Auday Exam 2 Research Methods
Assume you are an educational psychologist and you believe that there is a relationship between socioeconomic factors and academic performance. You are planning to conduct a study to investigate this belief. If such a relationship really does exist, to demonstrate the relationship would you be better off to collect data only on students from the wealthiest families or on students from all levels of the socioeconomic range? Discuss.
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If two variables are measured on different scales with different units, e.g., the number of crimes committed and phases of the moon, how is it possible to derive a number, like a correlation coefficient, that expresses the relationship between the two variables?
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It is sometimes said that the higher the correlation between two variables, the more likely the relationship is causal. Do you think this is correct? Discuss
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John has noticed that people seem happier in the summer than in the winter and concludes that this is because most people take their vacations in the summer. Is John justified in drawing this conclusion based on this reason? Discuss.
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Explanations for correlation between X and Y
1. Correlation may be spurious 2. X causes Y 3. Y causes X 4. Third variable causes the correlation between X and Y
Scatter plots
A scatter plot is a graph of paired X (one variable score) and Y (another variable score) values. By visually examining the graph one can get a good idea of the nature of the relationship between the two variables (i.e., linear or not).
Linear relationship
A) a linear relationship between two variables is one in which the relationship between two variables can accurately be represented by a straight line. b.. Curvilinear relationship. When a curved line fits a set of points better than a straight line it is called a curvilinear association or relationship.
A correlation coefficient expresses the direction but not the magnitude of a relationship.
ANS: F
An imperfect relationship generally yields exact prediction.
ANS: F
As the value of r increases, the proportion of variability of Y that is accounted for by X decreases.
ANS: F
Assuming a correlation exists, as the range of one of the variables decreases, r increases.
ANS: F
For a linear relationship to exist, all the points must fall on a straight line.
ANS: F
Generally, one can use the same regression equation for predicting Y given X as for X given Y.
ANS: F
Given a -1.00 correlation coefficient, a raw score of 32 on one measure must be accompanied by a score of -32 on the corresponding second measure.
ANS: F
If one calculates r for a set of data and r equals 0.84, one can be certain that the relationship between the variables is not spurious.
ANS: F
If one calculates r for a set of numbers and then adds a constant to each value of one of the variables, the correlation will change.
ANS: F
If r = -1.00, the relationship is imperfect.
ANS: F
If the relationship is imperfect, the value of the correlation coefficient must be negative.
ANS: F
If the value of r on ratio scaled raw data were 0.87 and the pairs of numbers were converted to ordinal data, and r calculated for the ordinal data, r would equal 0.87.
ANS: F
In a linear relationship all the points must fall on a straight line.
ANS: F
In a straight line the slope approaches zero as the line comes near the point X, Y.
ANS: F
In order to compute r, we must first convert each score to its z score and then do our calculations with the z scores.
ANS: F
In regression analysis we are only concerned with perfect as opposed to imperfect relationships.
ANS: F
Rho is used where one or both variables are at least of interval scaling.
ANS: F
Since r is so widely used, it is appropriate to calculate r for nonlinear data.
ANS: F
The coefficient of determination equals the square root of r .
ANS: F
The easiest way to determine if a relationship is linear is to calculate the regression line.
ANS: F
The least squares regression line insures the maximum number of direct hits.
ANS: F
The range of a correlation coefficient is 0 to +1.
ANS: F
The value aY is the X axis intercept for minimizing errors in Y.
ANS: F
When doing regression, it is customary to assign X to the predicted variable.
ANS: F
A correlation coefficient expresses quantitatively the degree of relationship between two variables.
ANS: T
A scatter plot is used to help determine if the relationship is linear or curvilinear.
ANS: T
Both Pearson r and Spearman rho can range from -1.00 to +1.00.
ANS: T
Causation implies correlation.
ANS: T
Correlation deals with the relationship between two variables.
ANS: T
For regression purposes, it is customary to assign X to the variable we are predicting from.
ANS: T
For regression purposes, it is customary to assign Y to the predicted variable.
ANS: T
For regression purposes, it is customary to assign Y to the variable we are predicting from.
ANS: T
If the correlation between two variables is 1.00, the standard error of estimate equals 0.
ANS: T
If the regression line is parallel to the X axis then the slope of the regression line equals 0.
ANS: T
If the relationship between two variables is perfect the standard error of estimate equals 0.
ANS: T
If the standard deviation of one of the variables equals zero, r cannot be calculated.
ANS: T
If the standard deviations of the X and Y distributions are equal, then r = bY.
ANS: T
If the standard error of estimate for relationship 1 equals 5.26 and for relationship 2 it equals 8.01 then we can reasonably infer that relationship 2 is less perfect than relationship 1.
ANS: T
In a perfect linear relationship all the points must fall on a straight line.
ANS: T
In a perfect positive correlation, each individual obtains the same z score on each variable.
ANS: T
In a positive relationship as X increases, Y increases.
ANS: T
In an inverse relationship as one variable gets larger the other variable gets smaller.
ANS: T
In general one is less confident in predictions of Y when the value of X used for the prediction is outside the range of the original data used to construct the regression line.
ANS: T
It is impossible to have a negative value for the standard error of estimate.
ANS: T
One reason for calculating r from z scores is to make r independent of units and scaling.
ANS: T
Pearson r requires that the data be of interval or ratio scaling.
ANS: T
Properly speaking, we should limit our predictions to the range of the base data
ANS: T
Restricting the range of either X or Y will generally lower the correlation between the variables.
ANS: T
Spearman rho really derives from Pearson r.
ANS: T
The coefficient of determination equals the proportion of variability accounted for by the relationship between the variables.
ANS: T
The correlation between two variables when N = 2 will always be perfect.
ANS: T
The correlation coefficient r is a descriptive statistic
ANS: T
The correlation coefficient when N = 2 is meaningless.
ANS: T
The farther away the points on a scatter diagram fall from the regression line, the lower the correlation.
ANS: T
The formula for rho is actually just the formula for Pearson's r simplified to apply to lower order scaling.
ANS: T
The higher the r value, the lower the standard error of estimate.
ANS: T
The regression line will always go through the point X bar, Y bar.
ANS: T
The slope of a line is a measure of its rate of change.
ANS: T
The slope of the line reveals whether the relationship is positive or negative.
ANS: T
The use of z scores allows comparisons between variables measured on different scales and units.
ANS: T
The value of r obtained by calculating the correlation between X and Y is the same as the correlation between Y and X.
ANS: T
To do linear regression, there must be paired scores on two variables.
ANS: T
When the relationship is perfect, the regression of Y on X is the same as the regression of X on Y.
ANS: T
r2 is called the coefficient of determination.
ANS: T
Causation
Correlation between X and Y does not prove causation.
Slope of regression line for z scores
Equals r. Y b X b X a (page 28)
Correlation coefficient
Expresses quantitatively the magnitude and direction of the correlation. 1. Range. Can range from +1 to -1. 2. Sign. The sign of the coefficient tells us whether the relationship is positive or negative.
Use of regression equation
For a given value of X, simply plug that value in the equation and solve for Y' using the regression constants bY and aY. Note that it is customary to label the variable to which we are predicting as the Y variable, and the variable we are predicting from as the X variable.
Regression constant aY.
Found in the usual way
SE of estimate definition
Gives a measure of the average deviation of the prediction errors about the regression line.
Least-squares criterion
In an imperfect relationship no single straight line will hit all the points. We pick the line that will minimize the total errors of prediction, i.e., construct the one line that minimizes (Y - Y')2 where Y' is the predicted value of Y for any value of X.
Other errors
One must be careful of sources of errors in making predictions. There are two major considerations in making predictions. 1. Linearity. The original relationship needs to be linear for accurate prediction using linear regression. 2. Prediction in the range. Generally one uses a sample to generate the data for calculating the regression constants (bY and aY). Predictions of Y should be based on values of X within the range of the sample upon which the constants are based.
Standard error of estimate ( Y X s | ).
Quantifying the magnitude of the error involves computing the standard error of estimate symbolized Y X s | . The standard error is much like the standard deviation.
Which of the following statements is(are) false? a. bY is the slope of the line for minimizing errors in predicting Y. b. aY is the Y axis intercept for minimizing errors in predicting Y. c. sYIX is the standard error of estimate for predicting Y given X. d. All of these statements are true. e. R^2 is the multiple coefficient of nondetermination.
R^2 is the multiple coefficient of nondetermination.
Explained Variability
The explained variability = r2. For example, if r = .7 then .49 or 49% of the variability of Y is accounted for by X. This is called the explained variability. If X is causal with respect to Y, r2 is also a measure of the size of the effect.
Negative relationships
This exists when there is an inverse relationship between X and Y. Low values of X are associated with high values of Y and vice versa.
Perfect relationship
This exists when there is an inverse relationship between X and Y. Low values of X are associated with high values of Y and vice versa.
Positive relationships
This indicates that there is a direct relationship between the variables. Higher values of X are associated with higher values of Y and vice versa.
Imperfect relationships
This is when a positive or negative, relationship exists but all of the points do not fall on the line.
Perfect relationship
This occurs when all the pairs of points fall on a straight line.
Correlation
This refers to the magnitude and direction of the relationship between two variables.
Linear regression
This topic deals with predicting scores of one distribution using information known about scores of a second distribution. For example, one might predict your height if they knew your weight and the nature of your relationship between height and weight from a sample of other people.
Role of experimentation
To establish that one variable is the cause of another, an experiment must be conducted by systematically varying only the causal variable and then measuring the effect on the other variable.
Prediction Errors
When relationships between X and Y variables are imperfect, there will be prediction errors.
During the past 5 years there has been an inflationary trend. Listed below is the average cost of a gallon of milk for each year. 1981 1982 1983 1984 1985 $1.10 $1.23 $1.30 $1.50 $1.65 Assuming a linear relationship exists, and that the relationship continues unchanged through 1986, what would you predict for the average cost of a gallon of milk in 1986? a. $1.77 c. $1.70 b. $1.72 d. $1.83
a. $1.77
A researcher wanted to know if the order in which runners finish a race is correlated with their weight. She conducts an experiment and the data are given below. Finishing order 1 2 3 4 5 6 Weight (lbs) 110 114 112 108 116 113 The correlation for these data equals _________. a. 0.31 c. 0.41 b. 0.32 d. 0.45
a. 0.31
A traffic safety officer conducted an experiment to determine whether there is a correlation between people's ages and driving speeds. Six individuals were randomly sampled and the following data were collected. Age Y 20 25 45 46 60 65 Speed X (mph) 60 47 55 38 45 35 The proportion of variability of Y accounted for by X is _________. a. 0.49 c. 0.40 b. 0.67 d. -0.49
a. 0.49
What is the slope for the points X1 = 30, Y1 = 50 and X2 = 25 and Y2 = 40? a. 2.00 c. -2.00 b. 0.50 d. -0.50
a. 2.00
If the correlation between two variables is -1.00 and the score of a given individual is 2.20 standard deviations above the mean on one of the variables, we would predict a score on the second variable of _________. a. 2.20 standard deviations below the mean b. 2.20 standard deviations above the mean c. more than 2.20 standard deviations above the mean d. more than 2.20 standard deviations below the mean
a. 2.20 standard deviations below the mean
A researcher collects data on the relationship between the amount of daily exercise an individual gets and the percent body fat of the individual. The following scores are recorded. Individual 1 2 3 4 5 Exercise (min) 10 18 26 33 44 % Fat 30 25 18 17 14 The least squares regression line for predicting the amount of exercise from % fat is _________. a. X' = -1.931Y + 66.363 c. X' = 1.931Y + 66.363 b. X' = -0.476Y + 33.272 d. X' = -1.905Y + 62.325
a. X' = -1.931Y + 66.363
In the equation Y = bX + a, X and Y, a is _________. a. a constant giving the value of the Y axis intercept b. a constant giving the value of the slope of the line c. a variable relating X to Y d. a variable relating Y to X
a. a constant giving the value of the Y axis intercept
In a perfect relationship, _________. a. all the points fall on the line b. none of the points fall on the line c. some of the points fall on the line d. the points form an ellipse around the line
a. all the points fall on the line
The regression coefficient for predicting Y given X is symbolized by _______ a. bY c. bX b. aY d. aX
a. bY
Knowing nothing more than that IQ and memory scores are correlated 0.84, you could validly conclude that _________. a. good memory causes high IQ b. high IQ causes good memory c. neither good memory nor high IQ cause each other d. a third variable causes both good memory and high IQ e. none of these
a. good memory causes high IQ
The closer the points on a scatter diagram fall to the regression line, the _________ between the scores. a. higher the correlation c. correlation doesn't change b. lower the correlation d. need more information
a. higher the correlation
Pearson r can be properly used on which of the following type(s) of relationships? a. linear c. exponential b. curvilinear d. all of these
a. linear
If the relationship between X and Y is perfect: a. r = bY b. r ?0? bY c. prediction is approximate d. r = bY and prediction is approximate e. all of these
a. r = bY
A correlation of r = 0.60 exists between a set of X and Y scores. If a constant of 10 is added to each score of both distributions, the value of r will _______. a. remain the same b. will increase c. decrease d. be less meaningful e. will increase and be less meaningful
a. remain the same
If one calculates r for raw scores, and then calculates r on the z scores of the same data, the value of r will _______. a. stay the same c. increase b. decrease d. equal 1.00
a. stay the same
If a relationship is linear, _________. a. the relation can be most accurately represented by a straight line b. all the points fall on a curved line c. the relationship is best represented by a curved line d. all the points must fall on a straight line
a. the relation can be most accurately represented by a straight line
Causation implies correlation. a. true b. false
a. true
If X and Y are transformed into z scores, and the slope of the regression line of the z scores is -0.80, what is the value of the correlation coefficient? a. -0.80 c. 0.40 b. 0.80 d. -0.40
a. -0.80
For the following points what would you predict to be the value of Y' when X = 19? Assume a linear relationship. X 6 12 30 40 Y 10 14 20 27 a. 16.35 c. 22.00 b. 24.69 d. 17.75
a. 16.35
Straight Line Equation.
a. General equation. Y = bX + a where a = the Y intercept and b = the slope of the line. b. Slope of the straight line equation (b). The slope tells us how much the Y score changes for each unit change in the X score. The slope is a constant value. In equation form: b = slope = (Y2 - Y1)/(X2 - X1) . c. Y intercept (a). The Y intercept is the value of Y where the line intersects the Y axis. It is the value of Y when X = 0.
For regression purposes, a. X is assigned to the variable being predicted. b. Y is assigned to the variable being predicted. c. It doesn't matter whether X or Y is assigned to the variable being predicted. d. none of these
a. X is assigned to the variable being predicted.
The points (0,5) and (5,10) fall on the regression line for a perfect positive linear relationship. What is the regression equation for this relationship? a. Y' = X + 5 b. Y' = 5X c. Y' = 5X + 10 d. cannot be determined from information given.
a. Y' = X + 5
If bY = 0, the regression line is _________. a. horizontal c. undefined b. vertical d. at a 45 angle to the X axis
a. horizontal
If Y X s | = 0.0 the relationship between the variables is _________. a. perfect c. curvilinear b. imperfect d. unknown )
a. perfect (look at equation on study guide page 33)
The primary reason we use a scatter plot in linear regression is _________. a. to determine if the relationship is linear or curvilinear b. to determine the direction of the relationship c. to compute the magnitude of the relationship d. to determine the slope of the least squares regression line
a. to determine if the relationship is linear or curvilinear
A traffic safety officer conducted an experiment to determine whether there is a correlation between people's ages and driving speeds. Six individuals were randomly sampled and the following data were collected. Age 20 25 45 46 60 65 Speed (mph) 60 47 55 38 45 35 The value of Pearson r equals _________. a. -0.82 c. -0.63 b. -0.70 d. +0.70
b. -0.70
A researcher collects data on the relationship between the amount of daily exercise an individual gets and the percent body fat of the individual. The following scores are recorded. Individual 1 2 3 4 5 Exercise (min) 10 18 26 33 44 % Fat 30 25 18 17 14 If an individual has 22% fat, his predicted amount of daily exercise is _________. a. 22.80 c. 24.76 b. 23.88 d. 20.22
b. 23.88
For the following X and Y scores, how much of the variability of Y is accounted for by knowledge of X? Assume a linear relationship. X 20 15 6 10 Y 6 5 4 0 a. 68% c. 58% b. 34% d. 27%
b. 34%
Which of the following statements is true? a. Correlation implies causation. c. neither of these b. Causation implies correlation. d. both of these
b. Causation implies correlation.
Which of the following statements concerning Pearson r is not true? a. r = 0.00 represents the absence of a relationship. b. The relationship between the two variables must be nonlinear. c. r = 0.76 has the same predictive power as r = -0.76. d. r = 1.00 represents a perfect relationship. e. All of these are true statements.
b. The relationship between the two variables must be nonlinear.
In an imperfect relationship, _________. a. all the points fall on the line b. a relationship exists, but all of the points do not fall on the line c. no relationship exists d. a relationship exists, but none of the points can fall on the line
b. a relationship exists, but all of the points do not fall on the line
The regression constant for predicting Y given X is symbolized by _________. a. bY c. bX b. aY d. aX
b. aY
In a positive relationship, _________. a. b is negative c. a must be positive b. b is positive d. a must be negative
b. b is positive
Correlation implies causation. a. true b. false
b. false
In order to properly use rho, the variables must be of at least _______ scaling. a. nominal c. interval b. ordinal d. ratio
b. ordinal
The proportion of variance accounted for by a correlation between two variables is determined by _________. a. Y2 c. r b. r2 d. b
b. r2
A researcher wanted to know if the order in which runners finish a race is correlated with their weight. She conducts an experiment and the data are given below. Finishing order 1 2 3 4 5 6 Weight (lbs) 110 114 112 108 116 113 What is the appropriate correlation coefficient for these data? a. r c. phi b. rho d. biserial
b. rho
A correlation between college entrance exam grades and scholastic achievement was found to be -1.08. On the basis of this you would tell the university that _________. a. the entrance exam is a good predictor of success b. they should hire a new statistician c. the exam is a poor predictor of success d. students who do best on this exam will make the worst students e. students are this school are underachieving
b. they should hire a new statistician
It is possible to compute a coefficient of correlation if one is given _________. a. a single score b. two sets of measurements on the same individuals c. 50 scores of a clerical aptitude test d. all of these e. none of these
b. two sets of measurements on the same individuals
If sY = sX = 1 and the value of bY = 0.6, what will the value of r be? a. 0.36 c. 1.00 b. 0.60 d. 0.00
b. 0.60
Regression coefficient
bY = r(sY/sX)
The correlation coefficient between heights from the ground of two people on the opposite ends of a seesaw would be _________. a. 1.0 b. 0 c. -1.0 d. cannot tell without further information
c. -1.0
If r = 0.4582, sY = 3.4383, and sX = 5.2165, the value of bY = _________. a. 0.695 b. 0.458 c. 0.302 d. 1 - 0.458 e. none of these
c. 0.302
If 49% of the total variability of Y is accounted for by X, what is the value of r? a. 0.49 c. 0.70 b. 0.51 d. 0.30
c. 0.70
If zX equals zY for each pair of points, r will equal _______. a. 0.00 c. 1.00 b. -1.00 d. 0.50
c. 1.00
A researcher collects data on the relationship between the amount of daily exercise an individual gets and the percent body fat of the individual. The following scores are recorded. Individual 1 2 3 4 5 Exercise (min) 10 18 26 33 44 % Fat 30 25 18 17 14 The value for the standard error of estimate in predicting % fat from daily exercise is _________. a. 3.35 b. 4.32 c. 2.14 d. 1.66 e. none of these
c. 2.14
A researcher collects data on the relationship between the amount of daily exercise an individual gets and the percent body fat of the individual. The following scores are recorded. Individual 1 2 3 4 5 Exercise (min) 10 18 26 33 44 % Fat 30 25 18 17 14 Assuming a linear relationship holds, the least squares regression line for predicting % fat from the amount of exercise an individual gets is _________. a. Y' = 0.476X + 33.272 c. Y' = -0.476X + 33.272 b. Y' = 1.931X + 66.363 d. Y' = -0.432X + 32.856
c. Y' = -0.476X + 33.272
In a positive relationship, _________. a. as X increases, Y increases b. as X decreases, Y decreases c. as X increases, Y increases and as X decreases, Y decreases d. as X increases, Y decreases
c. as X increases, Y increases and as X decreases, Y decreases
When deciding which measure of correlation to employ with a specific set of data, you should consider _________. a. whether the relationship is linear or nonlinear b. type of scale of measurement for each variable c. both of these d. none of these
c. both of these
Correlation and regression differ in that _________. a. correlation is primarily concerned with the size and direction of relationships b. regression is primarily used for prediction c. both of these are true d. neither of these are true
c. both of these are true
If N is small, an extreme score _________. a. won't affect robt unduly c. might have a large effect on robt b. should be thrown out d. has no effect on the value of robt
c. might have a large effect on robt
You go to a carnival and a sideshow performer wants to bet you $100 that he can guess your exact weight just from knowing your height. It turns out that there is the following relationship between height and weight. Height (in) 60.0 62.0 63.0 66.5 73.5 84.0 Weight (lbs) 99 107 111 125 153 195 Should you accept the performers bet? Explain. a. yes b. need more information c. no d. yes, if he measures my height in centimeters
c. no
You have conducted a brilliant study which correlates IQ score with income and find a value of r = 0.75. At the end of the study you find out all the IQ scores were scored 10 points too high. What will the value of r be with the corrected data? a. r will be increased c. r will remain the same b. r will be decreased d. cannot be determined
c. r will remain the same
If one takes a sample of pairs of points over a narrow range of X or Y scores, what effect might this have on the value of r? a. inflate r c. reduce r b. have no effect on r d. cannot be determined
c. reduce r
In the regression equation Y' = X, the Y-intercept is _________. a. X bar c. 0 b. Y bar d. 1
c. 0
In a particular relationship N = 80. How many points would you expect on the average to find within ±1 Y X s | of the regression line? a. 40 c. 54 b. 80 d. 0
c. 54
If X bar= 57.2, Y bar= 84.6, and bY = 0.37, the value of aY = _________. a. 141.80 c. 63.44 b. -25.90 d. 27.40
c. 63.44
If the regression equation for a set of data is Y' = 2.650X + 11.250 then the value of Y' for X = 33 is _________. a. 87.45 c. 98.70 b. 371.25 d. 76.20
c. 98.70
A researcher collects data on the relationship between the amount of daily exercise an individual gets and the percent body fat of the individual. The following scores are recorded. Individual 1 2 3 4 5 Exercise (min) 10 18 26 33 44 % Fat 30 25 18 17 14 Based on the above data, if an individual exercises 20 minutes daily, his predicted % body fat would be _________. a. 21.63 c. 27.88 b. 27.74 d. 23.75
d. 23.75
When predicting Y, adding a second predictor variable to the first predictor variable X, will _______. a. always increase prediction accuracy b. increase prediction accuracy depending on the relationship between the second predictor variable and X c. Increase prediction accuracy depending on the relationship between the second predictor variable and Y d. b and c
d. b and c
In a negative relationship, _________. a. b is positive c. a must be negative b. b can be either positive or negative d. b is negative
d. b is negative
18.If the correlation between variables X and Y is 0.95, which of the following is true? a. X is a cause of Y b. Y is a cause of X c. low scores on X are accompanied by high scores on Y d. high scores on X are accompanied by high scores on Y e. X is a cause of Y and high scores on X are accompanied by high scores on Y
d. high scores on X are accompanied by high scores on Y
In the equation Y = bX + a, X and Y are _________. a. constants c. population parameters b. statistics d. variables
d. variables
When using more than one predictor variable, _________ tells us the proportion of variance accounted for by the predictor variables. a. r c. SSY b. SSX d. R^2
d. R^2
When the relation between X and Y is imperfect, the prediction of Y given X is _________. a. perfect c. impossible to determine b. always equal to Y d. approximate
d. approximate
If the value for aY is negative, the relationship between X and Y is _________. a. positive b. negative c. inverse d. cannot be determined from information given
d. cannot be determined from information given
If bY is negative, higher values of X are associated with _________. a. lower values of X' c. higher values of (Y - Y') b. higher values of Y d. lower values of Y
d. lower values of Y
Which of the following is (are) not correct interpretations of Pearson r? a. ratio of the variability of Y to the variability of X b. measure of extent to which paired scores occupy the same or opposite positions within their own distributions c. difference between the variability of Y and the variability of X d. square root of the proportion of the total variability of Y accounted for by X e. a and c
e. a and c
Which of the following is(are) correct interpretation(s) of correlation? Correlation _________. a. indicates the degree of the relationship between two variables b. indicates a causal relationship between two variables c. is useful in deciding which variables to manipulate in an experimental study d. a and b e. a and c
e. a and c
The regression coefficient bY and the correlation coefficient r, _________. a. necessarily increase in magnitude as the strength of relationship increases b. are both slopes of straight lines c. are not related d. will equal each other when the variability of the X and Y distributions are equal e. are both slopes of straight lines and will equal each other when the variability of the X and Y distributions are equal
e. are both slopes of straight lines and will equal each other when the variability of the X and Y distributions are equal
The least-squares regression line minimizes _________. a. s b. Y X s | c. Σ(Y - Y )2 d. Σ(Y - Y')2 e. b and d
e. b and d
Constructing the regression line of Y on X.
equation on page 27
The higher the standard error of estimate is, a. the more accurate the prediction is likely to be b. the less accurate the prediction is likely to be c. the less confidence we have in the accuracy of the prediction d. the more confidence we have in the accuracy of the prediction e. the more accurate the prediction is likely to be and the more confidence we have in the accuracy of the prediction f. the less accurate the prediction is likely to be and the less confidence we having the accuracy of the prediction
f. the less accurate the prediction is likely to be and the less confidence we having the accuracy of the prediction
discussion questions chapter 7
page 28 and 29 study guide
SE of estimate equation
page 28 with interpretation
Short answer chapter 7
page 38-41
REMEMBER SHORT ANSWER AND SOLVING STUFF
pages 20-25 on study guide
Correlation coefficient definition
Correlation is a measure of the direction and degree of relationship that exists between two variables.
Assume you are a wealthy philanthropist. You want to contribute to help the children of single parents do better in elementary school. You enlist the aid of an educator who advises you to fund an organization that will provide tutors to help the children learn. Pilot work has shown a correlation of 0.30 between tutoring and 5 increased performance in elementary school. Would you follow the advice of the educator? Discuss.
...
Calculating r.
1. Computational formula from raw scores: (not listed here but you gotta know it)
Correlation implies causation.
ANS: F
Variability of Y
Pearson r can also be interpreted in terms of the variability of Y accounted for by X. 1. r = 0. Where r = 0, knowledge of X does not help us predict Y. Best prediction of Y when r = 0 is Y . 2. Deviation of Yi. Distance between a given score Yi and the mean of Y scores Y is divisible into two parts. 3. Total variability. As the relationship between X and Y gets stronger, the prediction error gets smaller causing ( i Y - Y' )2 to decrease, and (Y' - Y )2 to increase.
New definition of r.
Pearson r equals the square root of the proportion of the total variability of Y accounted for by X.
Pearson r A. Definition.
Pearson r is a measure of the extent to which paired scores occupy the same position within their own distributions. Standard scores allow us to examine the relative positions of variables independent of the units of measure.
Magnitude
The coefficient ranges from +1 to -1. Plus 1 is a perfect positive correlation, and minus 1 expresses a perfect negative relationship. A zero value of the correlation coefficient means there is no relationship between the two variables. Imperfect relationships vary between 0 and 1. They will be plus or minus depending on the direction of the relationship.
Which Pearson correlation coefficient shows the strongest relationship between two variables? a. -0.80 b. 0.00 c. 0.75 d. 0.20 e. 0.03
a. -0.80
What is the value of r for the following relationship between height and weight? Height 60 64 65 68 Weight 103 122 137 132 a. 0.87 c. 0.93 b. 0.76 d. 0.56
a. 0.87
2. A scatter plot _________. a. has to do with electron scatter c. must be linear b. is a graph of paired X and Y values d. is a frequency graph of X values
b. is a graph of paired X and Y values d. is a frequency graph of X values
When a correlation exists, lowering the range of either of the variables will _________. a. raise the correlation c. not change the correlation b. lower the correlation d. produce a causal relationship
b. lower the correlation
Rho is used _________. a. when both variables are dichotomous b. when both variables are of interval or ratio scaling c. when one or both variables are only of ordinal scaling d. when the data is nonlinear
c. when one or both variables are only of ordinal scaling
Which of the following values of r represents the strongest degree of relationship between two variables? a. 0.55 c. 0.78 b. 0.00 d. -0.80
d. -0.80
Y can be most accurately predicted from X if the correlation between X and Y is _________. a. 0.80 c. 0.45 b. 0.00 d. -0.98
d. -0.98
The lowest degree of correlation shown below is _________. a. 0.75 c. -0.25 b. -0.33 d. 0.15
d. 0.15
Pearson r is _______. a. a measure of the extent to which paired scores occupy the same or opposite positions within their own distributions. b. the square root of the proportion of the variability of Y that is accounted for by X. c. used when both variables are of interval or ratio scaling. d. All of these are true.
d. All of these are true.
In the equation Y = bX + a, X and Y, b is _________. a. a constant b. the slope of the line c. the Y axis intercept d. a constant and slope of the line e. a variable
d. a constant and slope of the line
A relationship can be _________. a. perfect c. nonexistant b. imperfect d. all of these
d. all of these
If a correlation is perfect, a. all the points must fall on a straight line b. all the points must fall on a curve line c. most the points must fall on the line, but some can miss it. d. all the points must fall on a straight or curved line,
d. all the points must fall on a straight or curved line,
In a negative relationship, _________. a. as X increases, Y increases b. as X decreases, Y decreases c. as X increases, Y increases, and as X decreases, Y decreases d. as X increases, Y decreases
d. as X increases, Y decreases
After several studies, Professor Smith concludes that there is a zero correlation between body weight and bad tempers. This means that _________. a. heavy people tend to have bad tempers b. skinny people tend to have bad tempers c. no one has a bad temper d. everyone has a bad temper e. a person with a bad temper may be heavy or skinny
e. a person with a bad temper may be heavy or skinny
You have noticed that as people eat more ice cream they also have darker suntans. From this observation, you conclude _______. a. eating ice cream causes people to tan darker b. when one's skin tans it causes an urge to eat ice cream c. the results were spurious d. perhaps a third variable is responsible for the correlation e. all of these are possible
e. all of these are possible
Which of the following is (are) not correlation coefficients? a. Pearson r b. eta c. rho d. phi e. they all are correlation coefficients
e. they all are correlation coefficients