Business Statistics Exam Statistics a way of thinking Collection of tools and methods to help make decisions analyze data identify patterns trends and relationships Uses samples make conclusions Descriptive lots of numbers numerical or graphical drawing graphs pictures calculating numbers mean median Inferential making predictions generalizing facts from a sample to a whole population Data values at a know context or values of variable The two types of variables numerical or quantitative numbers numbers measurements Categorical or qualitative categories Quantitative is either Discrete there s a natural gap between values Continuous values are arbitrarily close together Qualitative is either ordinal categories that have no natural order Nominal ordered Interval Data No meaningful 0 point Ratio Data meaningful 0 point Time Series Data ordered data values over time Cross Sectional Data observed at a single point in time Surveys and Sampling examines a part of a whole Biased Sample sample that over or under emphasized some characteristics of the population Selection Bias exclude one kind of individual from the survey Non Response Bias subjects don t answer skip answer Response Bias subjects lie interview effect Randomization gets rid of bias and helps the average sample look like the rest of the population The size of the sample matters not the size of the population 10 rule exception Parameter a number describing a characteristic of the population Sampling Techniques are either Non statistical Convenience most convenient manner for researcher ask whoevers around Voluntary individuals choose to be involved Statistical Simple Random Sampling every sample has an equal chance of being selected Stratified Random Sampling divide population into subgroups and select random sample from each group Combines samples from subgroups into one Cluster Sampling divides population into clusters Systemic Random Sampling decide on sample size divide ordered frame into groups of individuals randomly select one individual select every same rd person after that Sampling Frame list of population Sample Survey asks questions of a small group of people to learn something about the entire population Explanatory Variable predictor cause Response predicted effect Marginal Distribution row totals and column totals Conditional Distributions comparing explanatory and response variables Simpsons Paradox association or comparison that holds for all of several groups Can reverse direction when data are combined to form a single group Continuous Data may take on any value in some interval Range largest data point smallest data point A distribution is symmetric if the right and left sides of the histogram are approximately mirror images Skewed a distribution is skewed right if the right side extends much farther out then the left side Mode peak in the distribution IQR Interquartile range Q3 Q1 Standard Deviation average squared distance from the mean Population Set of Individuals of interest Parameter unknown characteristic of the population Sample Part of the population Statistic known a characteristic from the sample Regression Line line that measures the sum of the squared residual z z y x x x s x y y s y z value mean st dev A response variable measures or records an outcome of a study An explanatory variable explains changes in the response variable Typically the explanatory or independent variable is plotted on the x axis and the response or dependent variable is plotted on the y axis outlier is a data value that has a very low probability of occurrence Correlation can only be used to describe quantitative variables Categorical variables don t have means and standard deviations The correlation coefficient is a measure of the direction and strength of a linear relationship Properties of r 1 r 1 r zxzy n 1 Correlation Coefficient r if r 0 there is no linear association 1 2 r has no units 3 4 r of x y r of y x 5 r is interest to scale changes 6 r is not robust 7 correlation does not imply causation A lurking variable a variable not included in the study that does have an effect on the variables studied y b 0 xb 1 y is the predicted y value b1 is the slope b0 is the y intercept First we calculate the slope of the line b1 from statistics we already know r is the correlation sy is the standard deviation of the response variable y sx is the the standard deviation of the explanatory variable x b 1 r s s y x b0 y b1x where hat x and hat y are the sample means of the x and y variables b0 is the estimated average value of Y when the value of X is zero if x 0 is in the range of observed x values b1 measures the estimated change in the average value of Y as a result of a one unit change in X Once we know b1 the slope we can calculate b0 the y intercept The correlation is a measure of spread scatter in both the x and y directions in the linear relationship In regression we examine the variation in the response variable y given change in the explanatory variable x r2 the coefficient of determination is the square of the correlation coefficient r2 represents the percentage of the variance in y that can be explained by changes in x
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