C784 MODULE 6 CORRELATION & REGRESSION| 77 QUESTIONS AND ANSWERS.

lurking variable A variable that is not included in an analysis but that is related to two (or more) other associated variables which were analyzed. simple linear regression the prediction of one response variable's value from one explanatory variable's value Simpson's Paradox A counterintuitive situation in which a trend in different groups of data disappears or reverses when the groups are combined. degree The largest exponent in a mathematical expression or equation. causation A relationship of cause and effect between two or more variables. linear interpolation Estimation using the linear regression equation is between known data points. association A pattern or relationship between two variables. coordinate plane A tool for graphing consisting of a horizontal x-axis and a vertical y-axis. regression equation An equation used to model the relationship between two quantitative dependent and independent variables. scatterplot A graph that uses dots on a coordinate plane to show the relationship between variables. Regression Analysis a statistical tool that quantifies the relationship betwn a response variable and one or more explanatory variables least squares A technique for finding the regression line. slope-intercept form A common format for the equation of a line: y = mx + b, where m is the slope and b is the y-intercept. regression line The line of best fit to show the relationship between variables, the one that minimizes distance from each data point to the line. A linear regression equation takes the following form: y = mx^2 + b. True or False? false. This is not the form that a linear regression equation takes. Linear regression is always of degree 1, so the exponent of 2 associated with the x makes this a non-linear equation. A linear regression "best-fit-line" can be estimated using least squares. True or False? true. Least squares estimation is the most common technique used to estimate the best-fit-line in linear regression. Linear extrapolation is always a reliable method of prediction. True or False? false. Extrapolation assumes that the linear pattern of the data will continue outside of the range of data points. This may not always be the case and therefore may not always be a reliable method of prediction. Linear interpolation is a technique used to make a prediction that falls between known data points. True or False? true. Linear interpolation is a technique used to make a prediction that falls between known data points, using the linear regression equation. Least squares estimation is a technique for predicting future data values. True or False? false. Least squares estimation is a technique used to estimate the best-fit-line in linear regression. EXTRAPOLATE Using information from a data set to make predictions about data outside of the original set. POPULATION An entire pool from which a sample is drawn. SAMPLE SIZE Statistics: the number of individuals measured or observed in a study. Probability: number of possible outcomes in a trial or experiment. Extrapolation is always inappropriate. True or False? false. There are applications of extrapolation, and times in which it is necessary. Be mindful of the situation and try to avoid inappropriate extrapolation by considering the context. Which of the following statements is most appropriate with regards to representative samples? a. The risk of non-representative sample decreases as sample size increases. b. The risk of non-representative sample size decreases as sample size decreases. c. The risk of non-representative sample size increases as sample size increases. d. The sample size has no bearing on whether or not the sample size is representative a. In general, the risk of non-representative sample decreases as sample size increases. Which of the following qualities of a sample help ensure the accuracy of any analysis, including a regression analysis? a. a large sample b. a representative sample c. Both a and b c. When conducting a study, it is important to use a large, representative sample. Which of the following improves a study's reliability as it increases? a. Correlation coefficient b. Regression equation slope c. Sample size d. Simpson's Paradox c. Small study populations can impact the reliability of regression analysis. Nurses need to be aware of the study size when attempting to perform a regression analysis or interpret a study based on small study size. Analysis of the scatterplot below suggests that as testosterone levels increased, blood pressure decreased. What problem in regression is evident in this analysis? The Association is Not Causation This analysis is obviously missing a lurking variable which, in this case, is obesity. It is nonsense to try to estimate a patient's blood pressure based on testosterone level. Therefore, the association is not a causation. From the scatterplot below, if the trend line would be extended indefinitely, it would correspond with a patient's systolic blood pressure in excess of 250mmHg. What pitfall in regression analysis is evident in this chart? Inappropriate Extrapolation It is obvious that blood pressure cannot go indefinitely high, so therefore it would be inappropriate to extrapolate beyond the range of the study. This analysis suffers from inappropriate extrapolation. What factor is most important to obtain a correct conclusion when performing regression analysis? Large Sample Size With a greater sample size, the more likely to come to a correct conclusion. Through what method can you identify if missing data is skewing the results of the study? Obtain basic statistics for the entire population and compare those with the sample being studied. While it is difficult to identify if missing data is skewing the results of the study, one approach is to obtain basic statistics for the entire population and compare those with the sample being studied. In what form is a simple linear regression equation usually written? slope-intercept A simple linear regression equation is usually written in slope-intercept form Which of the following is true about simple linear regression? Simple linear regression is usually written in the form y= mx + b. Which of the following situations does NOT prevent an accurate regression analysis from being performed? the relationship between the explanatory and response variable is linear In simple linear regression, the relationship between the explanatory and response variable is expected to be linear, so a linear relationship would not prevent an accurate regression analysis from being performed. Which of the following needs to be true to perform a linear regression analysis? there needs to be a linear relationship between the two variables The correct answer is c. To perform a linear regression analysis, there needs to be a linear relationship between the two variables. Otherwise, there can be no effective "line-of-best-fit" to model the relationship. A drug company is testing what dosage works best on patients of various ages. The study includes children aged 5-18. It is found that there is a fairly strong, positive correlation between the age of the patient and the proper dosage. Can we solve for a 45-year-old patient to determine what dosage he should take? Why or why not? No, this would be inappropriate extrapolation This is inappropriate extrapolation, as the study only examined the changes in necessary dosage for people between the ages of 5-18, and tells us nothing about what dosage a 45-year-old would need. Which of the following best describes a situation in which there is too small of a sample size A presidential election poll asks 3 people who they are voting for president. A presidential election poll that only asks three people who they are voting for president is an example of a sample size that is too small. You can not determine much about the general populace from three people. Can you perform a simple, linear regression on an association that is not a correlation no. While regression analysis can be performed on a nonlinear association, this would not be a "simple, linear regression." A study is examining the correlation between a person's height as an adult, and their height as a teenager. For the sample, the statistician decides to use the set of all professional basketball players. What is the problem with this study? This is not a representative sample. Professional basketball players are much taller than the average person, and therefore it would be difficult to draw a conclusion about an average person's height from a group of professional basketball players' data. When performing a linear regression analysis, what role does a least squares estimate play? A least-squares estimate will find the line-of-best-fit that most closely models the existing data. The step to performing linear regression is 1. Collect the data 2. plot the data on a Scatterplot 3. Add the LINE OF BEST FIT 4. Perform Linear Regression Analysis 1. Collect the data Be sure to measure the relationship between to two quantitative entities. For example, we can measure the relationship between height and weight of people in a sample. 2. plot the data on a Scatterplot Each dot on the scatterplot represents one person from our group. The dot's x-value corresponds with that person's weight and the dot's y-value corresponds with that person's height 3. Add the LINE OF BEST FIT This line, also known as the trendline or regression line, is the line that most closely models the data. 4. Perform Linear Regression Analysis Now, we have all of the information we need to perform a linear regression analysis. Use the line of best fit to make estimates and predictions about your data. Regression analysis is a good tool that will leave us with the best estimate possible, but it is important to remember that it is simply an estimate.