how do you run a regression analysis?

Question

For Quantitative Research Methods / Statistical Analysis

Answer 1

On the off chance you want to know the steps, rather than a specific regression computer application, here's what you do:

Step 1: collect data. A minimum of two sets of data (like house prices and interest rates). So, in this case, a single data "point" (p) would have p(price,rate) as the two sets of data making up each point.

Step 2: after collecting a sufficient number of data points (more than 30 is good for better results), designate one set of data the "dependent" variable (e.g., y) and the other sets the "independent" variables (e.g., x1, x2, etc.)

Step 3: set up a general linear equation (for linear regression) in the form of y = mx + b or, more generally, y = m1*x1 + m2*x2 + ... + mN xN + b, where each x term represents a set of independent data, y is the dependent data set, and b is a constant called the intercept.

Step 4: enter the dependent and independent data sets into your regression tool (I use Excel's LINEST function for example). Make sure you enter your dependent data into the y part of your regression tool and the x's, your independent data, into the independent data slots of the tool. Otherwise, you'll get meaningless output from the tool

Step 5: run the regression tool with your data entered.

Step 6: note the output, which typically includes the mN coefficients for each x data set, the b intercept, R^2 the coefficient of determination, and measures of spread or uncertainty for each of the coeffcients and the intercept.

Answer 2

To estimate a regression in SST, you need to specify one or more dependent variables (in the DEP subop) and one or more independent variables (in the IND subop). Unlike some other programs, SST does not automatically add a constant to your independent variables. If you want one, you should create a constant and add it to the list of your independent variables. For example, to regress the variable y on x with an intercept:

set one=1
reg dep[y] ind[one x]

SST will produce two coefficients: an intercept and a slope parameter. The corresponding regression line passes through the point (0,b_0) and has slope equal to b_1:

where b_0 is the coefficient of one and b_1 is the coefficient of the variable x. If, on the other hand, you had omitted the variable one from the IND subop:


reg dep[y] ind[x]

SST would produce a "regression through the origin". That is, the regression line would pass through the point (0,0) with slope equal to the coefficient of x (b):

For most purposes you will want to include a constant, but SST allows you the flexibility to decide otherwise.

The IF and OBS subops can be used to restrict the range of observations used in the regression. Only the subset of observations activated by the current RANGE statement that meet the criteria set in the IF and OBS subops will be used. If any of the variables specified in the IND or DEP subops have missing data for an observation, the entire observation is deleted from the estimation range for that regression. For example, to run a regression of y on x (and a constant) including only observations one through ten:


reg dep[y] ind[one x] obs[1-10]

Using the OBS subop does not affect the observation range for subsequent commands.

SST also allows you to specify multiple dependent variables in the DEP subop. If one variable is specified in the DEP subop, it will be regressed on the variables specified in the IND subop. If more than one variable is specified in the DEP subop, separate regressions will be run for each of these variables on the variables listed in the IND subop. The same observation range will be used for all regressions.

Answer 3

Well, it all depends what stats program you're using. You're going to have to be more specific. If you don't have a stats program, I think you can get a trial version of Minitab that will do it.