Week 3 - Summary of lecture 3 PDF

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Summary of lecture 3...

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Week 3 Correlation detects a linear relationship if any between two variables Linear regression finds the line or plane which expresses this relationship Y = a + bx + error The goodness of fit of a regression revolves around the error term Use the independent variables to model the dependent variables Multiple regression Dependent variable - y (eg. Price) Independent variable - x1 / x2 / x3 etc (eg. Beds / area / baths) Model: y = a + b1x1 + b2x2 + b3x3 + error Use =linest to find the intercept (a) and b1 / b2 / b3 The first value calculated is the final value in the model Sample Model Independent variable = sales Dependent variables = area / distance y = -8.24 + (0.018)(area) + (0.137)(distance)  When area and distance are zero the expected sales are -8.24  If area increases by one square foot the sales increase by 0.018K provided distance remains constant  For every increase of one foot away from a competitor sales increase by 0.139K provided area remains constant  Using linest on excel the first result is the last variable R = correlation between the prediction and the actual values R^2 = what proportion of the variability of y is caused by the other variables Multiple regression takes into account a number of independent variables. It is presented as a plane when graphed The process for finding the model is the same regardless of the number f variables 1. Plot scatterplots of each variable against y to establish any relationship 2. Fit models 3. Examine plots of the error terms against y and against the independent variables to see if any patterns emerge For exponential models you can take the log of y or x to create a linear model  Log(y) for slide 23

Use linear regression to find a and b Y1 = loge(y) our estimate Y(hat) = eY(hat)1 

Log(x) for slide 26

Use linear regression to find a and b X1 = loge(x) our estimate x = eX1

If the model has a quadratic relationship, take the square of y (Slide 27) How to transform data sets to enhance linearity  Conduct standard regression on the raw data  Construct an error plot  If the pattern is random don’t transform the data  If there are patterns transform the data  Calculate the coefficient of determination (R2) using (y, y(hat))  Transform either the dependent, independent or both variables  Conduct regression analysis  Calculate R2 on transformed variables

Logistic Equation

1 ( −x ) 1+ e...