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- https://stats.libretexts.org/Courses/Queensborough_Community_College/MA336%3A_Statistics/03%3A_Examining_Relationships-_Quantitative_Data/3.05%3A_Assessing_the_Fit_of_a_Line_(2_of_4)In the graph below, we plotted the values of the residuals on their own. (The explanatory variable is still plotted on the horizontal axis, though it is not indicated this here.) This is called a resi...In the graph below, we plotted the values of the residuals on their own. (The explanatory variable is still plotted on the horizontal axis, though it is not indicated this here.) This is called a residual plot. The pattern in the residual plot suggests that our linear model may not be appropriate because the model predictions will be too high for values in the middle of the range of the explanatory variable and too low for values at the two ends of that range.
- https://stats.libretexts.org/Courses/Queensborough_Community_College/MA336%3A_Statistics/03%3A_Examining_Relationships-_Quantitative_Data/3.23%3A_Linear_Relationships_(4_of_4)Pay attention to the correlation coefficient calculated at the top left of the simulation. (Clicking on the garbage can lets you start over.) Once you are satisfied with your hypothetical data, create...Pay attention to the correlation coefficient calculated at the top left of the simulation. (Clicking on the garbage can lets you start over.) Once you are satisfied with your hypothetical data, create an outlier by clicking on one of the data points in the upper right of the graph and dragging it down along the right side of the graph.
- https://stats.libretexts.org/Courses/Queensborough_Community_College/MA336%3A_Statistics/01%3A_Introduction_to_Statistical_Studies/1.07%3A_Introduction_to_SamplingStatistics seeks to use information about variables or relationships from a statistical study (sample) to draw conclusions about what is true for the entire population from which the sample was chosen...Statistics seeks to use information about variables or relationships from a statistical study (sample) to draw conclusions about what is true for the entire population from which the sample was chosen. In this section, we will look at how we can create a sampling plan so that the sampling is carried out in such a way that the sample really does represent the population of interest.
- https://stats.libretexts.org/Courses/Queensborough_Community_College/MA336%3A_Statistics/01%3A_Introduction_to_Statistical_Studies/1.02%3A_Introduction_to_Types_of_Statistical_StudiesWhat you’ll learn to do: Describe various types of statistical studies and the types of conclusions that are appropriate. In statistical studies, the type of study design used and the details of the d...What you’ll learn to do: Describe various types of statistical studies and the types of conclusions that are appropriate. In statistical studies, the type of study design used and the details of the design are important in determining what kind of conclusions we may draw from the results. In this section, we will explore how the details of a study design play a crucial role in determining our ability to establish evidence of causation.
- https://stats.libretexts.org/Courses/Queensborough_Community_College/MA336%3A_Statistics/03%3A_Examining_Relationships-_Quantitative_Data/3.02%3A_Linear_Regression_(4_of_4)If we know the mean and standard deviation for x and y, along with the correlation (r), we can calculate the slope b and the starting value a with the following formulas: The slope of the least-square...If we know the mean and standard deviation for x and y, along with the correlation (r), we can calculate the slope b and the starting value a with the following formulas: The slope of the least-squares regression line is the average change in the predicted values of the response variable when the explanatory variable increases by 1 unit.
- https://stats.libretexts.org/Courses/Queensborough_Community_College/MA336%3A_Statistics/01%3A_Introduction_to_Statistical_Studies/1.09%3A_Sampling_(2_of_2)A representative sample is a subset of the population that reflects the characteristics of the population. The precision of the sample results depends on the size of the sample, not the size of the po...A representative sample is a subset of the population that reflects the characteristics of the population. The precision of the sample results depends on the size of the sample, not the size of the population. We draw a conclusion about the population on the basis of the sample. The size of the population does not affect the accuracy of a random sample as long as the population is large.
- https://stats.libretexts.org/Courses/Queensborough_Community_College/MA336%3A_Statistics/03%3A_Examining_Relationships-_Quantitative_Data/3.26%3A_Causation_and_Lurking_Variables_(2_of_2)When the scatterplot displays a linear relationship, we supplement it with the correlation coefficient (r), which measures the strength and the direction of a linear relationship between two quantitat...When the scatterplot displays a linear relationship, we supplement it with the correlation coefficient (r), which measures the strength and the direction of a linear relationship between two quantitative variables. It is a third variable that is neither the explanatory nor the response variable, but it affects your interpretation of the relationship between the explanatory and response variable.
- https://stats.libretexts.org/Courses/Queensborough_Community_College/MA336%3A_Statistics/03%3A_Examining_Relationships-_Quantitative_Data/3.17%3A_Scatterplots_(4_of_5)So the elephant is an outlier in the distribution of both the lifespan and the pregnancy variables. When you drive a car, what is the relationship between the speed you drive and the amount of gas the...So the elephant is an outlier in the distribution of both the lifespan and the pregnancy variables. When you drive a car, what is the relationship between the speed you drive and the amount of gas the car uses? The amount of fuel decreases rapidly to a low point when the speed is 60 kilometers per hour, so the car uses the least amount of fuel at a speed of 60 km/h.
- https://stats.libretexts.org/Courses/Queensborough_Community_College/MA336%3A_Statistics/03%3A_Examining_Relationships-_Quantitative_Data/3.22%3A_Linear_Relationships_(3_of_4)Because the form of the relationship is linear, we can use the correlation coefficient as a measure of direction and strength of the linear relationship. The correlation coefficient can be interpreted...Because the form of the relationship is linear, we can use the correlation coefficient as a measure of direction and strength of the linear relationship. The correlation coefficient can be interpreted only as the measure of the strength of a linear relationship, so we need the scatterplot to verify that the relationship indeed looks linear.
- https://stats.libretexts.org/Courses/Queensborough_Community_College/MA336%3A_Statistics/01%3A_Introduction_to_Statistical_Studies/1.14%3A_Putting_It_Together-_Types_of_Statistical_Studies_and_Producing_DataIn an observational study, we draw a conclusion about the population on the basis of a sample. The size of the population does not affect the accuracy of a random sample as long as the population is l...In an observational study, we draw a conclusion about the population on the basis of a sample. The size of the population does not affect the accuracy of a random sample as long as the population is large. If an attempt is made to include every individual from a population in a sample, then the investigation is called a census. To establish a cause-and-effect relationship, we want to make sure the explanatory variable is the only factor that impacts the response variable.
- https://stats.libretexts.org/Courses/Lumen_Learning/Statistics_for_the_Social_Sciences_(Pelz)/06%3A_Probability_and_Probability_Distributions/6.03%3A_Another_Look_at_Probability_(1_of_2)In the module Relationships in Categorical Data with Intro to Probability, we used the word probability to mean “likelihood” or “chance.” We used data to make statements about We can use the data from...In the module Relationships in Categorical Data with Intro to Probability, we used the word probability to mean “likelihood” or “chance.” We used data to make statements about We can use the data from the West Coast college that we saw in Relationships in Categorical Data with Intro to Probability and estimate that . Of course, this estimate assumes this college is a representative sample of community colleges.
