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 1^st order regression model they produced is 0.937; R_a² = 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