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# Chapters 13, 14, 15, 17, 18 STAT 1350 – 1000

OSU

GPA 3.7

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This 3 page Study Guide was uploaded by Kristen Motil on Friday October 30, 2015. The Study Guide belongs to STAT 1350 – 1000 at Ohio State University taught by Michelle Duda in Summer 2015. Since its upload, it has received 36 views. For similar materials see Elementary stats in Statistics at Ohio State University.

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Date Created: 10/30/15

Density curves describe the overall pattern of the distribution deaHzedquot The area under a density curve gives the proportion of observations that fall in a particular range of values 0 The total area is 100 The proportions obtained from the density curve will not exactly equal the observed proportions Normal curves bellshaped describe normal distribution Normal distributions are 0 Symmetric o Unimodal one peak 0 Bellshaped Mean population mean center u Standard deviation variability 0 Normal 104 refers to mean 10 SD 4 For normal distribution 0 68 of observations fall within i 1 SD of the mean 0 95 of observations fall within i 2 SD of the mean 0 997 of observations fall within i 3 SD of the mean Zscore means above mean means below mean 0 means at mean of deviations away from mean Z observation mean SD 0 Tells how many SD the observation x falls from the mean and in which direction 0 The table shows things under the curve not above Higher zscore means higher percentile Scatterplot shows graphically the relationship between 2 quantitative variables measured on the same individuals each individual appears as a point on the plot 0 Xaxis explanatory variable 0 Yaxis response variable 0 To determine if a pattern exists such that some values of one variable tend to occur more often with some values of the other variable Overall pattern is described by 0 Form linear curved or random 0 Direction positive association high low values of one variable corresponded to high low values of the other negative association high values of one variable correspond to low values of the other and vise versa 0 Strength asses the scatter of the points fairly strong or fairly weak 0 Outliers are there points outside of the overall pattern Correlation r a number that measures both the direction and strength of the linear relationship between 2 quantitative variables 0 An quotaveragequot of the product of the standardized values of the 2 variables 0 Correlation is the same regardless of which variable you abe x and y Both variables must be quantitative R 1 s r s 1 RgtO positive association RltO negative association R measures strength of linear relationships R near 0 weak linear relationship 0 R near 1 or 1 points ie close to a straight line 0000 O O o R has no units 0 Changing the units of measurement for one or both variables will not change the value of r o R is strongly affected by outliers Regression line a straight line that describes how a response variable y changes as an explanatory variable x changes 0 Y a bx 0 Correlation and slope signs are equal 0 Most common method of choosing the best line is least squares regression Extrapolation if x is outside of original data High correlation accurate predictions The usefulness of a regression line for prediction depends on the correlation between variables Coefficient of determination r2 measures the usefulness of the regression line of response variable that can be explained by explanatory variable 0 Ex 80 of variation in BAC can be explained by of beers 0 Check the sign of r with slope because every number squared is positive 0 The stronger the relationship between x and y the closer r2 is to 100 0 High correlation does not imply causann For every increase by 1 of explanatory variable response variable increases by slope When explanatory variable is 0 response variable equals y intercept R2 of the variation in explanatory variable can be explained by the regression equann Theoretical probability assume equally likely Empirical probability counting frequency Subjective probability personal probability based on opinion Probabilities are based on what happens in many many many repetitions Chance behavior random phenomenon unpredictable in short term predictable in long term Probability of chance behavior is the proportion of a very long series of repetitions on which the outcome occurs 0 Can never be negative 01 Probability model used to describe random phenomenon by assigning probabilities to the different possible outcomes 0 Consists of possible outcomes and probabilities Any probability is between 0 and 1 The sum of the probabilities of all possible outcomes must be 1 100 PA probability that event A occurs 0 Complement rule PAC PA does not occur 1 PA C complement not 0 Addition rule if events A and B have no outcomes in common PA or B occurring PA PB Why don t short random sequences need to look regular because each coin ip does not impact the next long term we expect 5050 o 2 random phenomena are 0 The more samples taken the more independent if they do not impact likely the probability one another

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