MAT 221 Chapter 2 Notes
MAT 221 Chapter 2 Notes MAT 221 - M200
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MAT 221 - M200
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MAT 221 M200
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This 2 page Class Notes was uploaded by Niki Neidhart on Tuesday February 9, 2016. The Class Notes belongs to MAT 221 - M200 at Syracuse University taught by X. Au in Spring 2016. Since its upload, it has received 28 views. For similar materials see Elements of Mathematical Statistics and Probability Theory in Math at Syracuse University.
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Date Created: 02/09/16
MAT 221 – Chapter 2 Looking at Data - Relationships 2.1 & 2.2: Relationships & Scatterplots Scatterplot- one axis is used to represent each of the variables and the data are plotted as points on the graph Three Aspects of a Relationship: 1. Direction- positive or negative a. Positive: greater values of one variable tend to occur w/ greater values of other values (ex. House size and price) b. Negative: greater values of one variable tend to occur w/ smaller values of other variable (ex. Weight of cars and fuel efficiency) 2. Form – linear, curved, clusters, no pattern 3. Strength – how closely the points fit the form No relationship- the variables are independent Explanatory (independent) variable – the one that controls the other variable [x-axis] Response (dependent) variable – the one that moves based on the other variable [y-axis] Outlier- anything that doesn’t follow the trend 2.3 Correlation Correlation (coefficient) r – a numerical measure of the direction and strength of the relationship between 2 quantitative variables Properties: - Value r ranges from -1 to 1 - Gives the direction of the relationship - Closer to 1 or -1 is a strong relationship - Closer to 0 is a weak relationship - Very sensitive to outliers How to calculate: - For each case in the sample we have a pair of values (x,y) - Suppose there are n cases (x1,y1), (x2,y2), … (x n,yn) Image from Professor Xu’s online notes: https://blackboa rd.syr.edu/bbcs webdav/pid- 3995343-dt- 12064908_1/cou rses/35384.116 2/Ch2Part2.pdf - R has no unit of measure - Correlation only describes linear relationships - Not resistant to outliers – will be very affected 2.4 Least-Squares Regression Regression Line – a straight line the describes the relationship between x and y variables - Distinction between explanatory and response is important Which line “best fits”? -need line to be as close to all points as possible Residual – the vertical distance from the point to the line Least-squares Regression Line – unique line that the sum of the squared vertical distances between the data points and the line is as small as possible - A straight line is simply a picture of a relationship between two variables Straight Line: Y= (slope) X + (y-intercept) - The y-intercept is where the line crosses the y-axis - The slope tells us which way and by how the line is tilted Finding the equation of the regression line: 1. Find the slope(b 1): B 1= r (S y/Sx) r = correlation coefficient Sx = SD of the x-values Sy = SD of the y-values 2. Find the y-intercept(b ): B 0= (average of y-values) Y – b 1(average of x-values) X 3. The equation is: y = b 1X + b 0
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