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VCU STAT 210 - Scatterplots and Correlations

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MKT 300 1st EditionLecture 11Last LectureI. Measures of Central Location (cont.)II. BoxplotsThis LectureIII. Relationships between variablesIV. ScatterplotsV. Correlation coefficientCurrent LectureVI. Causal = 1 variable causes or explains changes in the other variableVII. Association = 1 variable doesn’t cause change in another variable but there is associationVIII. Both are quantitative variables (X, Y)IX. We want to explain a linear relationshipX. Independent Variable (X)  explanatory; has no restrainsa. Ex.: x = age of a childXI. Dependent (Y)  response; measure outcomea. Ex.: y = weight of childXII. As x increases, y increasesXIII. Lurking variables  have important effect on relationship between x and y but isn’t included in the variables being studiedXIV. X = score on 1st chem test, y = score on 1st math testXV. X doesn’t cause y to happen, but there is a correlationXVI. Overall ability of student, time spent studying = lurking variablesXVII. We can describe relationship by direction, form and strength (scatterplot, correlation coefficient) XVIII. Scatterplot: displays relationship between x and yXIX. X is horizontal, y is verticalXX. Direction: a. Positive = upward trend from left to right (x decreases so y decreases)b. Negative = downward trend from left to right (x decreases so y decreases)c. Linear – points follow linear patternd. Quadratic – points follow parabolic systeme. Exponential – points follow curved patternXXI. Strength: measures amount of scatter around linear trend (weak association, moderate, strong)XXII. Correlation Coefficient is always between -1 and 1a. Negative r = negative relationshipb. Positive r = positive relationshipXXIII. Correlation Coefficient = r = 1/(n-1) x∑xi−xbarsxyi − ybarsy– sxy/√sxxsyyXXIV. Xbar = mean of x dataXXV. Ybar = mean of y dataXXVI. Sx = standard deviation of x dataXXVII. Sy = standard deviation of y


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VCU STAT 210 - Scatterplots and Correlations

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