Use the following data to answer Questions 25-29 Ticket sales for a certain football event are tracked yearly through 1995-2020 to study and forecast the tendency of future ticket sales (in thousands).  Coding 1995 as the zeroth year, the observations and tabulation for various model are given below. “Coded” is the coded year and “Quadratic” is the quadratic of coded year.    

What is the Variance Inflationary Factor (VIF) of X2?

Use the following data to answer Questions 6-8 In order to estimate the relationship between the sales and price of umbrellas we decided to test the following model: Y = β0 + β1X + β2X2 + ε Where, Y = sales (in thousands) and X = price of an umbrella. The data was collected from 30 major stores in Madison downtown and the ANOVA summary follows:  

Which of the following time series component is usually considered short-term?

Based on the quadratic model summary, the p-value for the price-squared term is 0.0865. Which of the following interpretations is most appropriate regarding the quadratic relationship between price and sales?

A fourth-order autoregressive model is fitted to a time series with monthly data for 5 years (i.e. sample size n=60). What are the degrees of freedom of the model?

What is the value in the cell at the intersection “Total” and “df”? 

Which of the following interpretations is most likely to be correct based on the insignificance of the price-square term?

Assume the smoothing coefficient W=0.3. What are the exponentially smoothed values for milk production in January and February of 2023? 

A third-order autoregressive model is fitted to a time series with monthly data for 4 years (i.e. sample size n=48). What are the degrees of freedom of the model?