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Lecture 23

Department

StatisticsCourse Code

STAT 101Professor

Richard WatermanLecture

23This

**preview**shows half of the first page. to view the full**3 pages of the document.**Stat 101 - Introduction to Business Statistics - Lecture 23: Line of Fit

Reasons to fit a line through data

● Graphically summarize

● Interpolate

● Forecast/extrapolate (with caution)

● Mathematically leverage the equation: derivatives and optimizations

Least Squares

● the best line minimizes the sum of the squares of the vertical distances from the point to

the line, and is called the Least Squares Line

● Sometimes, we may fit a line on a transformed scale, then back-transform, which gives

best fitting curves

● The difference between y and yhat (y - yhat) is called the residual (e)

● Fitted values given as:

○ yhat = b0 + b1x

○ b1 = r (sy / sx ) , where r is the correlation between y & x

○ b0 = ybar - (b1 * xbar)

● Graph the line:

○

○ Slope interpretation: the change in y for every one unit change in x

■ ie. 3.7 additional rooms per additional crew

○ Intercept interpretation: more problematic. sometimes the intercept does not

have a clear interpretation. sometimes it is an extrapolation outside the range of

data

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