Introducing Statistics: Do Those Points Align - AP Statistics
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Which test checks if a linear relationship exists between two variables?
Which test checks if a linear relationship exists between two variables?
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Pearson's correlation test. Formal test for linear association significance.
Pearson's correlation test. Formal test for linear association significance.
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What is the purpose of a scatterplot in statistics?
What is the purpose of a scatterplot in statistics?
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To visually display the relationship between two quantitative variables. Shows how one variable changes as another changes.
To visually display the relationship between two quantitative variables. Shows how one variable changes as another changes.
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Identify the axis typically used for the explanatory variable in a scatterplot.
Identify the axis typically used for the explanatory variable in a scatterplot.
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The x-axis. Convention places independent variable on horizontal axis.
The x-axis. Convention places independent variable on horizontal axis.
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Identify the axis typically used for the response variable in a scatterplot.
Identify the axis typically used for the response variable in a scatterplot.
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The y-axis. Convention places dependent variable on vertical axis.
The y-axis. Convention places dependent variable on vertical axis.
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What does a positive association in a scatterplot indicate?
What does a positive association in a scatterplot indicate?
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As one variable increases, the other variable also increases. Both variables move in the same direction together.
As one variable increases, the other variable also increases. Both variables move in the same direction together.
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What does a negative association in a scatterplot indicate?
What does a negative association in a scatterplot indicate?
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As one variable increases, the other variable decreases. Variables move in opposite directions to each other.
As one variable increases, the other variable decreases. Variables move in opposite directions to each other.
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Which term describes a scatterplot where points form a straight line?
Which term describes a scatterplot where points form a straight line?
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Linear relationship. Points cluster around an imaginary straight line.
Linear relationship. Points cluster around an imaginary straight line.
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Which term describes a scatterplot where points form a curved pattern?
Which term describes a scatterplot where points form a curved pattern?
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Non-linear relationship. Points follow a curve rather than straight line.
Non-linear relationship. Points follow a curve rather than straight line.
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What does it mean if a scatterplot shows a cluster of points?
What does it mean if a scatterplot shows a cluster of points?
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There may be a subset of data behaving differently. Indicates possible subgroups within the data.
There may be a subset of data behaving differently. Indicates possible subgroups within the data.
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What is an outlier in the context of a scatterplot?
What is an outlier in the context of a scatterplot?
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A data point that does not fit the general pattern of the data. Deviates significantly from the overall trend.
A data point that does not fit the general pattern of the data. Deviates significantly from the overall trend.
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Which statistical measure quantifies the strength and direction of a linear relationship?
Which statistical measure quantifies the strength and direction of a linear relationship?
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The correlation coefficient, $r$. Measures linear association between -1 and 1.
The correlation coefficient, $r$. Measures linear association between -1 and 1.
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What is the range of values for the correlation coefficient $r$?
What is the range of values for the correlation coefficient $r$?
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$-1 \text{ to } 1$. Bounded values indicating strength of linear relationship.
$-1 \text{ to } 1$. Bounded values indicating strength of linear relationship.
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What does $r = 1$ imply about the relationship between two variables?
What does $r = 1$ imply about the relationship between two variables?
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Perfect positive linear relationship. All points lie exactly on a straight line upward.
Perfect positive linear relationship. All points lie exactly on a straight line upward.
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What does $r = -1$ imply about the relationship between two variables?
What does $r = -1$ imply about the relationship between two variables?
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Perfect negative linear relationship. All points lie exactly on a straight line downward.
Perfect negative linear relationship. All points lie exactly on a straight line downward.
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What does a correlation coefficient close to 0 indicate?
What does a correlation coefficient close to 0 indicate?
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Weak linear relationship. Little to no linear association between variables.
Weak linear relationship. Little to no linear association between variables.
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Which graph is appropriate for visualizing the relationship between categorical variables?
Which graph is appropriate for visualizing the relationship between categorical variables?
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A bar chart. Categorical data requires bars, not scatterplots.
A bar chart. Categorical data requires bars, not scatterplots.
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Which option indicates a non-linear relationship in a scatterplot?
Which option indicates a non-linear relationship in a scatterplot?
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Curve of best fit. Curved patterns indicate non-linear relationships.
Curve of best fit. Curved patterns indicate non-linear relationships.
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What does the term 'homoscedasticity' refer to in a scatterplot?
What does the term 'homoscedasticity' refer to in a scatterplot?
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Consistent variance of errors across all levels of an independent variable. Equal spread of residuals at all levels.
Consistent variance of errors across all levels of an independent variable. Equal spread of residuals at all levels.
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Identify the effect of outliers on the correlation coefficient.
Identify the effect of outliers on the correlation coefficient.
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Can greatly increase or decrease the correlation coefficient. Outliers can dramatically alter correlation values.
Can greatly increase or decrease the correlation coefficient. Outliers can dramatically alter correlation values.
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What is the primary use of a linear regression line in a scatterplot?
What is the primary use of a linear regression line in a scatterplot?
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To predict values of the response variable. Line enables estimation of unknown y-values.
To predict values of the response variable. Line enables estimation of unknown y-values.
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State the equation for a simple linear regression line.
State the equation for a simple linear regression line.
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$y = b_0 + b_1x$. Standard form of linear equation with coefficients.
$y = b_0 + b_1x$. Standard form of linear equation with coefficients.
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What does $b_0$ represent in the regression equation?
What does $b_0$ represent in the regression equation?
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The y-intercept. Value of y when x equals zero.
The y-intercept. Value of y when x equals zero.
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What does $b_1$ represent in the regression equation?
What does $b_1$ represent in the regression equation?
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The slope of the line. Rate of change in y per unit x.
The slope of the line. Rate of change in y per unit x.
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Which concept describes how well a regression line fits the data?
Which concept describes how well a regression line fits the data?
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Coefficient of determination, $R^2$. Measures proportion of variance explained by model.
Coefficient of determination, $R^2$. Measures proportion of variance explained by model.
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What is the range of values for the coefficient of determination $R^2$?
What is the range of values for the coefficient of determination $R^2$?
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$0 \text{ to } 1$. Proportion values from 0% to 100% fit.
$0 \text{ to } 1$. Proportion values from 0% to 100% fit.
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What does an $R^2$ value of 0.75 imply?
What does an $R^2$ value of 0.75 imply?
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75% of the variability in the response variable is explained by the model. Model explains three-quarters of the variation.
75% of the variability in the response variable is explained by the model. Model explains three-quarters of the variation.
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Which metric measures the spread of residuals around the regression line?
Which metric measures the spread of residuals around the regression line?
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Standard error of the estimate. Quantifies typical distance from regression line.
Standard error of the estimate. Quantifies typical distance from regression line.
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Identify the type of plot used to assess the linearity assumption of a regression model.
Identify the type of plot used to assess the linearity assumption of a regression model.
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Scatterplot of residuals versus fitted values. Examines residuals to check linear assumption.
Scatterplot of residuals versus fitted values. Examines residuals to check linear assumption.
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What is the effect of adding a variable with no correlation to the response variable?
What is the effect of adding a variable with no correlation to the response variable?
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May reduce $R^2$. Irrelevant variables don't improve model fit.
May reduce $R^2$. Irrelevant variables don't improve model fit.
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Which concept describes the influence of a single point on a regression line?
Which concept describes the influence of a single point on a regression line?
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Leverage. Measures how much a point affects line.
Leverage. Measures how much a point affects line.
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