Perform Hypothesis Test for a Regression Model, Given R Squared
If you run into a problem, usually in an academic setting, where you only know the multiple coefficient of determination, R2, and are asked to test to see if the beta coefficients are non-zero, you can do this easily using Excel. You could also do it in StatCrunch using the Data > Compute tool, but I find it tedious compared to just building the solution in Excel. And, you can save the Excel solution for later reuse if you label and name it in a smart way.
Consider this problem:
Researchers want to use an analysis of social media to forecast the number of viewers, and thus ad revenues, for new TV series. They collected data on the pilot episodes for 33 series. The data included the number of times per minute a series was mentioned in the 24 hours after the pilots aired. It also included an analysis of the sentiment index of the mentions, i.e. ratio of positive to negative mentions. R2 for the 1st order regression model they produced is 0.937; Ra2 = 0.933.
Test the model to see if it might be useful in forecasting ad revenues for a new TV series.
Solution:
- A first-order model consists of terms for quantitative independent variables. Because we have two independent variables, the model will be of the form:
Perform Hypothesis Test for a Regression Model, Given R Squared
More on Multiple Regression Part 2
In the real world, we most often work with real data. And we build regression models using software such as Excel, StatCrunch, and, more recently, R. The output of those regressions give us a world of information about the regression models, enabling us to quickly determine if the overall model is statistically significant and if the individual regression coefficients are as well. And with most software, getting confidence intervals associated with the regression model is straightforward.
But in the world of academia, my students often are confronted with an inability to work on the actual data and are instead presented with partial regression output. I know the intent is to make sure students understand the nuts and bolts of regression, but my sense that could be done just as well or better with real data.
That said, I want to help my students learn about regression and get through their academic course with a satisfactory grade.
Here is a typical problem probing understanding of regression intermediates:More on Multiple Regression Part 2
More on Multiple Regression Part 1
This post is in development. In the interim, please try out the attached Excel workbook with a couple of useful calculators Multiple Regression-Given_Betas_and_Standard_Errors_find_Confidence_Interval_for_Prediction