Hawaii is a popular tourist destination during the winter months, and Honolulu offers many outdoor attractions. However, the months of December through February are the rainy season, and records indicate that the most rain falls during the month of January. Using data from random years,37 a multiple linear regression model was used to explain the total January rainfall (y) that consisted of four predictor variables, one of which was a dummy variable (a variable with a value of either 0 or 1). The independent variables were monthly rainfall total in the previous December, January, and February (x1, x2, and x3, respectively) and a dummy variable (x4) which indicated whether there was a moderate to weak El Niño during the previous year. Rainfall totals were recorded in inches. HAWAII
a. Construct the ANOVA table and conduct a model utility test. Use technology to find the p value associated with this test. Find the value of r 2 . Use these results to describe the overall significance of the model.
b. Find the value of the test statistic and the p value associated with each hypothesis test for a significant regression coefficient. Use these results to determine the most important predictor variables in this model.
c. Consider a reduced model with the two most important predictor variables. Conduct a model utility test. Describe the significance of this model compared to the full model in part (a).
d. Find the most recent rainfall totals for Honolulu and records on El Niño. Use this information to find a 95% prediction interval for the most recent January rainfall total in Honolulu. Does the actual value lie in this interval? What does this suggest about the reduced model?