Deck 10: Regression Analysis: Estimating Relationships

Question 1

Correlation is used to determine the strength of the linear relationship between an explanatory variable X and response variable Y.

Answer 1

True

Question 2

To help explain or predict the response variable in every regression study,we use one or more explanatory variables.These variables are also called response variables or independent variables.

Answer 2

False

Question 3

A regression analysis between X = sales (in $1000s)and Y = advertising (in $)resulted in the following least squares line: = 32 + 8X.This implies that an increase of $1 in advertising is expected to result in an increase of $40 in sales.

Answer 3

False

Question 4

The residual is defined as the difference between the actual and predicted,or fitted values of the response variable.

Question 5

An outlier is an observation that falls outside of the general pattern of the rest of the observations on a scatterplot.

Question 6

Correlation is measured on a scale from 0 to 1,where 0 indicates no linear relationship between two variables,and 1 indicates a perfect linear relationship.

Question 7

The two primary objectives of regression analysis are to study relationships between variables and to use those relationships to make predictions.

Question 8

Cross-sectional data are usually data gathered from approximately the same period of time from a population.

Question 9

The least squares line is the line that minimizes the sum of the residuals.

Question 10

In regression analysis,we can often use the standard error of estimate to judge which of several potential regression equations is the most useful.

Question 11

A negative relationship between an explanatory variable X and a response variable Y means that as X increases,Y decreases,and vice versa.

Question 12

In every regression study there is a single variable that we are trying to explain or predict.This is called the response variable or dependent variable.

Question 13

A regression analysis between weight (Y in pounds)and height (X in inches)resulted in the following least squares line: = 140 + 5X.This implies that if the height is increased by 1 inch,the weight is expected to increase on average by 5 pounds.

Question 14

In reference to the equation, ,the value 0.10 is the expected change in Y per unit change in X.

Question 15

A useful graph in almost any regression analysis is a scatterplot of residuals (on the vertical axis)versus fitted values (on the horizontal axis),where a "good" fit not only has small residuals,but it has residuals scattered randomly around zero with no apparent pattern.

Question 16

A regression analysis between X = sales (in $1000s)and Y = advertising ($)resulted in the following least squares line: = 84 +7X.This implies that if advertising is $800,then the predicted amount of sales (in dollars)is $140,000.

Question 17

Scatterplots are used for identifying outliers and indicating what you should do about the outliers you may find.

Question 18

A regression analysis between X = sales (in $1000s)and Y = advertising ($)resulted in the following least squares line: = 84 +7X.This implies that if there is no advertising,then the predicted amount of sales (in dollars)is $84,000.

Question 19

Regression analysis can be applied equally well to cross-sectional and time series data.

Question 20

When the scatterplot appears as a shapeless swarm of points,this can indicate that there is no relationship between the response variable Y and the explanatory variable X,or at least none worth pursuing.

Question 21

In a multiple regression problem with two explanatory variables if,the fitted regression equation is then the estimated value of Y when and is 49.4.

Question 22

We should include an interaction variable in a regression model if we believe that the effect of one explanatory variable on the response variable Y depends on the value of another explanatory variable .

Question 23

In a multiple regression analysis with three explanatory variables,suppose that there are 60 observations and the sum of the residuals squared is 28.The standard error of estimate must be 0.7071.

Question 24

In a simple regression analysis,if the standard error of estimate = 15 and the number of observations n = 10,then the sum of the residuals squared must be 120.

Question 25

The adjusted R² is adjusted for the number of explanatory variables in a regression equation,and it has the same interpretation as the standard R².

Question 26

For the multiple regression model ,if were to increase by 5 units,holding and constant,the value of Y would be expected to decrease by 50 units.

Question 27

If the regression equation includes anything other than a constant plus the sum of products of constants and variables,the model will not be linear.

Question 28

In a simple regression with a single explanatory variable,the multiple R is the same as the standard correlation between the Y variable and the explanatory X variable.

Question 29

If a categorical variable is to be included in a multiple regression,a dummy variable for each category of the variable should be used,but the original categorical variables should not be used.

Question 30

The primary purpose of a nonlinear transformation is to "straighten out" the data on a scatterplot.

Question 31

In a simple linear regression problem,suppose that = 12.48 and = 124.8.Then = 0.90.

Question 32

The multiple R for a regression is the correlation between the observed Y values and the fitted Y values.

Question 33

R² can only increase when extra explanatory variables are added to a multiple regression model.

Question 34

In the multiple regression model we interpret X₁ as follows: holding X₂ constant,if X₁ increases by 1 unit,then the expected value of Y will increase by 9 units.

Question 35

The adjusted R² is used primarily to monitor whether extra explanatory variables belong in a multiple regression model.

Question 36

The regression line = 3 + 2X has been fitted to the data points (4,14),(2,7),and (1,4).The sum of the residuals squared will be 8.0.

Question 37

In a nonlinear transformation of data,the Y variable or the X variables may be transformed,but not both.

Question 38

In a simple linear regression problem,if = 0.95,this means that 95% of the variation in the explanatory variable X can be explained by the regression.

Question 39

In simple linear regression,the divisor of the standard error of estimate is n - 1,because there is only one explanatory variable.

Question 40

An interaction variable is the product of an explanatory variable and the dependent variable.

Question 41

A scatterplot that appears as a shapeless mass of data points indicates _____ relationship among the variables.

A)a curved
B)a linear
C)a nonlinear
D)no

Question 42

A "fan" shape in a scatterplot indicates

A)unequal variance.
B)a nonlinear relationship.
C)the absence of outliers.
D)sampling error.

Question 43

In a constant elasticity,or multiplicative,relationship the dependent variable is expressed as a product of explanatory variables raised to powers.

Question 44

_____ is/are especially helpful in identifying outliers.

A)Linear regression
B)Regression analysis
C)Normal curves
D)Scatterplots

Question 45

The correlation value ranges from

A)0 to +1.
B)-1 to +1.
C)-2 to +2.
D)0 to 100.

Question 46

Correlation is a summary measure that indicates

A)a curved relationship among the variables.
B)the rate of change in Y for a one unit change in X.
C)the strength of the linear relationship between pairs of variables.
D)the magnitude of difference between two variables.

Question 47

Outliers are observations that

A)lie outside the sample.
B)render the study useless.
C)lie outside the typical pattern of points on a scatterplot.
D)disrupt the entire linear trend.

Question 48

The covariance is not used as much as the correlation because

A)it is not always a valid predictor of linear relationships.
B)it is difficult to calculate.
C)it is difficult to interpret because it depends on the units of measurement.
D)of all of these options.

Question 49

In regression analysis,the variables used to help explain or predict the response variable are called the _____ variables.

A)independent
B)dependent
C)regression
D)statistical

Question 50

Regression analysis asks

A)if there are differences between distinct populations.
B)if the sample is representative of the population.
C)how a single variable depends on other relevant variables.
D)how several variables depend on each other.

Question 51

A logarithmic transformation of the response variable Y is often useful when the distribution of Y is symmetric.

Question 52

If a scatterplot of residuals shows a parabola shape,then a logarithmic transformation may be useful in obtaining a better fit.

Question 53

In regression analysis,the variable we are trying to explain or predict is called the _____ variable.

A)independent
B)dependent
C)regression
D)statistical

Question 54

Data collected from approximately the same period of time from a cross-section of a population are called _____ data.

A)time series
B)linear
C)cross-sectional
D)historical

Question 55

A single variable X can explain a large percentage of the variation in some other variable Y when the two variables are

A)mutually exclusive.
B)inversely related.
C)directly related.
D)highly correlated.

Question 56

A correlation value of zero indicates _____ relationship.

A)a strong linear
B)a weak linear
C)no linear
D)a perfect linear

Question 57

In regression analysis,which of the following causal relationships are possible?

A)X causes Y to vary.
B)Y causes X to vary.
C)Other variables cause both X and Y to vary.
D)All of these options are possible.

Question 58

In regression analysis,if there are several explanatory variables,it is called _____ regression.

A)simple
B)multiple
C)compound
D)nonlinear

Question 59

The effect of a logarithmic transformation on a variable that is skewed to the right by a few large values is to "squeeze" the values together and make the distribution more symmetric.

Question 60

The coefficients for logarithmically transformed explanatory variables should be interpreted as the percent change in the dependent variable for a 1% percent change in the explanatory variable.

Question 61

In linear regression,we can have an interaction variable.Algebraically,the interaction variable is the _____ of two variables.

A)sum
B)ratio
C)product
D)mean

Question 62

Which of the following is an example of a nonlinear regression model?

A)A quadratic regression equation
B)A logarithmic regression equation
C)Constant elasticity equation
D)All of these choices

Question 63

In linear regression,the fitted value is

A)the predicted value of the dependent variable.
B)the predicted value of the independent value.
C)the predicted value of the slope.
D)the predicted value of the intercept.

Question 64

The term autocorrelation refers to

A)the analyzed data refers to itself.
B)the sample is related too closely to the population.
C)the data are in a loop (values repeat themselves).
D)time series variables are usually related to their own past values.

Question 65

The regression line has been fitted to the data points (28,60),(20,50),(10,18),and (25,55).The sum of the squared residuals will be

A)20.25.
B)16.00.
C)49.00.
D)94.25.

Question 66

In linear regression,we fit the least squares line to a set of values (or points on a scatterplot).The distance from the line to a point is called the

A)fitted value.
B)residual.
C)correlation.
D)covariance.

Question 67

The adjusted R² adjusts R² for

A)non-linearity.
B)outliers.
C)low correlation.
D)the number of explanatory variables in a multiple regression model.

Question 68

Approximately what percentage of the observed Y values are within one standard error of the estimate ( )of the corresponding fitted Y values?

A)67%
B)95%
C)99%
D)99.7%

Question 69

In multiple regression,the coefficients reflect the expected change in _____ by one unit.

A)Y when the associated X value increases
B)X when the associated Y value increases
C)Y when the associated X value decreases
D)X when the associated Y value decreases

Question 70

In choosing the "best-fitting" line through a set of points in linear regression,we choose the one with the

A)smallest sum of squared residuals.
B)largest sum of squared residuals.
C)smallest number of outliers.
D)largest number of points on the line.

Question 71

Given the least squares regression line, ,which statement is true?

A)The relationship between X and Y is positive.
B)The relationship between X and Y is negative.
C)As X increases,so does Y.
D)As X decreases,so does Y.

Question 72

The weakness of scatterplots is that they

A)do not help identify linear relationships.
B)can be misleading about the types of relationships they indicate.
C)only help identify outliers.
D)do not actually quantify the relationships between variables.

Question 73

The percentage of variation ( )can be interpreted as the fraction (or percent)of variation of the

A)explanatory variable explained by the independent variable.
B)explanatory variable explained by the regression line.
C)response variable explained by the regression line.
D)error explained by the regression line.

Question 74

In multiple regression,the constant

A)is the expected value of the dependent variable Y when all of the independent variables have the value zero.
B)is necessary to fit the multiple regression line to set of points.
C)must be adjusted for the number of independent variables
D)is all of these options.

Question 75

The multiple standard error of estimate will be

A)0.901.
B)0.888.
C)0.800.
D)0.953.

Question 76

In linear regression,a dummy variable is used to

A)represent residual variables.
B)represent missing data in each sample.
C)include hypothetical data in the regression equation.
D)include categorical variables in the regression equation.

Question 77

An important condition when interpreting the coefficient for a particular independent variable X in a multiple regression equation is that

A)the dependent variable will remain constant.
B)the dependent variable will be allowed to vary.
C)all of the other independent variables remain constant.
D)all of the other independent variables be allowed to vary.

Question 78

The standard error of the estimate ( )is essentially the

A)mean of the residuals.
B)standard deviation of the residuals.
C)mean of the explanatory variable.
D)standard deviation of the explanatory variable.

Question 79

The percentage of variation (R²)ranges from

A)0 to +1.
B)-1 to +1.
C)-2 to +2.
D)-1 to 0.

Question 80

In a simple linear regression analysis,the following sums of squares are produced: The proportion of the variation in Y that is explained by the variation in X is

A)20%.
B)80%.
C)25%.
D)50%.