Chapter 16: Predicting Who’ll Win the Super Bowl: Using Linear Regression Test Bank MULTIPLE CHOICE What can be used as the basis for prediction? a t-test b Correlation c F-test d Cohen’s d ANS: REF: OBJ: COG: B PTS: DIF: Easy What Is Prediction All About? How prediction works and how it can be used in the social and behavioral sciences Knowledge What statistical technique is used to make predictions of future outcomes based on present data? a Analysis of variance b Repeated measures c Linear regression d Correlational analysis ANS: REF: OBJ: COG: C PTS: DIF: Easy What Is Prediction All About? How and why linear regression works when predicting one variable from another Knowledge Which of the following is used to illustrate the “best guess” as to the predicted Y variable score based on X? a Regression equation b Scatter plot c Standard error of the estimate d Regression line ANS: D PTS: DIF: Medium REF: The Logic of Prediction OBJ: How and why linear regression works when predicting one variable from another COG: Knowledge More accurate predictions are associated with a Correlations having higher absolute values b Correlations having lower absolute values c Correlations having higher values d Correlations having lower values ANS: A PTS: DIF: Medium REF: What Is Prediction All About? COG: Comprehension OBJ: How to judge the accuracy of predictions When computing a predicted value, you first a Add the slope to the value of the independent variable b Multiply the slope by the value of the independent variable c Add the constant to the value of the independent variable d Subtract the constant from the value of the independent variable ANS: REF: OBJ: COG: B PTS: DIF: Medium Drawing the World’s Best Line (for Your Data) How and why linear regression works when predicting one variable from another Comprehension When computing a predicted value, your second step is to a Multiply the slope by the independent variable b Add the slope to the independent variable c Add the intercept, or a, to the value of step one d Subtract the constant ANS: REF: OBJ: COG: C PTS: DIF: Medium Drawing the World’s Best Line (for Your Data) How and why linear regression works when predicting one variable from another Comprehension If the absolute value of your correlation coefficient is 1, your error in prediction will be _ a Very high b c d Unknown ANS: C PTS: REF: How Good Is Our Prediction? COG: Comprehension DIF: Medium OBJ: How to judge the accuracy of predictions If the absolute value of your correlation is very close to 0, your error in prediction will be _ a High b Low c Very low d ANS: A PTS: REF: How Good Is Our Prediction? COG: Comprehension DIF: Medium OBJ: How to judge the accuracy of predictions To predict one variable from another, you must first a Compute the mean b Compute the standard deviation c Compute the correlation d Compute the variance ANS: REF: OBJ: COG: C PTS: DIF: Medium Drawing the World’s Best Line (for Your Data) How and why linear regression works when predicting one variable from another Comprehension 10 In a scatter plot, if all data points were aligned along a 45° angle, your correlation would be _ a Of medium strength b Of weak strength c Perfect d ANS: C PTS: DIF: Medium REF: The Logic of Prediction OBJ: How and why linear regression works when predicting one variable from another COG: Knowledge 11 When adding additional predictors to a regression analysis, you should try to find predictors that are related to _ but not _ a The independent variable; the dependent variables b The dependent variable; the independent variables c The predictors; the outcome d All main effects; any interaction effect ANS: B PTS: DIF: Medium REF: The Big Rule When It Comes to Using Multiple Predictor Variables OBJ: What multiple regression is and why it is useful COG: Comprehension 12 What is another name for a regression line? a Line of best fit b Scatter plot line c Line graph d Line of the estimate ANS: A PTS: DIF: Medium REF: The Logic of Prediction OBJ: How and why linear regression works when predicting one variable from another COG: Knowledge 13 What is the distance between each data point and the regression line called? a Error of the estimate b Standard error of the estimate c Standard deviation d Standardized error ANS: A PTS: REF: How Good Is Our Prediction? COG: Knowledge DIF: Medium OBJ: How to judge the accuracy of predictions 14 Which of the following is the correct formula for linear regression? a = aY + b b = aX + b c = bX + a d = bY + a ANS: REF: OBJ: COG: C PTS: DIF: Hard Drawing the World’s Best Line (for Your Data) How and why linear regression works when predicting one variable from another Knowledge 15 Which of the following symbols is associated with the predicted score in the regression equation? a X b c a d b ANS: REF: OBJ: COG: B PTS: DIF: Medium Drawing the World’s Best Line (for Your Data) How and why linear regression works when predicting one variable from another Knowledge 16 Which of the following symbols is associated with the independent variable in the regression equation? a X b c a d b ANS: REF: OBJ: COG: A PTS: DIF: Medium Drawing the World’s Best Line (for Your Data) How and why linear regression works when predicting one variable from another Knowledge 17 Which of the following symbols is associated with the slope in the regression equation? a X b c a d b ANS: REF: OBJ: COG: D PTS: DIF: Medium Drawing the World’s Best Line (for Your Data) How and why linear regression works when predicting one variable from another Knowledge 18 Which of the following symbols is associated with the y-intercept in the regression equation? a X b c a d b ANS: REF: OBJ: COG: C PTS: DIF: Medium Drawing the World’s Best Line (for Your Data) How and why linear regression works when predicting one variable from another Knowledge 19 In regression, the criterion variable is also known as the _ a Dependent variable b Independent variable c Predictor variable d Correlated variable ANS: REF: OBJ: COG: A PTS: DIF: Medium Drawing the World’s Best Line (for Your Data) How and why linear regression works when predicting one variable from another Knowledge 20 How would you represent the predicted score of Y based on a known value of X? a y b y-intercept c d Y = Xa ANS: REF: OBJ: COG: C PTS: DIF: Medium Drawing the World’s Best Line (for Your Data) How and why linear regression works when predicting one variable from another Comprehension 21 Which of the following determines the direction of the regression line? a Intercept b Predicted score c Criterion score d Slope ANS: REF: OBJ: COG: D PTS: DIF: Medium Drawing the World’s Best Line (for Your Data) How and why linear regression works when predicting one variable from another Knowledge 22 Which of the following is the point at which the regression line crosses the y-axis? a Intercept b Predicted point c Criterion point d Slope ANS: REF: OBJ: COG: A PTS: DIF: Medium Drawing the World’s Best Line (for Your Data) How and why linear regression works when predicting one variable from another Knowledge 23 Using the regression formula with a slope = 704 and an intercept = 719, what would the predicted college GPA be for a student whose current high school GPA = 3.2? a 2.69 b 2.97 c 3.00 d 3.20 ANS: REF: OBJ: COG: B PTS: DIF: Medium Drawing the World’s Best Line (for Your Data) How and why linear regression works when predicting one variable from another Application 24 Using the regression formula with a slope = 2,000 and an intercept = 15,000, what would the predicted income be for someone who has 16 years of education? a $40,000 b $42,000 c $45,000 d $47,000 ANS: REF: OBJ: COG: D PTS: DIF: Medium Drawing the World’s Best Line (for Your Data) How and why linear regression works when predicting one variable from another Application 25 Using the regression formula with a slope = 1,000 and an intercept = 25,000, what would the predicted income be for someone who has 20 years of education? a $40,000 b $42,000 c $45,000 d $47,000 ANS: REF: OBJ: COG: C PTS: DIF: Medium Drawing the World’s Best Line (for Your Data) How and why linear regression works when predicting one variable from another Application 26 How is the symbol interpreted? a Y intercept b Y predictor c Y prime d Y score ANS: REF: OBJ: COG: C PTS: DIF: Medium Drawing the World’s Best Line (for Your Data) How and why linear regression works when predicting one variable from another Comprehension 27 A positive trend line is associated with what type of slope? a Negative slope b Direct slope c Positive slope d Nondirectional slope ANS: REF: OBJ: COG: C PTS: DIF: Medium Drawing the World’s Best Line (for Your Data) How and why linear regression works when predicting one variable from another Comprehension 28 Which of the following is like a standard deviation for all error scores in regression? a Error of the estimate b Error standard deviation c Standard error of the estimate d Precision of error score ANS: C PTS: REF: How Good Is Our Prediction? COG: Knowledge DIF: Medium OBJ: How to judge the accuracy of predictions 29 What must be done to categorical variables in order to use them in a regression analysis? a Nothing b Dummy coding c Problem coding d Categorical coding ANS: B PTS: DIF: Medium REF: How Good Is Our Prediction? COG: Knowledge OBJ: How to judge the accuracy of predictions 30 What must be used to examine an outcome that is predicted from two independent variables? a Multivariate regression b Multiple regression c Simple regression d Complicated regression ANS: B PTS: DIF: Medium REF: The More Predictors, the Better? Maybe OBJ: What multiple regression is and why it is useful COG: Comprehension 31 Which of the following is also known as a regression weight? a X b c a d b ANS: REF: OBJ: COG: D PTS: DIF: Medium Drawing the World’s Best Line (for Your Data) How and why linear regression works when predicting one variable from another Knowledge 32 When using two predictor variables, these variables should be _ a Correlated b Related c Independent d Dependent ANS: C PTS: DIF: Medium REF: The Big Rule When It Comes to Using Multiple Predictor Variables OBJ: How to judge the accuracy of predictions COG: Comprehension 33 In the multiple-regression formula, what does X2 represent? a Value of the second dependent variable b Value of the second independent variable c Value of the criterion variable d Value of the predicted score ANS: REF: OBJ: COG: B PTS: DIF: Medium Drawing the World’s Best Line (for Your Data) How and why linear regression works when predicting one variable from another Knowledge 34 If the correlation between X and Y is equal to -1.0, what we know about the prediction of Y by X? a It’s weak b It’s positive c It’s perfect d It’s direct ANS: C PTS: REF: How Good Is Our Prediction? COG: Comprehension DIF: Medium OBJ: How to judge the accuracy of predictions 35 A regression equation can be visually represented on a(n) _ a Histogram b Scatter plot c Ogive d Pie chart ANS: B PTS: DIF: Medium REF: The Logic of Prediction OBJ: How and why linear regression works when predicting one variable from another COG: Knowledge 36 If you are trying to predict Y scores from X scores, Y is referred to as the _ a Nominal variable b Independent variable c Predictor variable d Criterion variable ANS: REF: OBJ: COG: D PTS: DIF: Medium Drawing the World’s Best Line (for Your Data) How and why linear regression works when predicting one variable from another Comprehension 37 If you are trying to predict Y scores from X scores, X is referred to as the _ a Nominal variable b Dependent variable c Predictor variable d Criterion variable ANS: REF: OBJ: COG: C PTS: DIF: Medium Drawing the World’s Best Line (for Your Data) How and why linear regression works when predicting one variable from another Comprehension 38 The general formula for a regression line is _ a a2 + b2 = c2 b aX + b = Y c bX + a = d dX + a = ANS: REF: OBJ: COG: C PTS: DIF: Hard Drawing the World’s Best Line (for Your Data) How and why linear regression works when predicting one variable from another Knowledge 39 Based on the formula for a regression line, what does b represent? a Known value of X b Slope of a line c y-intercept d Predictor score ANS: REF: OBJ: COG: B PTS: DIF: Medium Drawing the World’s Best Line (for Your Data) How and why linear regression works when predicting one variable from another Knowledge 40 Based on the formula for a regression line, what does a represent? a Known value of X b Slope of a line c y-intercept d Predictor score ANS: REF: OBJ: COG: C PTS: DIF: Medium Drawing the World’s Best Line (for Your Data) How and why linear regression works when predicting one variable from another Knowledge 41 Not all lines that are the best fit for a bunch of data points are straight Rather, they could be _ a Linear b Invalid c Curvilinear d Parallel-linear ANS: REF: OBJ: COG: C PTS: DIF: Hard Drawing the World’s Best Line (for Your Data) How and why linear regression works when predicting one variable from another Knowledge 42 The INTERCEPT function in Excel computes the location where the regression line crosses the _ a c-axis b b-axis c x-axis d y-axis ANS: D PTS: DIF: Medium REF: And Now Using Excel’s INTERCEPT Function OBJ: How to use the INTERCEPT and SLOPE functions COG: Knowledge 43 The Excel output for a completed regression includes the following EXCEPT _ a Intercept value b p value c r value d L value ANS: REF: OBJ: COG: D PTS: DIF: Medium Using the Amazing Data Analysis Tools to Compute the Regression Equation How to use the always cool Data Analysis Regression tool Comprehension 44 When setting up the regression line in the Excel dialog box, you should define the _ of the data you want Excel to use a Validity b Error of estimate c Standard error of estimate d Range ANS: REF: OBJ: COG: D PTS: DIF: Medium Using the Amazing Data Analysis Tools to Compute the Regression Equation How to use the always cool Data Analysis Regression tool Comprehension 45 When determining the number of predictor variables to use to predict a criterion variable, you need to keep all of the following guidelines in mind EXCEPT this: a The unique contribution of each predictor b The practical costs of adding new predictors c The relationship between predictors and the criterion variable d The length of the dialog box ANS: D PTS: DIF: Medium REF: The Big Rule When It Comes to Using Multiple Predictor Variables OBJ: What multiple regression is and why it is useful COG: Comprehension 46 In multiple regression, added variables must be related to the outcome variable but a Correlated with and unrelated to each other b Independent of and correlated with each other c Independent of and uncorrelated with each other d Dependent of and uncorrelated with each other ANS: C PTS: DIF: Medium REF: The Big Rule When It Comes to Using Multiple Predictor Variables OBJ: What multiple regression is and why it is useful COG: Comprehension TRUE/FALSE Linear regression uses correlations between variables as the basis for the prediction of the value of one variable based on the value of another ANS: T PTS: DIF: Medium REF: The Logic of Prediction OBJ: How and why linear regression works when predicting one variable from another COG: Knowledge The higher the absolute value of the correlation coefficient, the less accurate the prediction is of one variable based on the other variable ANS: F PTS: REF: What Is Prediction All About? COG: Comprehension DIF: Medium OBJ: How to judge the accuracy of predictions A perfect correlation would translate into perfect prediction in the case of linear regression ANS: T PTS: DIF: Medium REF: The Logic of Prediction OBJ: How and why linear regression works when predicting one variable from another COG: Comprehension In linear regression, a regression equation is determined, which can be used to plot a regression line ANS: T PTS: DIF: Medium REF: The Logic of Prediction OBJ: How and why linear regression works when predicting one variable from another COG: Comprehension The regression line reflects the best estimate of predicted scores for the independent variable based on levels of the dependent variable ANS: F PTS: DIF: Medium REF: The Logic of Prediction OBJ: How and why linear regression works when predicting one variable from another COG: Knowledge Error in prediction (error of estimate) is calculated as the distance between each individual data point and the regression line ANS: T PTS: REF: How Good Is Our Prediction? COG: Knowledge DIF: Medium OBJ: How to judge the accuracy of predictions Standard error of estimate is computed as the variance of all values for error in prediction ANS: F PTS: DIF: Medium REF: How Good Is Our Prediction? COG: Comprehension OBJ: How to judge the accuracy of predictions The standard error of estimate tells you how much imprecision there is overall in regard to the predictive power of the linear regression analysis ANS: T PTS: REF: How Good Is Our Prediction? COG: Comprehension DIF: Medium OBJ: How to judge the accuracy of predictions In linear regression, the outcome variable is called the criterion or dependent variable ANS: REF: OBJ: COG: T PTS: DIF: Medium Drawing the World’s Best Line (for Your Data) How and why linear regression works when predicting one variable from another Comprehension 10 Simple linear regression consists of a type of regression in which more than one independent variable is included in the analysis ANS: REF: OBJ: COG: F PTS: DIF: Medium The More Predictors, the Better? Maybe How and why linear regression works when predicting one variable from another Comprehension 11 One of the values of regression is that you can use data from past events (such as the existing relationship between two variables) and then apply it later with different cases in which you have knowledge of only one variable ANS: REF: OBJ: COG: T PTS: DIF: Medium What Is Prediction All About? How prediction works and how it can be used in the social and behavioral sciences Comprehension 12 Prediction through regression is the computation of past outcomes based on knowledge of present ones ANS: REF: OBJ: COG: F PTS: DIF: Medium What Is Prediction All About? How prediction works and how it can be used in the social and behavioral sciences Comprehension 13 The error of estimate and the error of prediction are not the same thing ANS: F PTS: REF: How Good Is Our Prediction? COG: Knowledge SHORT ANSWER DIF: Easy OBJ: How to judge the accuracy of predictions What is linear regression? ANS: Linear regression is a statistical procedure used to predict a Y score from an X score based on the correlation between a distribution of X scores and a distribution of Y scores PTS: DIF: Hard REF: The Logic of Prediction OBJ: How and why linear regression works when predicting one variable from another COG: Knowledge If the correlation between variable X and variable Y is perfect, what you know about the prediction? ANS: The prediction will be perfect as well PTS: DIF: Medium REF: What Is Prediction All About? OBJ: How prediction works and how it can be used in the social and behavioral sciences COG: Comprehension What does the regression line represent? ANS: The regression line represents four things First, it is the line of best fit, which minimizes that distance between the line and each of the points of the predicted variable on a scatter plot Second, the line allows us to predict one score given the value of the independent variable The regression line also represents the distance between each individual point and the regression line, called the error in prediction or error in estimate Finally, the line allows us to see how far off each of the data points are from a perfect correlation If the correlation were perfect, all the data points would be lined up along a 45 angle PTS: DIF: Hard REF: The Logic of Prediction OBJ: How and why linear regression works when predicting one variable from another COG: Comprehension Why is the regression line called the line of best fit? ANS: Because the regression line minimizes the distance between each individual point and the regression line PTS: DIF: Medium REF: The Logic of Prediction OBJ: How and why linear regression works when predicting one variable from another COG: Knowledge Why we use and not Y in the regression equation? ANS: We use because it is the predicted value of Y, not the actual Y value PTS: DIF: Medium REF: Drawing the World’s Best Line (for Your Data) OBJ: How and why linear regression works when predicting one variable from another COG: Comprehension What is the standard error of estimate? ANS: The standard error of estimate is the measurement for how well (or poorly) one variable predicts another variable When these differences from a distribution of data points are averaged, the standard error of estimate reflects how good the prediction is PTS: DIF: Hard REF: How Good Is Our Prediction? OBJ: How to judge the accuracy of predictions COG: Knowledge How does linear regression differ from multiple regression? ANS: Linear regression is a statistical technique using a regression equation to determine the line of best fit from which a Y score can be predicted from an X score Multiple regression has the same goal as linear regression (determining the line of best fit) but uses two or more independent variables rather than one independent variable (which is what is used in linear regression) PTS: DIF: Hard REF: The More Predictors, the Better? Maybe OBJ: What multiple regression is and why it is useful COG: Analysis How is the regression line related to the correlation coefficient? ANS: The regression line is a direct reflection of the correlation between two variables The correlation coefficient is represented as a value while the regression line is a visual representation PTS: DIF: Hard REF: The Logic of Prediction OBJ: How and why linear regression works when predicting one variable from another COG: Analysis What does a unique contribution mean for a variable? ANS: A unique contribution means the variable explains differences in the predicted variable that the other variables used did not PTS: DIF: Medium REF: The Big Rule When It Comes to Using Multiple Predictor Variables OBJ: What multiple regression is and why it is useful COG: Comprehension 10 What important guideline should you keep in mind when choosing independent variables for multiple regression? ANS: When using a multiple-regression model, the predictor variables should be independent and unrelated with one another but related to the outcome variable PTS: DIF: Medium REF: The Big Rule When It Comes to Using Multiple Predictor Variables OBJ: What multiple regression is and why it is useful COG: Comprehension 11 If you are not satisfied with the percentage of variability on your criterion variable accounted for by the variability in the predictor variable, and if you have an idea of other variables that could account for the variability in the criterion variable, you could run a _ ANS: multiple regression PTS: DIF: Medium REF: The More Predictors, the Better? Maybe OBJ: What multiple regression is and why it is useful COG: Comprehension