STAT 3006 Lecture Notes - Lecture 16: Dependent And Independent Variables

• School: Virginia Tech
• Department: Statistics
• Course: STAT 3006
• Professor: Z Zhang

Document Summary

A regression line is a straight line that describes how a response variable y changes as an explanatory variable x changes. This line can be used to predict the value of y for a given value of x. (cid:2207) =(cid:2184)(cid:2777)+(cid:2184)(cid:2778)(cid:2206) or (cid:2207) =(cid:2183)+(cid:2184)(cid:2206) (cid:2207) =(cid:1814)(cid:1820)(cid:1805)(cid:1818)(cid:1803)(cid:1805)(cid:1816)(cid:1820)+(cid:1819)(cid:1812)(cid:1815)(cid:1816)(cid:1805) (cid:2206) (cid:2207) = the predicted value of the response variable for a given value of (cid:2206). (cid:2184)(cid:2778)= the slope (the amount y changes for each one-unit increase with x. (cid:2184)(cid:2777)= is the intercept (the value of y when (cid:2206)=(cid:2777)) this is only a mathematical descriptor of the regression line, for it does not describe the property of the data. The least-squares regression line sums the vertical distances between the data points and the line. Slope: (cid:2184)=(cid:2200)(cid:2201)(cid:2207)(cid:2201)(cid:2206)=(cid:4666)(cid:1803)(cid:1815)(cid:1818)(cid:1818)(cid:1805)(cid:1812)(cid:1820)(cid:1815)(cid:1814) (cid:1803)(cid:1815)(cid:1805)(cid:1806)(cid:1806)(cid:1803)(cid:1805)(cid:1814)(cid:1820)(cid:4667)(cid:4672)(cid:1819)(cid:1820)(cid:1814)(cid:1804)(cid:1818)(cid:1804) (cid:1804)(cid:1805)(cid:1820)(cid:1815)(cid:1814) (cid:1815)(cid:1806) (cid:2207) (cid:1819)(cid:1820)(cid:1814)(cid:1804)(cid:1818)(cid:1804) (cid:1804)(cid:1805)(cid:1820)(cid:1815)(cid:1814) (cid:1815)(cid:1806) (cid:2206)(cid:4673) Coefficient of determination ((cid:1818)(cid:2779)): the percentage of the variance in y that.