My Cheat Sheet - Business Statistics - Exam | BMGT 230M, Exams of Business Statistics

Download My Cheat Sheet - Business Statistics - Exam | BMGT 230M and more Exams Business Statistics in PDF only on Docsity! Statistics consists of two parts: Descriptive statistics (coping with lots of numbers) Draw a picture (graph, charts etc) calculate a few numbers which summarize the data (mean, median, percentile) Inferential statistics How can one make decisions and predictions about a population even if we have data for relatively few subjects from that population? We need to generalize the facts we learn from a sample ( i.e. a part of the population) to the entire population Variable: the aspect/characteristic that differs from subject to subject, individual to individual Data: the value of the variables Quantitative or numerical variable Simpson’s paradox: - of specific, unrecorded variables -Numbers, measurements do not combine data-Keep track -Age, height, miles travelled Qualitative or categorical variables -Classifying each observation -Sex, year in school, major Discrete variables: there is a natural gap between the values -Number of children -Number of credit cards Continuous variables: the values can be arbitrarily close together -Weight -Height -Age Ordinal variables: categories that have a natural ordering -Numbers could be assigned to categories (freshman, sophomore, junior, senior) -A,B,C,D (Gpa/ grades) Nominal variables: categories that have no natural ordering -Major business, mathematics, history -Eye colour blue, green, black b1 is the slope b0 is the y -intercept xbby 10ˆ  Variance Standard Deviation Standardizing Sum of cross product   2 2 1 1 n i i X X S n        2 1 1 n i i X X S n      .,),(           yx yx s yy s xx zz   r  zxzy n  1 A response variable measures or records an outcome of a study. An explanatory variable explains changes in the response variable. After plotting two variables on a scatterplot, we describe the relationship by examining the form, direction, and strength of the association. We look for an overall pattern -Form: linear, curved, clusters, no pattern -Direction: positive, negative, no direction -Strength: how closely the points fit the “form” Positive association: High values of one variable tend to occur together with high values of the other variable. Negative association: High values of one variable tend to occur together with low values of the other variable. No relationship: X and Y vary independently. Knowing X tells you nothing about Y. The strength of the relationship between the two variables can be seen by how much variation, or scatter, there is around the main form. 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 -The correlation coefficient “r” -r does not distinguish between x and y -r has no units of measurement -r ranges from -1 to +1 -Correlation of zero means no linear relationship -Correlation is not affected by changes in the center or scale of either variable -Correlation is sensitive to unusual observations A lurking variable is a variable not included in the study design that does have an effect on the variables studied. -A lurking variable is a variable that is not among the explanatory or response variables in a study and yet may influence the interpretation of relationships among those variables. -Two variables are confounded when their effects on a response variable cannot be distinguished from each other. The confounded variables may be either explanatory variables or lurking variables. -Association is not causation. Even if an association is very strong, this is not by itself good evidence that a change in x will cause a change in y. -A regression line is a straight line that describes how a response variable y changes as an explanatory variable x changes. x y s s rb 1 First we calculate the slope of the line, b1; from statistics we already know: xbyb 10  Where x and y are the sample means of the x and y variables 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. 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). Extrapolation is the use of a regression line for predictions outside the range of x values used to obtain the line. r2, the coefficient of determination, is the square of the correlation coefficient r2 represents the percentage of the variance in y (vertical scatter from the regression line) that can be explained by changes in x. -The distances from each point to the least-squares regression line give us potentially useful information about the contribution of individual data points to the overall pattern of scatter. These distances are called “residuals.” Distance= (y- ŷ )= residual R=(x-x)(y-y)/ (n-1)SxSy