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# slides_class3 - Managerial Economics Class 3 Quantitative...

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Managerial Economics – Class 3 1. Fitting Lines to Data 2. Multiple Regression Models 3. Mini Case Study Quantitative Demand Analysis via Multiple Regression

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Fitting Lines to Data The basic problem: Available data Formulate a model to predict a variable of interest Use prediction to make a business decision
Example: Predicting House Prices Problem: Predict market price based on observed characteristics Solution: Look at property sales data where we know the price and some observed characteristics Build a prediction rule that predicts price as a function of the observed characteristics

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Housing Data What characteristics do we use? We must select factors useful for prediction and we have to develop a specific quantitative measure of these factors (a variable) Many factors or variables affect the price of a house size number of baths garage air conditioning, etc. Easy to quantify price and size but what about other variables such as aesthetics, workmanship, etc? For simplicity, let’s focus only on size
Housing Data Now we can use price and size to develop a prediction rule to estimate the price of a house. The variable that we seek to predict is called the dependent variable (or “response” variable) We will denote this as: Y = price of house (thousands of dollars) The variable that we use to predict the dependent variable is called the independent variable (or “predictor” variable) We will denote this as: X = size of house (thousands of square feet)

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Consider a scatter plot of the data: What do we see? Housing Data
The relation between price and size appears to be linear Note that the line shown was fit by the “eyeball” method. Linear Prediction 3 2 1 150 100 50 Size Price

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Linear Prediction Recall that the equation of a line is: Y = b 0 + b 1 X Where: b 0 = is the intercept b 1 = is the slope The intercept is in units of Y (\$1,000) The slope is in units of Y/unit of X (\$1,000/1,000sq ft)
Linear Prediction Y X b 0 2 1 b 1 Y = b 0 + b 1 X Our “eyeball” line has b 0 = 35 b 1 = 40

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Linear Prediction We can now predict the price of a house when we know only the size. We simply “read the value off the line” that we drew: For example, given a house with a size = 2.2 Predicted price = 35 + 40(2.2) = 123, i.e., 123 thousand dollars
Linear Fitting & Prediction in Minitab Minitab output: Regression Analysis: Price versus Size The regression equation is Price = 38.9 + 35.4 Size Predictor Coef SE Coef T P Constant 38.885 9.094 4.28 0.001 Size 35.386 4.494 7.87 0.000 S = 14.14 R-Sq = 82.7% R-Sq(adj) = 81.3% Analysis of Variance Source DF SS MS F P Regression 1 12393 12393 62.00 0.000 Residual Error 13 2599 200 Total 14 14992 Unusual Observations Obs Size Price Fit SE Fit Residual St Resid 13 1.40 58.00 88.43 4.18 -30.43 -2.25R R denotes an observation with a large standardized residual Predicted Values for New Observations New Obs Fit SE Fit 95.0% CI 95.0% PI 1 116.73 3.97 ( 108.16, 125.31) ( 85.01, 148.46) Values of Predictors for New Observations New Obs Size 1 2.20

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Linear Fitting & Prediction in Minitab Minitab chooses a different line from ours Minitab fit: Price = 38.9 + 35.4 Size 3 2 1 150 100 50 Size Price Our line Minitab line
How did Minitab find this Line?

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slides_class3 - Managerial Economics Class 3 Quantitative...

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