F test of a multiple regression model
The finance department of an automobile insurance company uses a multiple regression model to estimate the total number of accident claims that will be filed each month. Based on the most recent 20 months of claims data, the company has selected 2 independent variables that it believes are related to accident claims. Let β1 and β2 denote the coefficients of the 2 variables in this model. When this data is entered into a regression software program, the error sum of squares (SSE) associated with the model is reported to be 55.96 and the corresponding regression sum of squares (SSR) is 13.50. Using a significance level of 0.10, can you conclude that at least one of the independent variables in the model provides useful (i.e., statistically significant) information for predicting monthly accident claims?
Perform a one-tailed test. Then fill in the table below.
Carry your intermediate computations to at least three decimal places.
1. What is the null hypothesis?
2. In this F-test, what are the degrees of freedom in the numerator? The denominator?
3. What is the value of the test statistic? (Round to at least two decimal places)
4. What is the p-value?