Determining Factors of Market Success. DMD #4 David Kopcso and Richard Cleary Babson College F. W. Olin Graduate School of Business. Learning Objectives. Determine the strength of (linear) relationships Describe a regression model with one or more explanatory variables
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David Kopcso and Richard Cleary
F. W. Olin Graduate School of Business
Investigate variables individually and jointly.
Numerically: Standard Stats Correlation
Graphically: Histogram Scatter Plot
X Y = exp(X)
Do you think knowing the size of a house helps “explain” the variation in house prices?
Price = b0 + b1 Sq. Footage + e
Est. Price = b0 + b1 Sq. Footage^or Price = b0 + b1 Sq. Footage
Est. Price = b0 + b1 Sq. Footage
Est. Price = 117,663 + 173 Sq. Footage
R2 is the percentage of variation of the Y variable that is explained by (accounted for by or reduced by) knowing the X variable (i.e., by using the regression to predict the response rather than the average response value).
Is it small enough to make the predictions from the regressions useful?
Compare it to the standard deviation of the response (dependent) variable.
S: (SEE) S: St Dev(Price)
$28,765 vs. $161,666
About two-thirds (68%) of the data should fall within +/- SEE of the value determined by the regression equation. Similarly about 95% should fall within 2*SEE. Therefore, a 95% interval for the prediction of a specific house at 533 Main St. which has2000 sq. ft., 4 bedrooms, & 2 baths can be computed as Est Price +/- 2*SEE.That is, we are 95% confident that this specific house’s price is between these two values.Since this is about a specific house, the interval is called a prediction interval not a confidence interval.