlation coefficient was r=.75 with a regression equation of y=515x+17500. What can you say about the relationship between these variables? a There is an association between these variables b There is a causation between these variables.
{{ Scatterplot displaying data points distributed along a line from upper left to lower right. The points fall relatively close to the line. }} a No correlation b Strong positive c Moderate negative d Moderate positive - Correct answer Moderate negative The following regression equation estimates total profit ($, measured in 1000s) based on x units produced (in 1000s) with data that was gathered from x=5 thousand units to x=35 thousand units. y=28.07+6.49x Determine the total profit (round to the nearest thousand) for a production level ( x ) of 25 thousand units. Round your answer to the nearest whole number. a $190, b $864, c $708, d $59,000 - Correct answer $190, What does a weak, negative correlation look like on a scatterplot? a The points follow closely along a line that moves down and to the right. b The points loosely follow a line that moves down and to the right. c The points follow closely along a line that moves up and to the right. d None of the above. - Correct answer The points loosely follow a line that moves down and to the right. Which of the following correlation coefficients describes a strong, positive correlation? a −0. b 0. c 0. d 0.21 - Correct answer 0. What should be true about the dots on a scatterplot once a line of best fit is drawn on the graph?
a The y should form a perfect line. b The distance each dot is from the line is equal. c The dot furthest from the line is always an outlier. d There should be approximately the same number of dots above and below the line. - Correct answer There should be approximately the same number of dots above and below the line. Consider the following equation, y+8x=−2. What is the y -intercept of a line with this equation? a − b 2 c 8 d −8 - Correct answer - When constructing a line of best fit, what must be minimized? a The vertical distances between that line and the data points. b The length of the line. c The correlation coefficient. d The p-value - Correct answer The vertical distances between that line and the data points. Which correlation coefficient suggests the strongest correlation? a −0. b −0. c 0. d 0.8 - Correct answer -0. The following table shows the performance of two airlines in two different cities. Is there a Simpson's Paradox occurring? Airline A Delayed Flights Airline A % Delayed Airline B Delayed Flights Airline B % Delayed Total Delayed Total % Delayed Los Angeles 62/559 11.10% 460/3450 13.30% 522/4009 13% San Diego 46/396 11.60% 30/221 13.60% 76/617 12.30% a No, because an equal number of flights departed from each city. b No, because it's clear from the data that Los Angeles has a higher rate of delayed flights.
Using the scatterplot above, what can we expect the percent increase in sales to be for an advertising expenditure of $ 165 thousand dollars? Round your answer to the nearest whole number. a Around 121 % b Around 139 % c Around 161 % d Around 198 % - Correct answer Around 139 % Using a line of best fit in slope-intercept form, y=mx+b , what must be true if there is a negative correlation? a m must be >. b m must be <. c Both m and b must be <. d Both m and b must have the opposite signs. - Correct answer m must be < Using the scatterplot below, estimate a possible correlation coefficient. {{ Scatterplot displaying data points distributed along a line from lower right to upper left. The points fall very close to the line. }} a 0. b 0. c −0. d −1 - Correct answer -0. A study is done relating computer programming aptitude to typing speed. In this case, what type of variable would the amount of computer programming experience be considered, if it was not measured in the study? a Independent variable b Confounding variable c Dependent variable d Lurking variable - Correct answer Lurking variable Which of the following statements is not a causal relationship?
a The higher the temperature in the oven, the faster the food will cook. b The more miles a car is driven, the more fuel is consumed. c The time of day determines when the sun will rise. d The faster a runner goes, the shorter time it will take to complete the race. - Correct answer The time of day determines when the sun will rise. {{ Percentage of people age 12 and older who watched a movie in the past month after viewing an ad for it targeted to their age group. For all ages, seven point five percent of the population watched a movie, for men, five point five percent watched a movie, nine point five percent of women watched a movie. For ages twelve to seventeen, five point five percent of the population watched a movie, four percent of men watched a movie and seven point five percent of women watched a movie. For ages eighteen to thirty-nine, seven point five percent of the population, five point five percent of men were depressed and nine percent of women watched a movie. For people between the ages of forty and fifty-nine, nine point five percent of the population watched a movie. Seven percent of men were depressed and twelve percent of women in that age bracket watched a movie. Of the people who were sixty years or over, five percent of t - Correct answer Can't tell from this display A car company wanted to study the relationship between the weight of the car and the car's average gas mileage, so they collected data from several of their cars and wrote down their weights and average gas mileage and plotted this data on the scatterplot below. The least squares regression line for the data is y=−0.0084x+48.8 , where x is the weight of the car in pounds and y is the average gas mileage (in miles per gallon). What is the predicted gas mileage for a car that weighs 2500 pounds? {{ Scatterplot illustrating Average Miles per Gallon and Weight of car in pounds. }} a) 29.18 miles per gallon b) 26.4 miles per gallon c) 27.8 miles per gallon d) 69.8 miles per gallon - Correct answer 27.8 miles per gallon Which of the following can help prevent Simpson's Paradox from occurring?
a) The point at which the line crosses the y-axis b) The value of y when x=0. c) Neither A nor B d) Both A and B - Correct answer Both A and B A college wants to study if there is a relationship between the health of students enrolled at the university and the number of credit hours they are enrolled in. They pull the student numbers of all students who used the gym in the last month and randomly selected 200. They then asked them how many hours he/she exercised in the last week and how many credit hours he/she is enrolled in and based on the data announced that the fewer credit hours a student is enrolled in at the university, the more hours per week the student exercises. Is this a valid conclusion? a) No, the sample is biased because the sample was too small. b) No, the sample is biased because only students at one university were questioned. c) No, the sampling frame in this study introduced bias because it is not representative of the population. d) Yes, the study was conducted in a fundamentally random way. - Correct answer No, the sampling frame in this study introduced bias because it is not representative of the population. Please select the correct definition for least squares. a) A method that minimizes the squared distances of data points from a line that captures the trend in paired data. b) The criteria by which the best-fit line is selected for paired data c) Both A & B d) None of the above - Correct answer Both A & B A researcher studied the effect of epidural steroid injections for chronic lumbar pain. Patients eligible for the study were randomly assigned to two groups. One group received an epidural injection with the steroid and a local anesthetic. The second group received an epidural injection with the local anesthetic. It was found that the epidural injection of the steroid produced a decrease in pain level among the patients. Can the researcher claim there is a causal relationship between the steroid injection and decreased pain level?
a) No, because this was an observational study so only an association is established. b) No, because the researcher controlled for all lurking variables. c) Yes, because this is a controlled experiment. d) Yes, because the researcher did not control for all lurking variables. - Correct answer Yes, because this is a controlled experiment. In the study of the effects of carbon emissions on global warming, the quantity of carbon released in the atmosphere is an explanatory variable for changes in global temperature (response variable). True or False? a) True b) False - Correct answer True Consider the following equation y=7.5x+9.3. What is the slope of a line with this equation? a) 9. b) 7. c) −9. d) −7.5 - Correct answer 7. Extrapolation is always appropriate. True or False? a) True b) False - Correct answer False In order to study the relationship between customer satisfaction and health plan type, an insurance company surveyed 100 members from each of its 5 health plans offered. What sampling method did they employ? a) Stratified b) Cluster c) Voluntary d) Simple Random - Correct answer Stratified Suppose there is a linear regression equation y=10+.5x where x is equal to money spent on advertising, measured in dollars, and y is equal to people visiting the company website. Which of the following is the correct interpretation of this slope?
a) For every increase by 1 pound in a car's weight, there will be a corresponding increase in the car's miles per gallon by 0.0084. b) For every increase by 1 pound in a car's weight, there will be a corresponding decrease in the car's miles per gallon by 0.0084. c) For every inc - Correct answer For every increase by 1 pound in a car's weight, there will be a corresponding decrease in the car's miles per gallon by 0.0084. {{ Scatterplot of widget production levels and incidence of defects. The points decrease on the y-axis as the value in the x-axis increase. The points can be connected in a nearly straight line. }} Which of the following is the best estimate of the correlation coefficient for the above scatterplot? a). b). c) −. d) −.3 - Correct answer -. {{ Scatterplot of Free Media vs. Quarterly Revenue. The linear equation for this scatterplot is y equals six point four nine five seven times x plus eighteen point five one four. y=6.4957x + 18.514 }} company is measuring the effect of free news media on its quarterly revenue. Using the scatterplot Free Media vs. Quarterly Revenue, what would the total quarterly revenue be for a year that had 21 news articles about Zenish Corp.? Round your answer to the nearest whole number. a) $154, b) $155, c) $153, d) $156,000 - Correct answer $155, Which of the following best describes a scatterplot that has a correlation coefficient of −0.3? a) The points loosely follow a line that is moving down and to the right. b) The points closely follow a line that is moving down and to the right. c) The points roughly move up and to the right, but do not follow that close to a linear pattern.
d) None of the above. - Correct answer The points loosely follow a line that is moving down and to the right. Consider the following equation, y+9x=−4. What is the y -intercept of a line with this equation? a) − b) − c) 9 d) 4 - Correct answer -
