11 Chapter 5 The Research Process – Hypothesis Development – (Stage 4 in Research Process) © 2009 John Wiley & Sons Ltd.

 Recall the Research process: 1)Broad problem area 2)Problem statement 3)Theoretical Framework 4)Generation of hypotheses 5)Data collection: 6)Data analysis: 7)Report Writing( Interpretation of results) 2 © 2009 John Wiley & Sons Ltd.

Stage 4 : Hypothesis  A proposition that is empirically testable. It is an empirical statement concerned with the relationship among variables.  Good hypothesis: –Must be adequate for its purpose –Must be testable –Must be better than its rivals 3 © 2009 John Wiley & Sons Ltd.

The Simple Regression Model  Regression analysis is a statistical tool for the investigation of relationships between variables.  Usually, the investigator seeks to determine the causal effect of one variable upon another.  To explore such issues, the investigator assembles data on the underlying variables of interest and employs regression to estimate the quantitative effect of the causal variables upon the variable that they influence. The investigator also typically assesses the “statistical significance” of

The Simple Regression Model  The investigator also typically assesses the “statistical significance” of the estimated relationships, that is, the degree of confidence that the true relationship is close to the estimated relationship.  Regression techniques have long been central to the field of economic statistics (“econometrics”).

 Definition of the simple linear regression model Dependent variable, explained variable, response variable,… Independent variable, explanatory variable, regressor,… Error term, disturbance, unobservables,… Intercept Slope parameter "Explains variable in terms of variable " The Simple Regression Model

 Example: Soybean yield and fertilizer  Example: A simple wage equation Measures the effect of fertilizer on yield, holding all other factors fixed Rainfall, land quality, presence of parasites, … Measures the change in hourly wage given another year of education, holding all other factors fixed Labor force experience, tenure with current employer, work ethic, intelligence … The Simple Regression Model

 In order to estimate the regression model one needs data  A random sample of observations First observation Second observation Third observation n-th observation Value of the explanatory variable of the i-th observation Value of dependent variable of the i-th observation The Simple Regression Model

 Fit as good as possible a regression line through the data points: Fitted regression line For example, the i-th data point The Simple Regression Model

 What does "as good as possible" mean?  Regression residuals  Minimize sum of squared regression residuals  Ordinary Least Squares (OLS) estimates The Simple Regression Model

 CEO Salary and return on equity  Fitted regression  Causal interpretation? Salary in thousands of dollars Return on equity of the CEO‘s firm Intercept If the return on equity increases by 1 percent, then salary is predicted to change by 18,501 $ The Simple Regression Model

 Wage and education  Fitted regression Hourly wage in dollars Years of education Intercept In the sample, one more year of education was associated with an increase in hourly wage by 0.54 $ The Simple Regression Model

 CEO Salary and return on equity The regression explains only 1.3 % of the total variation in salaries The Simple Regression Model

Multiple Regression Analysis: Estimation  Definition of the multiple linear regression model Dependent variable, explained variable, response variable,… Independent variables, explanatory variables, regressors,… Error term, disturbance, unobservables,… InterceptSlope parameters "Explains variable in terms of variables "

 Motivation for multiple regression –Incorporate more explanatory factors into the model –Explicitly hold fixed other factors that otherwise would be in –Allow for more flexible functional forms  Example: Wage equation Hourly wage Years of educationLabor market experience All other factors… Now measures effect of education explicitly holding experience fixed Multiple Regression Analysis: Estimation

 Example: Wage equation –Test whether, after controlling for education and tenure, higher work experience leads to higher hourly wages Standard errors Test against. One would either expect a positive effect of experience on hourly wage or no effect at all. Multiple Regression Analysis: Inference

 Example: Wage equation (cont.) "The effect of experience on hourly wage is statistically greater than zero at the 5% (and even at the 1%) significance level." t-statistic Degrees of freedom; here the standard normal approximation applies Critical values for the 5% and the 1% significance level (these are conventional significance levels). The null hypothesis is rejected because the t-statistic exceeds the critical value. Multiple Regression Analysis: Inference

 Testing against two-sided alternatives Test agai nst. Reject the null hypothesis in favour of the alternative hypothesis if the absolute value of the estimated coefficient is too large. Construct the critical value so that, if the null hypothesis is true, it is rejected in, for example, 5% of the cases. In the given example, these are the points of the t-distribution so that 5% of the cases lie in the two tails. ! Reject if absolute value of t-statistic is less than or greater than 2.06 Multiple Regression Analysis: Inference

 Guidelines for discussing economic and statistical significance –If a variable is statistically significant, discuss the magnitude of the coefficient to get an idea of its economic or practical importance –The fact that a coefficient is statistically significant does not necessa-rily mean it is economically or practically significant! –If a variable is statistically and economically important but has the "wrong“ sign, the regression model might be misspecified –If a variable is statistically insignificant at the usual levels (10%, 5%, 1%), one may think of dropping it from the regression –If the sample size is small, effects might be imprecisely estimated so that the case for dropping insignificant variables is less strong Multiple Regression Analysis: Inference

 Computing p-values for t-tests –If the significance level is made smaller and smaller, there will be a point where the null hypothesis cannot be rejected anymore –The reason is that, by lowering the significance level, one wants to avoid more and more to make the error of rejecting a correct H 0 –The smallest significance level at which the null hypothesis is still rejected, is called the p-value of the hypothesis test –A small p-value is evidence against the null hypothesis because one would reject the null hypothesis even at small significance levels –A large p-value is evidence in favor of the null hypothesis –P-values are more informative than tests at fixed significance levels Multiple Regression Analysis: Inference