In: Statistics and Probability
You have just started working at large wine distribution company and have been tasked with analyzing how the company should be pricing their bottles of wine. You have data on a number of different wines that include very detailed reviews, the country of origin, the wine’s rating and designation, and the price that is has been sold at in the past. You hypothesize that higher rated wines should sell for a higher price (duhhh), but want to figure out how much more you can sell wine for that has higher ratings. Use your wine data, which is included below, to answer the following questions.
For this question, you will need to download the Wine Rating Data and then use the data analysis tool pack in Excel to run a regression. Note, you will need to install the data analysis tool pack on your computer. How to do this differs based on the type of computer you are using, but instructions can be found on google for both Mac and PC.
https://arizona.grtep.com/core/uploadfiles/components/286567/files/Wine%20Ranking%20Data.xlsx (Wine Data)
Use the exponential model to predict the sales price of a wine that has a rating of 92. Hint, round all of the estimates to 4 decimals prior to making your predictions. Round intermediary calculations to 4 decimals and round your final answer to 4 decimals
Estimate the sample regression equation below and fill in the estimated coefficients. Pay close attention the form of the variables prior to estimating the model. Round the coefficient estimates to 4 decimals.
Linear Model: Priceˆ= _____________ + ______________ Rating + ______________ Rating2
SUMMARY OUTPUT | ||||||||
Regression Statistics | ||||||||
Multiple R | 0.543771157 | |||||||
R Square | 0.295687072 | |||||||
Adjusted R Square | 0.295676807 | |||||||
Standard Error | 30.48331263 | |||||||
Observations | 137235 | |||||||
ANOVA | ||||||||
df | SS | MS | F | Significance F | ||||
Regression | 2 | 53536057.86 | 26768028.93 | 28806.60469 | 0 | |||
Residual | 137232 | 127520413.7 | 929.2323487 | |||||
Total | 137234 | 181056471.5 | ||||||
Coefficients | Standard Error | t Stat | P-value | Lower 95% | Upper 95% | Lower 95.0% | Upper 95.0% | |
Intercept | 5622.506072 | 47.2410031 | 119.0174997 | 0 | 5529.914591 | 5715.097554 | 5529.914591 | 5715.097554 |
Rating | -132.3245732 | 1.073794523 | -123.2308141 | 0 | -134.4291904 | -130.219956 | -134.4291904 | -130.219956 |
Rating^2 | 0.781009186 | 0.006097088 | 128.0954366 | 0 | 0.769059007 | 0.792959365 | 0.769059007 | 0.792959365 |
Linear Model:
Use the exponential model to predict the sales price of a wine that has a rating of 92.