Linear Regression

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Re-expressing Data Often the conditions necessary for performing linear regression aren’t satisfied in a data set. However, it may still be possible to use these methods if we reexpress one or both of the variables. To re-express data we need be able to create new variables using STATA. We can do this using the generate command. For example to create a new variable named logx which is the logarithm of an already existing variable x, we type: generate logx = log(x) If we instead wanted to create a variable that is the square root of x, we could type generate sqx = sqrt(x) In general, the command is on the format: generate new_variable = expression(old_variable) where expression is the mathematical function applied to the old variable. Note that by default STATA uses log base e. <strong>Linear</strong> regression using re-expressed data In this portion of the tutorial we will be working with the data set discussed in example 10.11 on page 256 of the textbook. The data set gives information on the highest paid baseball players in the period spanning 1980-2001. The data set consists of 3 variables player, year and salary. To access the data type: use http://www.stat.columbia.edu/~martin/W1111/Data/salary in the command window. We begin by making a scatter plot of salary and year. scatter salary year
This gives rise to the following plot: salary 0 5 10 15 20 25 1980 1985 1990 1995 2000 year The relationship between year and highest salary is moderately strong, positive and curved. Since the scatter plot shows a curved relationship, a linear model is not appropriate. However, it appears that taking the logarithm of salary may help straighten the plot. We can generate a new variable named logsalary, which is the logarithm of the variable salary, by typing: generate logsalary = log(salary) We can make a scatter plot of this new variable against year by typing scatter logsalary year This gives rise to the following plot: logsalary 0 1 2 3 1980 1985 1990 1995 2000 year It appears that the transformation has significantly straightened the scatter plot. We can now proceed with fitting a linear regression model to the transformed data by typing: regress logsalary year Note that now the response variable is logsalary instead of salary.
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Linear Regression

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