Marietta College Week 2 1

Collect Asst 2: Due Tuesday in class 1.#3, Page 25 2

Return Asst 1 (Teams of 2) 1.What is regression analysis? 2.Describe the 3 major tasks that regression analysis allows the researcher to perform. 3.When will the study guide for this class be posted online? As promised, those of you who attended Econ Capstone Presentations last semester received 5 bonus points 3

Let’s review what we know so far Show the equation representing the theoretical relationship between GPA, hours of study and IQ scores of Marietta College students as of January 19, – Coefficients/ variables? – Stochastic/deterministic components? – What is the researcher’s job? 4

5 The Estimated Equation Ŷ i =  ^ 0 +  ^ 1 X i1 +  ^ 2 X i2 Where  ^ 0 “beta hat zero” is the estimated constant term (β 0, the true (theoretical) constant)  ^ 1 “beta hat one” is the estimated β 1 But what is Ŷ i ? – It is not the true GPA – It is the predicted (estimated) GPA – The true GPA (Y i ) may be above or below the predicted GPA Y i =  ^ 0 +  ^ 1 X i1 +  ^ 2 X i2 + e i

6 Let’s assume our estimated equation looks like this Ŷ i = X i X i2 Let’s draw the graph of GPA and hours of study (holding IQ constant) – Where are the observations in our sample? – Where is our fitted line? – The line shows the predicted (estimated) value of GPA at various hours of study and holding other factors (IQ) constant. – Are all observations on the line? – No, there are errors – To make sure we don’t mistake these errors for the stochastic errors in the theoretical equation, we call these errors RESIDUALS – e i measures the size of the residual on individual i – What is e i equal to? – Y i – Ŷ i = e i

7 What is the difference between the error terms and the residuals? The stochastic error terms are The residuals are The stochastic error terms are not observable but the residuals are ; Why? – True regression equation (line) is theoretical (not observable) – Estimated regression equation (line) is observable Residuals exist for the same reasons that errors exist plus – Residuals may be due to sampling and estimation errors /biases

8 The OLS Method Chapter 2 Chooses the intercept (β^ 0 ) and β^ 1 (slope coefficient) of the line (regression equation) in such a way that the sum of squared residuals (Σ e i 2 ) is minimized – Why not just minimize the sum of residuals? Positive errors will cancel the negative errors – The formulas for calculating β^ 0 and β^ 1 in a simple (2 variable equation) are given on Page 38 (Equations 2.4 & 2.5)

Let’s think of the relationship between height and weight Which variable is more likely to be the dependent variable? – Weight – Estimated model – Ŷ i =  ^ 0 +  ^ 1 X i – To estimate the model we collect cross sectional data set on height and weight in our classroom 9

10 Asst 3: Use the following data set and the formulas on Page 38 to estimate  ^ 0 and  ^ 1. Note: you must create a table similar to the one on Page 39. Obs iWeight (Y i ) Height (X i )Obs iWeight (Y i ) Height (X i ) 1. Jackie Tina Seth Yuan Xi Ni Mason Nate Steven Sally Mike Linda Yang Aaron Nick Charlotte Elliot Phillip155 70

Thursday, January Exam 1Tuesday, February 10

Return and discuss Asst 2 Question #3, Page 25 a)positive b)Negative (cross sectional sample) or first positive and then negative (time series sample) c)positive d)negative e)ambiguous (since there is likely to be an accidental correlation) or no relationship f)negative 12

Collect and Discuss Asst 3 1.The estimation results 2.The meaning of the coefficients – The omitted variables are ignored (not held constant) 3.What if we added another variable to our model? – Like what? – Would the coefficient on height change? – How would that change the meaning of the coefficient on height ? The other included variables are held constant The omitted variables are ignored (not held constant) 13

14 Asst 3: Use the following data set and the formulas on Page 38 to estimate  ^ 0 and  ^ 1. Note: you must create a table similar to the one on Page 39. Obs iWeight (Y i ) Height (X i )Obs iWeight (Y i ) Height (X i ) 1. Jackie Tina Seth Yuan Xi Ni Mason Nate Steven Sally Mike Linda Yang Aaron Nick Charlotte Elliot Phillip155 70

15 Let’s use EViews to estimate this regression line File New Workfile Unstructured/undated Observations 17 ok

16 In dialogue box type: data H W Enter Enter data using the keyboard View Graph Scatter – Does the graph make sense to you? Quick Estimate equation Type: W C H

17 Let’s look at the graph of actual weight, predicted weight and the residuals View Actual fitted residual Graph

Asst 4: Due Tuesday in Class 1.Use Eviews to estimate the coefficients in our classroom height – weight example; attach a)the estimation output b) the graph of actual weight, predicted weight and the residuals c)Is Jackie above the estimated line or below it; why? 2. # 5, Page 26 3.# 6, Page 26 18