Statistics Chapter 3 Exam Questions and Answers Latest Update 2024 Already Passed

Statistics Chapter 3 Exam Questions and Answers Latest Update 2024 Already Passed Procedure with 2 variable statistics - Answers 1.) Plot data and calculate numerical summaries 2.) Look for overall patterns and deviations from those patterns 3.) When there's a regular overall pattern, use a simplified model to describe it Response variable - Answers Measures an outcome of a study Explanatory variable - Answers May help explain or influence changes in a response variable Specific values of variables - Answers It is easiest to identify explanatory and response variables when we actually specify values of one variable to see how it affects another variable. Causation - Answers Often we want to know whether changes in the explanatory variable causes a change in the response variable. Remember, correlation does NOT imply causation. Graph for displaying relationship between two quantitative variables - Answers Scatterplot Scatterplot - Answers Shows the relationship between two quantitative variables measured on the same individuals. The values of one variable (explanatory variable) appear on the horizontal axis and the values of the other variable (response variable) appear on the vertical axis. Each individual in the data appears as a point in the graph. Explanatory-response relationship - Answers Always plot explanatory variable if there is one on horizontal axis (x axis) of the scatterplot. We usually call the explanatory variable x and the response variable y. If there is no explanatory-response distinction, either variable can go on the horizontal axis. How to make a scatterplot - Answers 1.) Decide which variable should go on each axis 2.) Label and scale your axes - Don't start at (0,0) - Start scale to highlight main body of points 3.) Title your plot 4.) Plot individual data values How to examine scatterplots - Answers Look for the overall pattern and striking departures from that pattern. 1.) To describe the OVERALL PATTERN of a scatterplot, discuss the direction/trend, the form/shape, clusters and the strength of the relationship 2.) To describe DEPARTURES from the OVERALL PATTERN discuss outliers (an individual that falls outside the overall pattern of the relationship) Form/shape - Answers The general shape of the graph Ex: linear relationships/curved relationships/outliers/clusters Direction/trend - Answers Draw oval around data and find the slope of the major axis: negative slope means negative trend while positive slope means positive trend If relationship has a clear direction, we speak of positive association (high values of one variable tend to occur together) or negative association (high values of one variable tend to occur with low values of the other variable) Strength (heteroscedasticity) - Answers How scattered is the data (based on the oval) How close the points in a scatterplot lie to a simple form such as a line - Thin hot dog shape = strong - Football shape = moderate - Basketball shape = week - Fan out = differs for different values of explanatory variable *Correlation coefficient Cluster - Answers There are a bunch of data points together - Name ranges of each variable where cluster appears Outlier - Answers There's a lot of white space around the data point - Outlier in response variable (y) - Outlier in explanatory variable - Outlier in both - Outlier b/c doesn't follow the overall pattern/trend Positive association - Answers Positive association, negative association Two variables have a positive association when above-average values of one tend to accompany above-average values of the other, and when below-average values also tend to occur together. Negative association - Answers Two variables have a negative association when above-average values of one tend to accompany bleow-average values of the other Problems w/ positive and negative association - Answers Not all relationships have a clear direction that we can describe as a positive association or negative association Caution w/ scatterplots - Answers Association does not imply causation because there may be other variables lurking in the background that contribute to the relationship between two variables Linear relationships - Answers Linear relationships are important because a straight line is a simple pattern that is quite common; a linear relationship is strong if the points lie close to a straight line and weak if they are widely scattered about a line. Problem with judging linear relationships - Answers Our eyes are not a good judge of strength of a linear relationship. It is easy to be fooled by different scales are the amount of space around the cloud of points. We need to use a numerical measure to supplement the graph. Correlation is the measure we use. Correlation (coefficient) - Answers The correlation r measures the direction and strength of the linear relationship between two quantitative variables. - The correlation r is always a number b/w -1 and 1. - Correlation indicates the direction of a linear relationship by its sign: r > 0 for a positive association and r <0 for a negative association - Values of r near 0 indicate a very weak linear relationship. The strength of the linear relationship increases as r moves away from 0 toward -1 or 1. - The extreme values r = -1 and r = 1 occur only in the case of a perfect linear relationship, when the points lie exactly along a straight line How to calculate the correlation - Answers Suppose that we have data on variables x and y for n individuals. The means and the standard deviations of the two variables are xbar and sx for the x-values and ybar and sy for the y values. The correlation r between x and y is 1/(n-1) times the sum of the products of zx and zy (Use calculator: 6 1 4) Another meaning of correlation - Answers The average of the products of the standardized scores Problems with correlation calculation - Answers A value of r close to 1 or -1 does not guarantee a linear relationship between two variables. A scatterplot with a clear curved form can have a correlation near 1 or -1. Always plot your data. Facts about correlation: #1 - Answers Correlation makes no distinction between explanatory and response variables. It makes no difference which variable you call x and which you call y in