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Dr. Holt is trying to determine which of her patients has the highest likelihood of developing depression. She calculates a linear regression equation using the scores on an anxiety measure, which are positively correlated with scores on a scale measuring depression. Dr. Holt converts patient D's anxiety score to a z score and predicts the z score for the depression scale to be 0.62. Is patient D's raw score for depression above or below the mean, and why? t is below the mean because the z score is negative. It is above the mean because the z score is negative. It is below the mean because the z score is positive. It is above the mean because the z score is positive.
It is above the mean because the z score is positive.
The standardized regression coefficient, which is equal to the Pearson correlation coefficient in a simple linear regression, is also called: alpha. standardized deviation prediction. beta weight. slope.
beta weight.
Regression is a type of statistical analysis that is most useful for: calculating z scores. predicting behavior. determining differences among three or more groups. finding the direction and strength of a relation between two variables.
predicting behavior.
The idea that patterns of extreme scores will balance out if sampling continues indefinitely or trends are looked at over the long run is known as: attrition. regression to the mean. history of the mean. correlation.
regression to the mean.
You want to predict your score on the statistics final exam using your average quiz performance for the semester. Which statistical technique is best for this type of analysis? bar graph correlation simple linear regression standardized z scores
simple linear regression
Clicker: regression to the mean
tendency of scores that are particularly high or low to drift towards he mean over time
Clicker: How is a correlation different from a regression analysis?
A regression enables us to make predictions, while a correlation describes relationships
According to the text, a good statistician examines the data points before proceeding and questions causality after the statistical analysis. What would that statistician be doing during each of these two phases of a regression analysis? - Before the test, examine the data for linearity, and after the test, consider confounding variables that might help to understand cause. - Before the test, examine the data for errors in the data set, and after the test, conjecture about possible causes using the ABC model. - Before the test, create appealing visual displays of data, and after the test, create theories about causation. - Before the test, check for outliers, and after the test, run an experiment to reveal causal relations.
Before the test, examine the data for linearity, and after the test, consider confounding variables that might help to understand cause.
_____ is a useful statistical analysis for predicting behavior, and _____ is a useful technique for finding the direction and strength of a relation between two variables. Psychometrics; correlation Correlation; regression Regression; correlation Psychometrics; regression
Regression; correlation
Assume a positive correlation is found between the number of hours students spend studying for an exam and their grade on the exam. If the regression equation for these data is calculated and the y intercept is 64, what conclusion can be drawn? - The standard error of the estimate is low. - The regression line crosses the x-axis at a score of 64. - The slope of the regression line is 64 when students do not study at all. - When students do not study at all, we would predict a score of 64 on the exam.
When students do not study at all, we would predict a score of 64 on the exam.
The statistic that describes the variability of a set of data points to the line of best fit in a linear regression is the standard: deviation. deviation of the estimate. error of the estimate. error.
error of the estimate.
If a person's score on a(n) _____ variable is known, the person's score on the _____ variable can be predicted using simple linear regression. dependent; independent independent; dependent scale; nominal nominal; z score
independent; dependent
Predicting an individual's grade on a final exam from two variables—for example, midterm test grade and percentage of classes attended—would involve the use of: bivariate regression. simple linear regression. multiple regression. nonlinear correlation.
multiple regression.
If the points on a scatterplot are all close to the regression line: the standard error of the estimate is small. r is a positive number. r is close to 0. the standard error of the estimate is large.
the standard error of the estimate is small.
Multiple regression differs from simple linear regression in that it: repeats a linear regression several times, which can improve the results by averaging. uses more than one independent variable to make predictions. uses higher-order polynomials to make predictions. employs the mathematical framework of calculus.
uses more than one independent variable to make predictions.
There is an extremely high negative correlation between altitude and the percentage of oxygen in the air. Is it correct to say that high altitudes cause low amounts of oxygen in the air based on a linear regression equation and the Pearson correlation coefficient? - Yes, because the regression analysis reveals a strong correlation. - Yes, because the correlation is negative. - No, because the correlation is negative. - No, because regression analysis does not imply causation.
No, because regression analysis does not imply causation.
There is an extremely high negative correlation between altitude and the percentage of oxygen in the air. Is it correct to say that high altitudes cause low amounts of oxygen in the air based on a linear regression equation and the Pearson correlation coefficient? Yes, because the regression analysis reveals a strong correlation. Yes, because the correlation is negative. No, because the correlation is negative. No, because regression analysis does not imply causation.
No, because regression analysis does not imply causation.
In looking at a graph of data, there seems to be a curved pattern, possibly because of the influence of a third variable. Should simple linear regression be used?
No, because the data are nonlinear.
an independent variable that makes a separate & distinct contribution
Orthogonal Variable
Dr. Holt is trying to determine which of her patients has the highest likelihood of developing depression. She calculates a linear regression equation using the scores on an anxiety measure, which are positively correlated with scores on a scale measuring depression. Dr. Holt converts patient D's anxiety score to a z score and predicts the z score for the depression scale to be -0.45. Is patient D's raw score for depression above or below the mean, and why?
It is below the mean because the z score is negative.
Good sleep habits have been correlated with many medical benefits, particularly in relation to blood pressure. A regression equation predicting an individual's blood pressure based on the number of hours of sleep each night results in a negatively sloped line of best fit. What does this statement mean? - People who get enough sleep at night are predicted to have low blood pressure, and people who do not get enough sleep at night are predicted to have high blood pressure. - Low amounts of sleep cause high blood pressure; high amounts of sleep cause low blood pressure. - There is no correlation between blood pressure and number of hours of sleep. - People who do not get enough sleep at night have low blood pressure, and people who get enough sleep at night probably have high blood pressure.
People who get enough sleep at night are predicted to have low blood pressure, and people who do not get enough sleep at night are predicted to have high blood pressure.
_____ refers to the accuracy of a prediction based on the regression equation or the amount of error that is eliminated compared to predictions based on the mean of the dependent variable. Predictive validity Orthogonal regression coefficient Reliability Proportionate reduction in error
Proportionate reduction in error
James thinks his new tutoring method, "Statistics 360," is highly effective compared to commercially available methods. He selects the worst students in his statistics class and tries his new tutoring strategy. Which statement describes a threat to the validity of his hypothesis even if the students do very well after the tutoring sessions? Instrumentation errors will skew the results. Regression to the mean is likely to occur. Confirmation bias is likely to occur. The testing sequence is a confounding factor.
Regression to the mean is likely to occur.
A statistics professor wants to determine whether class attendance can predict students' grades on their final exam. For his class of 16 students, he finds that the proportion reduction in error is 0.36. What would the adjusted r2 be for this data set? 0.64 0.36 0.31 0.09
0.36 0.31 0.09
A multiple regression analysis revealed the following equation relating the time (in hours) it takes to complete a puzzle based on the number and size of pieces: Ŷ = 1.6 + 0.02 (Xnumber of pieces) - 1.25 (Ysize of pieces). If a puzzle has 500 pieces, with a size value of 0.4 inch, how long will it take to complete?
11.1 hours
Susan is figuring the regression line for some data but needs help in first figuring the predicted value of Y. She knows that the slope is 2 and the intercept is 7. What is the predicted Y value for an X score of 7?
21
A multiple regression analysis revealed the following equation relating the time (in hours) it takes to complete a puzzle based on the number and size of pieces: Ŷ = 1.6 + 0.02 (Xnumber of pieces) - 1.25 (Ysize of pieces). If a puzzle has 1000 pieces, with a size value of 0.4 inch, how long will it take to complete?
21.1 hours
Body mass index can be predicted based on the amount of calories consumed by an individual due to the positive correlation between the two variables. When looking at the line of best fit for the linear regression, the data points are clustered close together. Predicted shyness based on the number of friendships a person has is also correlated, but the data points are more scattered around the line of best fit, showing a general negative correlation. Which has the higher predictive power, and why? - Calories consumed and body mass index, because it is a positive correlation. - Calories consumed and body mass index, because the variance is lower. - Shyness and number of friendships, because it is a negative correlation. - Shyness and number of friendships, because the variance is lower.
Calories consumed and body mass index, because the variance is lower.
If social anxiety is negatively correlated with the number of friendships a person has, which statement regarding the line of best fit, or regression line, would be true? - The line will start in the lower-left corner of the graph and end in the upper-right corner. - The line will start in upper-left corner of the graph and end in the lower-right corner. -Because the correlation is negative, a regression line cannot be drawn. - The y intercept will be negative.
The line will start in upper-left corner of the graph and end in the lower-right corner.
When drawing a line of best fit, it is "best" to use _____ point(s) of _____ value(s). 1; low 2; high and medium 3; low at least 2; low and high
at least 2; low and high
In the equation for a line in statistics, the _____ is the predicted amount of increase for Y when X is increased by 1, and the _____ is the predicted value for Y when X crosses the y-axis (X = 0). intercept; slope intercept; standard error slope; standard error slope; intercept
slope; intercept
If the points on a scatterplot are all far away from the regression line: the standard error of the estimate is small. r is a positive number. r is close to 0. the standard error of the estimate is large.
the standard error of the estimate is large.
If the points on a scatterplot are all far away from the regression line: -the standard error of the estimate is small. - r is a positive number. - r is close to 0. - the standard error of the estimate is large.
the standard error of the estimate is large.
