6: Scatterplots, Association, And Correlation Flashcards
1
Q
What is the cause of lightning according to Alice?
A
Alice believes the cause of lightning is the thunder, but she corrects herself to say it is the other way around.
This reflects a moment of confusion in her reasoning.
2
Q
What is the relationship between brain size and gestation period in mammals?
A
Brain size generally increases as gestation period increases, indicating a positive association.
This is visually represented in a scatterplot.
3
Q
What is a scatterplot?
A
A scatterplot is a graph that shows one quantitative variable versus another quantitative variable.
It helps visualize relationships between two variables.
4
Q
What does the y-axis represent in the scatterplot discussed?
A
The y-axis represents the average neonatal brain weight in grams.
This is plotted against the average gestation period on the x-axis.
5
Q
What does the x-axis represent in the scatterplot discussed?
A
The x-axis represents the average gestation period in days for each species.
This is plotted against average neonatal brain weight on the y-axis.
6
Q
What is a positive association in the context of the scatterplot?
A
A positive association means that as one variable increases, the other variable also increases.
In this case, as gestation period increases, brain weight also increases.
7
Q
How does the pattern of brain weight increase with longer gestation periods appear?
A
The pattern resembles a curved line that steepens with longer gestation periods.
This indicates that the increase in brain weight per additional day of gestation is greater for longer gestation periods.
8
Q
Fill in the blank: The longer the gestation period, the _______ the brain weight increase per day.
A
greater
This suggests a non-linear relationship between gestation period and brain weight.
9
Q
What might happen if brain weight was measured using logarithmic values?
A
It might produce a more linear pattern in the scatterplot.
This suggests that different methods of data expression can impact the visual representation of relationships.
10
Q
True or False: The brain weight dividend is constant regardless of gestation period.
A
False
The brain weight increase per additional day of gestation is greater for longer periods.
11
Q
What unusual observation is noted about brain weight at around 270 days?
A
One species’ brain weight seems unusually high at about 340 g.
This observation raises questions about the normal range of brain weights among species.
12
Q
What is the brain weight of one species that appears unusually low?
A
130 g
This species is identified as humans, indicating a comparison between brain weights across species.
13
Q
What are the two main groups identified among the eight species?
A
Carnivores and primates
The distinction between these two groups is crucial for analyzing their brain weight and gestation relationships.
14
Q
What does the scatterplot reveal about the relationship between brain weight and gestation?
A
There are two distinct subgroups with different relationships between brain weight and gestation.
The relationship appears to curve upward more sharply for carnivores.
15
Q
What is a lurking variable?
A
A hidden variable that may influence the relationship being studied.
In this context, carnivore/primate status is identified as a lurking variable.
16
Q
What is the primary purpose of scatterplots in data analysis?
A
To observe patterns, trends, and relationships between two quantitative variables.
Scatterplots help visualize the association between different data points.
17
Q
What question is posed regarding the age of puberty in current generations?
A
Do people tend to reach puberty at a younger age than in previous generations?
This question relates two quantitative variables and seeks to identify trends over time.
18
Q
What is the ideal way to picture associations between two quantitative variables?
A
Scatterplots
They effectively display relationships and can highlight extraordinary values.
19
Q
Fill in the blank: The relationship between gestation and brain weight appears to curve upward even more sharply for _______.
A
carnivores
This indicates a stronger correlation in this subgroup compared to primates.
20
Q
What philosophical quote is referenced regarding observation?
A
You can observe a lot by watching.
This emphasizes the importance of careful observation in data analysis.
21
Q
True or False: The relationship between brain weight and gestation is the same for both carnivores and primates.
A
False
The relationship differs significantly between the two groups.
22
Q
What is a scatterplot?
A
A graphical representation of the relationship between two variables
Scatterplots display data points on a two-dimensional graph, allowing for visual assessment of relationships.
23
Q
What are the four main features to look for in a scatterplot?
A
- Direction
- Form
- Strength
- Unusual Features
Understanding these features helps in accurately interpreting the data represented in a scatterplot.
24
Q
What does a negative association in a scatterplot look like?
A
A pattern that runs from the upper left to the lower right
This indicates that as one variable increases, the other decreases.
25
What does a positive association in a scatterplot indicate?
A pattern running from the lower left to the upper right
## Footnote
This suggests that both variables increase together.
26
What is the form of a scatterplot if there is a straight-line relationship?
The points appear in a generally consistent, straight form
## Footnote
This is described as a linear association.
27
What does it mean if a scatterplot has a moderate degree of scatter?
It indicates a moderately strong relationship between the variables
## Footnote
For example, the relationship between brain weight and gestation period shows moderate scatter.
28
What should you look for regarding the strength of the relationship in a scatterplot?
Whether the points are tightly clustered or form a vague cloud
## Footnote
Tightly clustered points suggest a stronger relationship, while a vague cloud indicates a weaker one.
29
What are outliers in a scatterplot?
Points that stand away from the overall pattern
## Footnote
Outliers are significant as they can indicate interesting anomalies or errors in data collection.
30
Fill in the blank: A scatterplot with a curve that increases or decreases steadily indicates a _______.
[non-linear relationship]
## Footnote
Such relationships may require transformation to achieve linearity.
31
True or False: Clusters or subgroups in a scatterplot should be ignored.
False
## Footnote
Clusters or subgroups may indicate different trends and should be analyzed separately.
32
What is a timeplot?
A scatterplot where the variable is time
## Footnote
Timeplots can reveal complex patterns like cyclical and seasonal trends.
33
What is the purpose of time series methods of analysis?
To analyze complex patterns in timeplots
## Footnote
These methods help in understanding trends over time.
34
What is the purpose of assigning variables to the x- and y-axes in statistics?
To convey information about their roles as predictor or response variable
## Footnote
This assignment helps clarify the relationship being analyzed.
35
What should you label the axes with when creating a scatterplot?
The names of the variables rather than using y and x
## Footnote
This practice enhances clarity and understanding of the data being represented.
36
What are the two roles variables can play in a scatterplot?
Response variable and explanatory (predictor) variable
## Footnote
The response variable is typically plotted on the y-axis and the explanatory variable on the x-axis.
37
In the context of a scatterplot, what does the response variable represent?
The variable of interest that we want to predict or understand
## Footnote
It is often placed on the y-axis.
38
What is an example of a question that can be analyzed using a scatterplot?
Do older houses sell for less than newer ones of comparable size and quality?
## Footnote
This question involves comparing two variables to analyze their relationship.
39
True or False: The choice of which variable to place on the x-axis or y-axis is arbitrary.
False
## Footnote
The choice should be based on how it helps to answer the research question.
40
What is the significance of the roles we choose for variables in scatterplots?
They reflect our understanding of the relationship rather than the variables themselves
## Footnote
The assignment of roles can influence the interpretation of the scatterplot.
41
What may indicate a positive association in a scatterplot of Height and Weight?
Taller students tend to weigh more
## Footnote
This reflects a general trend observed in the data.
42
Fill in the blank: Older textbooks often refer to the x- and y-variables as _______ and _______.
independent; dependent
## Footnote
These terms can lead to confusion due to their different meanings in statistics.
43
What can high outliers in a scatterplot indicate?
They can affect the overall interpretation of the data
## Footnote
Outliers may skew the perceived relationship between the variables.
44
What does the form of a scatterplot indicate?
The relationship pattern between the two variables
## Footnote
A straight form suggests a linear relationship.
45
What does changing the units of measurement for weight and height affect in a correlation study?
It did not change the direction, form, or strength of the association between the variables.
## Footnote
This highlights the principle that correlation is unit-independent.
46
What color represents a positive association in the scatterplot?
Green
## Footnote
Different colors are used to indicate the type of association: green for positive, red for negative, and blue for neutral.
47
What is the range of values for quantifying the strength of an association?
Between 0 and 1
## Footnote
This numerical representation allows for a standardized measure of correlation strength.
48
How does subtracting the mean from each variable affect the strength of the association?
It shouldn't change the strength of the association.
## Footnote
This operation simply shifts the data to center around zero.
49
What do the green points in the upper right and lower left quadrants of the scatterplot indicate?
They are consistent with a positive association.
## Footnote
Positive associations are represented by data points that lie in these specific quadrants.
50
What do the red points in the scatterplot signify?
They are consistent with a negative association.
## Footnote
This indicates that as one variable increases, the other decreases.
51
What color is used for points that do not add information in the scatterplot?
Blue
## Footnote
Points on the x- or y-axis are colored blue, indicating neutrality in association.
52
Fill in the blank: The scatterplot summarizes the strength of a _______ relationship.
[linear]
## Footnote
Linear relationships are depicted to show how closely data points cluster around a line.
53
What is the formula for the covariance of x and y?
Cov(X, Y) = Sxy = (1/(n-1)) * Σ((xi - x̄)(yi - ȳ))
## Footnote
This formula calculates the covariance between two variables, indicating the degree to which they change together.
54
What does the covariance of x and x represent?
The variance of x
## Footnote
Variance is a measure of how much the values of a variable differ from the mean.
55
What adjustment is made when calculating the correlation coefficient?
The sum is divided by n - 1
## Footnote
This adjustment serves to correct for bias when estimating the population correlation from a sample.
56
What is the range of values for the correlation coefficient?
-1 to +1
## Footnote
A correlation of -1 indicates a perfect negative linear relationship, while +1 indicates a perfect positive linear relationship.
57
True or False: The correlation coefficient has units.
False
## Footnote
Correlation coefficients are dimensionless and do not depend on the units of measurement of the variables.
58
What does a correlation coefficient of 0.644 indicate?
A moderate positive correlation
## Footnote
This means there is a tendency for one variable to increase as the other variable increases.
59
What is the purpose of using z-scores in correlation calculations?
To standardize the data
## Footnote
Standardization removes units and centers the data around the origin, making comparisons easier.
60
Fill in the blank: The natural way to remove the original units is to _______.
standardize each variable
## Footnote
Standardization involves converting raw scores into z-scores.
61
What happens to the plotted points when using z-scores?
They are centered around the origin
## Footnote
This means that the mean of the z-scores is 0, and they reflect the standard deviations from the mean.
62
How is the strength of the association between two variables measured?
By adding up the products of their z-scores
## Footnote
This provides a quantitative measure of how strongly the two variables are related.
63
What do points farther from the center of the plot indicate?
Stronger influence on the correlation
## Footnote
Points that are further from the center can disproportionately affect the correlation coefficient.
64
What does correlation measure?
The strength of linear association between two quantitative variables.
## Footnote
Correlation is specifically about quantitative variables, not categorical ones.
65
What are the three conditions to check before using a correlation?
* Straight Enough Condition
* Quantitative Variables Condition
* Assumptions about the data collection method
## Footnote
These conditions help ensure the validity of the correlation analysis.
66
What is the formula to calculate the correlation coefficient?
r = covariance / (sX * sY)
## Footnote
Here, sX and sY are the standard deviations of the X and Y variables, respectively.
67
Fill in the blank: The assumption that there is a true underlying _______ relationship is essential to interpret a correlation.
linear
68
True or False: Correlation can be used to analyze categorical variables.
False
## Footnote
Correlation is only applicable to quantitative variables.
69
What does the notation 'n - 1' represent in correlation calculations?
The degrees of freedom used when calculating sample covariance.
70
How do we check the plausibility of correlation assumptions?
By looking at the data and thinking about how it was collected.
## Footnote
Visual inspection of scatterplots can also help assess the relationship.
71
What is the significance of the value 'r' in statistics?
It represents the correlation coefficient.
## Footnote
The correlation coefficient quantifies the degree of linear relationship between two variables.
72
Fill in the blank: To calculate the covariance, you divide the sum of the products of deviations by _______.
n - 1
73
What is the first step in finding the correlation coefficient manually?
Calculate the summary statistics for both variables: X, Y, sX, and sY.
74
What does a scatterplot help determine regarding correlation?
Whether the relationship between variables looks reasonably straight enough.
75
What is the product of deviations used for in correlation calculations?
To calculate covariance by summing the products of deviations from the mean.
76
True or False: A correlation coefficient of 0 indicates a strong linear association.
False
## Footnote
A correlation coefficient of 0 indicates no linear association.
77
How is the covariance related to the correlation coefficient?
The correlation coefficient is the covariance normalized by the product of standard deviations.
78
What does the term 'Straight Enough Condition' refer to?
The assumption that the scatterplot of the data shows a linear relationship.
79
What are the two values reported when blood pressure is measured?
Systolic blood pressure and diastolic blood pressure
80
What is the purpose of a scatterplot in relation to variables?
To examine the relationship between two variables
81
What does a correlation value of -0.022 suggest?
No linear association
82
What does a correlation of -0.576 between Clothes Index and Working Hours indicate?
Moderate negative association
83
What does a correlation of 0.774 between Food Costs and Women's Clothing Costs indicate?
Strong positive association
84
What is the effect of adding 10 points to each Exam 1 score on the correlation?
It does not change the correlation
85
If scores on Exam 1 and Exam 2 have a correlation of 0.75, can you predict performance on Exam 2 based on Exam 1?
Not necessarily; correlation does not imply causation
86
What happens to the correlation when scores are standardized?
Correlation remains unchanged
87
What is the 'No Outliers Condition' in correlation analysis?
Outliers can distort the correlation dramatically
88
What do you check before using correlation?
Conditions for using correlation
89
True or False: A correlation of 0.8 indicates a weak association.
False
90
Fill in the blank: A correlation of _______ indicates a strong positive association.
0.8
91
What should you do if you suspect that conditions for correlation are not satisfied?
Be cautious in interpreting the correlation
92
What can outliers in a scatterplot indicate?
They can distort the correlation
93
What does a correlation value of 0.3 indicate?
Weak association
94
What is the correlation value between Food Costs and Vacation Days?
-0.022
95
What is a key characteristic of all variables examined in the context?
All are quantitative
96
What are the two values reported when blood pressure is measured?
Systolic blood pressure and diastolic blood pressure
97
What is the purpose of a scatterplot in relation to variables?
To examine the relationship between two variables
98
What does a correlation value of -0.022 suggest?
No linear association
99
What does a correlation of -0.576 between Clothes Index and Working Hours indicate?
Moderate negative association
100
What does a correlation of 0.774 between Food Costs and Women's Clothing Costs indicate?
Strong positive association
101
What is the effect of adding 10 points to each Exam 1 score on the correlation?
It does not change the correlation
102
If scores on Exam 1 and Exam 2 have a correlation of 0.75, can you predict performance on Exam 2 based on Exam 1?
Not necessarily; correlation does not imply causation
103
What happens to the correlation when scores are standardized?
Correlation remains unchanged
104
What is the 'No Outliers Condition' in correlation analysis?
Outliers can distort the correlation dramatically
105
What do you check before using correlation?
Conditions for using correlation
106
True or False: A correlation of 0.8 indicates a weak association.
False
107
Fill in the blank: A correlation of _______ indicates a strong positive association.
0.8
108
What should you do if you suspect that conditions for correlation are not satisfied?
Be cautious in interpreting the correlation
109
What can outliers in a scatterplot indicate?
They can distort the correlation
110
What does a correlation value of 0.3 indicate?
Weak association
111
What is the correlation value between Food Costs and Vacation Days?
-0.022
112
What is a key characteristic of all variables examined in the context?
All are quantitative
113
What does correlation treat symmetrically?
Correlation treats x and y symmetrically
## Footnote
The correlation of x with y is the same as the correlation of y with x.
114
Does correlation have units?
No, correlation has no units
## Footnote
This is significant when data variables are vague.
115
Why is correlation sometimes given as a percentage discouraged?
It suggests a percentage of something, which correlation lacks
## Footnote
Correlation has no 'something' of which to be a percentage.
116
What does changing the center or scale of either variable do to the correlation coefficient?
It has no effect on the correlation coefficient
## Footnote
Correlation depends only on z-scores, which are unaffected by changes in center or scale.
117
What does correlation measure?
The strength of the linear association between two variables
## Footnote
Variables can be strongly associated but still have a small correlation if the association isn't linear.
118
How does correlation respond to outliers?
Correlation is sensitive to outliers
## Footnote
A single outlying value can significantly alter the correlation value.
119
What terms are often used to characterize correlation strength?
Weak, moderate, or strong
## Footnote
There is no consensus on what these terms mean, and context matters.
120
What is the effect of changing measurement units on correlation?
There is no effect on correlation
## Footnote
Correlation remains unchanged regardless of whether prices are measured in dollars or euros.
121
What do correlation tables display?
Correlations between every pair of variables
## Footnote
The rows and columns name the variables, and the cells hold the correlations.
122
What is a risk associated with correlation tables?
They may show inflated or hidden correlations due to outliers
## Footnote
Correlation tables can present meaningless correlations if the underlying relationship is not linear.
123
What do the diagonal cells of a correlation table show?
Correlations of exactly 1
## Footnote
This occurs because each variable is perfectly correlated with itself.
124
What type of table is sometimes arranged like a correlation table?
A scatterplot matrix
## Footnote
It visually represents the relationships between pairs of variables.
125
What does a correlation table show?
A correlation table shows the relationship between different financial measures for large companies.
126
True or False: Strong correlation guarantees that variables are linearly associated and free from outliers.
False
127
What can a scatterplot indicate about two variables?
A scatterplot can indicate a visual association between two variables but does not confirm causation.
128
What was the correlation coefficient between human population and the number of storks in Oldenburg, Germany?
0.97
129
Fill in the blank: Whenever we have a strong correlation, it's tempting to try to explain it by imagining that the ______ has caused the response to change.
[predictor variable]
130
What misconception does the example of storks and babies illustrate?
It illustrates that correlation does not imply causation.
131
What is the actual reason for the correlation between storks and human population in Oldenburg?
More people means more houses, leading to more nesting sites for storks.
132
What is necessary to determine the real mechanism behind a correlation?
Additional information, not just the data.
133
Who was Sir Ronald Aylmer Fisher?
A prominent statistician who testified in court regarding the correlation of smoking and cancer.
134
What did Fisher suggest about the relationship between lung cancer and smoking?
He suggested that lung cancer might be one of the causes of smoking.
135
What irony is mentioned regarding Fisher's work and smoking-related cancer?
The proof that smoking causes many cancers came from experiments based on the principles Fisher developed.
136
What does the term 'correlation' refer to in statistics?
A statistical measure that describes the extent to which two variables change together.
137
True or False: Correlation can tell us what causes what.
False
138
What type of relationship can a strong correlation suggest?
A potential relationship between two variables, but not necessarily causal.
139
What is the correlation coefficient range?
From -1 to 1
140
Fill in the blank: A correlation of 1.0 indicates a ______ relationship.
[perfect positive]
141
Fill in the blank: A correlation of -1.0 indicates a ______ relationship.
[perfect negative]
142
What is needed to understand the causation behind observed correlations?
Experimentation and additional contextual information.
143
What does a correlation table show?
A correlation table shows the relationship between different financial measures for large companies.
144
True or False: Strong correlation guarantees that variables are linearly associated and free from outliers.
False
145
What can a scatterplot indicate about two variables?
A scatterplot can indicate a visual association between two variables but does not confirm causation.
146
What was the correlation coefficient between human population and the number of storks in Oldenburg, Germany?
0.97
147
Fill in the blank: Whenever we have a strong correlation, it's tempting to try to explain it by imagining that the ______ has caused the response to change.
[predictor variable]
148
What misconception does the example of storks and babies illustrate?
It illustrates that correlation does not imply causation.
149
What is the actual reason for the correlation between storks and human population in Oldenburg?
More people means more houses, leading to more nesting sites for storks.
150
What is necessary to determine the real mechanism behind a correlation?
Additional information, not just the data.
151
Who was Sir Ronald Aylmer Fisher?
A prominent statistician who testified in court regarding the correlation of smoking and cancer.
152
What did Fisher suggest about the relationship between lung cancer and smoking?
He suggested that lung cancer might be one of the causes of smoking.
153
What irony is mentioned regarding Fisher's work and smoking-related cancer?
The proof that smoking causes many cancers came from experiments based on the principles Fisher developed.
154
What does the term 'correlation' refer to in statistics?
A statistical measure that describes the extent to which two variables change together.
155
True or False: Correlation can tell us what causes what.
False
156
What type of relationship can a strong correlation suggest?
A potential relationship between two variables, but not necessarily causal.
157
What is the correlation coefficient range?
From -1 to 1
158
Fill in the blank: A correlation of 1.0 indicates a ______ relationship.
[perfect positive]
159
Fill in the blank: A correlation of -1.0 indicates a ______ relationship.
[perfect negative]
160
What is needed to understand the causation behind observed correlations?
Experimentation and additional contextual information.
161
What is the term for proving causation in the absence of controlled experiments?
Exceedingly difficult
## Footnote
This highlights the challenges faced in establishing direct cause-and-effect relationships without experimental data.
162
What is a common response explanation for the increased incidence of cancer among smokers?
Confounding factors
## Footnote
These factors can obscure the true relationship between smoking and cancer.
163
What is a lurking variable?
A hidden variable that may affect or change our understanding of the relationship
## Footnote
Lurking variables can complicate causal claims, making it difficult to establish clear connections.
164
What might confound the effects of smoking on cancer?
Lifestyle differences
## Footnote
Factors such as alcohol consumption and diet may influence both smoking habits and cancer risk.
165
What is one possible explanation for the observed association between cancer and smoking?
Genetic predisposition
## Footnote
This theory suggests that some individuals may be genetically predisposed to both cancer and nicotine addiction.
166
What does Figure 6.8 illustrate regarding firefighters and damage?
Firefighters exhibit a common response to the size of the blaze
## Footnote
The size of the blaze influences both the number of firefighters and the amount of damage caused.
167
True or False: Scatterplots and correlation coefficients can prove causation.
False
## Footnote
Correlation does not imply causation; establishing causality requires more rigorous evidence.
168
What took years to establish regarding smoking and lung cancer?
Evidence that smoking actually causes lung cancer
## Footnote
Despite strong associations, definitive proof required extensive research and time.
169
Fill in the blank: The effect of smoking on cancer is confounded with the effect of _______.
Lifestyle
## Footnote
This highlights the complexity of isolating the effects of smoking from other lifestyle factors.
170
What is a possible reverse association suggested in the relationship between cancer and smoking?
Cancer causes increased smoking
## Footnote
This theory posits that individuals may smoke more as a response to cancer, rather than smoking causing cancer.
171
What does Fechner's Law state about sensation?
Sensation increases as the logarithm of stimulus
## Footnote
Fechner's Law relates to the perception of changes in stimuli.
172
What is the formula for intensity in relation to the logarithm?
S = k log R
## Footnote
S represents intensity, k is a constant, and R is the stimulus.
173
What is the purpose of re-expressing data in scientific analysis?
To make curved relationships straighter
## Footnote
Re-expressing data can help in identifying patterns and relationships.
174
What does the '2 power' signify in mathematical terms?
Taking the square root
## Footnote
The square root operation is the inverse of squaring a number.
175
What is the relationship between shutter speed and f/stop in photography?
Halving the shutter speed requires opening the aperture
## Footnote
This relationship helps control exposure in photography.
176
True or False: A high correlation indicates a linear relationship.
False
## Footnote
High correlation does not always imply linearity; relationships can be non-linear.
177
What is the significance of the f/stop in photography?
It expresses the size of the aperture
## Footnote
The f/stop controls the amount of light entering the camera.
178
Fill in the blank: The correlation of shutter speeds and f/stops is ______.
0.979
## Footnote
This indicates a strong correlation between the two variables.
179
What is the effect of increasing the f/stop number?
It corresponds to a halving of the light allowed through
## Footnote
This impacts exposure settings in photography.
180
What does a scatterplot reveal about the relationship between two variables?
It shows the pattern of association
## Footnote
Scatterplots are essential for visualizing relationships and correlations.
181
What can scientific laws often include?
Re-expressions and transformations
## Footnote
These methods help in simplifying complex relationships.
182
What is the goal of the Ladder of Powers in data analysis?
To achieve various transformations of data
## Footnote
Different power transformations can normalize data distributions.
183
What type of relationships does correlation measure effectively?
Straight relationships only
## Footnote
Correlation is not suitable for assessing non-linear relationships.
184
What happens when the histogram of data is transformed using logarithms?
It can become more nearly symmetric
## Footnote
This transformation aids in data interpretation.
185
What is one method to check the appropriateness of a correlation?
Examine the scatterplot
## Footnote
A scatterplot can reveal the nature of the relationship between variables.
186
What is the base of natural logarithms?
e
## Footnote
The base e (approximately 2.718) is commonly used in natural logarithms.
187
What is the effect of using logarithms in data analysis?
Logarithms can help straighten scatterplots and improve interpretability of data relationships
## Footnote
Logarithmic transformations are often used to handle skewed data.
188
True or False: The logarithm of a number maintains the order of values.
True
## Footnote
Larger numbers yield larger logarithmic values.
189
Fill in the blank: To undo a logarithm, raise _____ to the power of each value.
10
190
What is a common re-expression for data with zeros?
Add a small constant before applying logarithms or reciprocals
## Footnote
This prevents undefined operations when data contain zero values.
191
What is the reciprocal of a number y?
1/y
192
What is the reciprocal square root of a number y?
1/√y
193
When is the square root re-expression particularly beneficial?
For counted data or measurements that cannot be negative
## Footnote
Examples include population counts and certain types of measurements.
194
What does adding a small constant to all values before finding the reciprocal do?
It helps preserve the direction of relationships
## Footnote
This is important when original ratios may be in the 'wrong' order.
195
What is the raw data referred to as in the context of data transformations?
'home base'
196
What happens to the order of values when using negative powers?
It reverses the order
## Footnote
For instance, if 4 > 2, then -1/2 would imply 2 > 4.
197
What is a common re-expression for data that grows exponentially?
Logarithmic transformation
198
What is the square of the data values represented as?
y²
199
Fill in the blank: Measurements that grow significantly, such as population sizes, often benefit from _____ increases.
percentage
200
What type of distributions might benefit from a square root re-expression?
Unimodal distributions that are skewed
## Footnote
This transformation can help normalize such distributions.
201
What is the importance of choosing the right power for re-expressing data?
It helps straighten scatterplots and enhances data interpretability.
202
True or False: The logarithm and power transformations are invertible.
True
## Footnote
You can revert back to original values easily using appropriate inverse operations.
203
What is the common mistake people make regarding correlation?
Confusing correlation with causation
## Footnote
Correlation indicates an association between variables, not necessarily that one causes the other.
204
What does correlation measure?
The strength and direction of the linear relationship between two variables
## Footnote
Correlation is a precise statistical term.
205
Can correlation be used for categorical variables?
No
## Footnote
Correlation is only valid for quantitative variables.
206
What is the difference between correlation and association?
Correlation is a specific term; association is a general term
## Footnote
Association is a deliberately vague term describing the relationship between two variables.
207
True or False: A high correlation between two variables always indicates that one causes the other.
False
## Footnote
High correlation does not imply causation.
208
What should one be cautious of when interpreting scatterplots?
Scatterplots that turn around
## Footnote
Non-linear relationships can mislead interpretations.
209
When can correlation be considered valid?
When variables are quantitative
## Footnote
It is essential to check if the variables meet this condition.
210
What is one method to analyze linear associations?
Using statistical methods that require a roughly linear form
## Footnote
Familiar methods include the least-squares criterion.
211
Fill in the blank: Correlation is often misused by people when they really mean _______.
association
## Footnote
This misuse can lead to misunderstandings in statistical discussions.
212
What is one way to improve the fit of data that is not linear?
Re-express the variables
## Footnote
Transformations like taking the square root can help linearize data.
213
What does the term 'Ladder of Powers' refer to?
A concept suggesting better transformations for fitting data
## Footnote
It guides the choice of mathematical functions to apply to data.
214
Why is it usually better to linearize data?
Straight lines are easier to fit and understand
## Footnote
Linear relationships simplify analysis and interpretation.
215
What happens when people misuse the term 'correlation'?
They may incorrectly imply a causal relationship
## Footnote
This can lead to significant errors in analysis and interpretation.
216
What command do you enter to perform linear regression on the TI-83/84 calculator?
LinReg(a + bx) L1, L2
217
What is the first step to collect data for linear regression on a TI-83/84 calculator?
Specify the lists where the data are stored
218
Which menu do you go to for linear regression calculations?
STAT CALC menu
219
Which option do you select in the STAT CALC menu to perform linear regression?
8: LinReg(a + bx)
220
How can you find the correlation on a TI-83/84 calculator?
Use DiagnosticOn in the calculator settings
221
What should you do if the calculator does not show the correlation after entering the LinReg command?
Scroll down until you find DiagnosticOn and hit ENTER
222
What must you do to set up a scatterplot on the TI-83/84 calculator?
Set up the STAT PLOT by choosing the scatterplot icon
223
What should you adjust to view your graph appropriately on the calculator?
Set the graphing WINDOW to the appropriate scale
224
What happens when you TRACE the scatterplot on the calculator?
The calculator will tell you the x and y-value at each point
225
What is the function of the ZoomStat command on the TI-83/84 calculator?
It adjusts the viewing window to fit the data
226
True or False: You can find the correlation by changing the calculator's batteries.
False
227
Fill in the blank: To enter a LinReg command, you hit _______.
2nd CATALOG
