If you did Option 1 (your own data) in Assignment #3: 1. Can you find any predictor (x) to forecast using simple linear regression (SLR) for your data? Give your reasoning by plotting the data and visual inspection. If you cannot find any appropriate predictor, you can simply use time index (t). 2. Run simple linear regression (SLR) and answer following questions. (a) What is the slope of your chosen predictor? Is the sign as what you expected? Please explain. (b) What is the t-ratio of the slope and is it statistically significantly different from zero at alpha=0.01 level? Please explain. (c) What is R2 , and what does it imply? (d) Is there any evidence of serial correlation using Durbin-Watson test? Please show your calculation and reasoning. If yes, what would you recommend to correct it? (e) Plot the residuals. Does it show any evidence of heteroscedasticity? If yes, what would you recommend to correct it? (f) Please use this regression to forecast 1 period beyond your data set. What is the 95% confidence interval for the forecast? (g) Calculate the RMSE and plot the actual and forecast. Does it work better than any of the time-series models you’ve done? If you did Option 2 (Napa) in Assignment #3: Use the attached data with CPI (Consumer Price Index) provided for each time period. 1. Do you think simple linear regression would be appropriate to forecast Northern’s sales using CPI as a predictor? Give your reasoning by plotting the data and visual inspection. 2. Run simple linear regression (SLR) in spreadsheet and answer following questions. (a) What is the slope of your regression? Is the sign as what you expected? (b) What is the t-ratio of the slope and is it statistically significantly different from zero at alpha=0.01 level? Please show the steps of the hypothesis testing. (c) What is R2 , and what does it imply? (d) Is there any evidence of serial correlation using Durbin-Watson test? If yes, what would you recommend to correct it? (e) Plot the residuals. Does it show any evidence of heteroscedasticity? If yes, what would you recommend to correct it? (f) Please use this regression to forecast until Sep-09. What is the 95% confidence interval for the forecast of Sep-09? (g) Compared to time-series decomposition, which forecast would you recommend, and why?
