Get to know what the data set is about

Size: px

Start display at page:

Download "Get to know what the data set is about"

Kellie Elliott
6 years ago
Views:

1 Learning objectives You at last will get some real practice! See today's session as a training for the linear regression problem in the nal exam. Indeed: the statement of this lab session is copied from a past exam! SPSS data set Was sent by . If you cannot retrieve it, ask your instructor. How we operate this lab session Each of you will follow her/his own pace. Don't expect us to rst show the SPSS manipulation and to only reproduce it. We will circulate and help as needed, we will read again live your answers and provide tips on how to better write them. To that end: please write your answers as if this was your nal exam, that is, in a crisp but concise manner. Get to know what the data set is about Unlike all linear-regression data sets discussed in the handouts, which are real data sets, this is a simulated data set: made up by an instructor (namely, Jean-Michel Gautier). We will use it to illustrate some real-world diculties when applying linear regression. We consider, for a given company, various variables (in constant euros), whose value is reported by semester (variable: Semester). We consider the best-selling product of this company. The dependent variable is called Sales. The independent (explanatory) variables are described below. Variable Denition Units Semester Semester index [N/A] Sales Total sales for the product in the semester Ke Overall market Overall market for this type of products Me Discounts to wholesalers Value of the discounts oered to wholesalers ke Unit price Unit price of the product studied e Research budget Research & development budget ke Investment budget Investment budget, following accounting rules a ke Advertising budget Advertising budget ke a which is why we observe some negative values Statistics for MiM at HEC Paris SPSS Lab session Prof. Chopin, Stoltz, Wang 1

2 1. Simple linear regressions Compute all simple linear regressions and read them attentively before answering the questions below. (Produce the outputs with Analyze / Regression / Linear.) 1. Which are the statistically valid models? Among the latter, which are also economically valide? 2. Which is the best such statistically and economically valid model? Write out the linear relation that it proposed. 3. Interpret (the coecients of) this linear relation; indicate in particular which share of the increase in the overall market we get on average. Statistics for MiM at HEC Paris SPSS Lab session Prof. Chopin, Stoltz, Wang 2

3 2. Linear regression with all variables In all variables we include as well the variable Semester. 1. What do you think of the linear model taking into account all variables? 2. Let us improve this, by using a backward selection. (In the SPSS linear regression window, under the list of dependent variables to consider, change the method from Enter into Backward.) How many steps are necessary, which are the variables that are successively eliminated? 3. Try to determinate, for each of the eliminated variables, why 1 it did not provide a signicant additional contribution to the linear modeling, given the other variables. 1 It is an intrinsic lack of signicance, or is there some redundancy taking place? You can base your intuition on the scatter plots given on the last page of this statement. To prove a given redundancy the best would be to compute a well-chosen linear regression. On the other hand, how would you prove a given intrinsic lack of signicance? Statistics for MiM at HEC Paris SPSS Lab session Prof. Chopin, Stoltz, Wang 3

4 3. How to construct a nal satisfactory model? The questions below are more subjective than usual; please explain your preferences. 1. From an economic viewpoint, why is the model recommended by the backward selection not so satisfactory? Indicate two models that are close to the result of the backward selection but that look better from an economic viewpoint. 2. Thus, we have three models in competition. Compare their statistical and economic merits, explain which one you prefer (and why). Write and interpret the linear relation that your favorite model proposes. 3. Take a close look to the data set (e.g., its last line). To what purpose do you think we constructed the model discussed in the previous question? Go ahead and use the model for this purpose. (Do the calculations yourself, as you will do in the exam.) Statistics for MiM at HEC Paris SPSS Lab session Prof. Chopin, Stoltz, Wang 4

5 4. Scatter plots Of course one must always plot the data rst, and then analyze them. The lab session statement should thus have started with these scatter plots. We however put them as a nal section because they are delicate to produce! Use Graphs / Chart builder to build individual scatter plots as well as a matrix of scatter plots. Double-click on the plots to make them bigger, to plot the linear regression line, etc. 1. Produce again the scatter plots below and on the next page. Call us when done, so that we check that your plots are as readable as our ones! 2. Find again, in a visual manner, some of the results previously shown in a quantitative manner (e.g., which is the best or worst single independent variable, etc.). R 2 Linear = 0, Sales Research budget Statistics for MiM at HEC Paris SPSS Lab session Prof. Chopin, Stoltz, Wang 5

6 Beware! SPSS is full of bugs and, depending on the versions, it miserably crashes when asked to build a matrix of scatterplots with too many variables. (The problems used to start with 8 variables in the good old past, now, we have the feeling that even 6 is an issue. Try and let us know!) Sales Unit price Discounts to wholesalers Overall market Semester Semester Overall market Discounts to wholesalers Unit price Sales Statistics for MiM at HEC Paris SPSS Lab session Prof. Chopin, Stoltz, Wang 6

A Research Note on Correlation

A Research Note on Correlation A Research ote on Correlation Instructor: Jagdish Agrawal, CSU East Bay 1. When to use Correlation: Research questions assessing the relationship between pairs of variables that are measured at least at