4.regression and correlation

4.regression and correlation - STP 226 STP 226 ELEMENTARY...

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1 STP 226 STP 226 ELEMENTARY STATISTICS CHAPTER 4 DESCRIPTIVE MEASURES IN REGRESSION AND CORRELATION Linear Regression and correlation allows us to examine the relationship between two or more quantitative variables. 4.1 Linear Equations with one Independent Variable y = b 0 + b 1 x is a straight line where b 0 and b 1 are constants, b 0 is the y-intercept ( value of y for x=0) and b 1 is the slope of the line. Slope (b 1 ) represents change in y for corresponding change in x, for every 1 unit increase in x value there is a b 1 unit vertical increase/decrease in y value , depending on the line. The straight-line graph of the linear equation y = b 0 + b 1 x slopes upward if b 1 > 0, slopes downward if b 1 < 0, and is horizontal if b 1 = 0. Note: on the picture b 0 = β 0 , b 1 1
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2 STP 226 4.2 The Regression Equation Often, in real life situations, it is not likely to have data that follow some straight line perfectly. A scatterplot (scatter diagram) is useful in visualizing apparent relationships between two variables x and y y – response variable or dependent variable x – predictor variable/explanatory variable or independent variable Example(Table 4.2) (Age and price of a Orion) Car (Orion) 1 2 3 4 5 6 7 8 9 10 11 Age (yr): x 5 4 6 5 5 5 6 6 2 7 7 Price ($100): y 85 103 70 82 89 98 66 95 169 70 48 If the points seem to follow a straight line, then a straight line can be used to approximate the relationship. Scatter plot above shows relatively strong positive linear trend. Sometimes the plot may show another type of the relationship , like quadratic or exponential. Fitting the line to the data that shows no linear trend or other than linear trend is not
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4.regression and correlation - STP 226 STP 226 ELEMENTARY...

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