Question 11.57

11.57 Canada’s Small Business Financing Program.

The Canada Small Business Financing Program (CSBFP) seeks to increase the availability of loans for establishing and improving small businesses. A survey was performed to better understand the experiences of small businesses when seeking loans and the extent to which they are aware of and satisfied with the CSBFP.14 A total of 1050 survey interviews were completed. To understand the drivers of perceived fairness of CSBFP terms and conditions, a multiple regression was undertaken. The response variable was the subject’s perceived fairness scored on a 5-point scale, where 1 means "very unfair’’ and 5 means "very fair.’’ The 15 explanatory variables included characteristics of the survey participant (gender, francophone, loan history, previous CSBFP borrower) and characteristics of his or her small business (type, location, size).

  1. What are the degrees of freedom for the statistic of the model that contains all the predictors?
  2. The report states that the -value for the overall test is and that the complete set of predictors has an of 0.031. Explain to a statistical novice how the test can be highly significant but with a very low .
  3. The report also reports that only two of the explanatory variables were found significant at the 0.05 level. Suppose the model with just an indicator of previous CSBFP participation and an indicator that the business is in transportation and warehousing explained 2.5% of the variation in the response variable. Test the hypothesis that the other 13 predictors do not help predict fairness when these two predictors are already in the model.

11.57

(a) are 15 and 1034. (b) The test is significant, meaning the model is good at predicting the response variable, but there is still a lot of variance that is unexplained (a lot of scatter around our current regression line) because is small. This small just means there are other potential predictors that may also help us, in addition to our current predictors, to account for this remaining scatter or variation in the response. (c) are 13 and 1034, . The added 13 variables do not contribute significantly in explaining the response when these 2 predictors are already in the model.