Wine Nerds: Is there a Correlation between WS Scores & Prices for Napa Wines

This hypothesis testing is to try to understand if there is correlation between the average scores given by wine spectator and the average prices for wineries in Napa.

Step 1 Define my Hypothesis
Ho: There is no correlation between WS Score and Price for Napa Wines
H1: there is a correlation between WS Score and price for Napa wines

Step 2 run the regression Analysis
The regression equation is Napa Price = - 2040 + 23.5 Napa Score

Predictor        Coef       StDev          T        P
Constant      -2040.3       318.8      -6.40    0.000
Napa Sco       23.488       3.557       6.60    0.000 
S = 33.21       R-Sq = 57.7%     R-Sq(adj) = 56.4%
Analysis of Variance
Source            DF          SS          MS         F        P
Regression         1       48111       48111     43.61    0.000
Residual Error    32       35301        1103
Total             33       83412

Unusual Observations
Obs   Napa Sco   Napa Pri         Fit   StDev Fit    Residual    St Resid
21       92.5             68.33        132.36   11.72         -64.03       -2.06R
29      94.4            275.00       176.99   17.92          98.01        3.51RX
R denotes an observation with a large standardized residual
X denotes an observation whose X value gives it large influence.

Step 3 Explain the results
We Reject the null hypothesis.

The P-value for Napa Score  is <.05 which leads us to conclude that Score is a good predictor of Price and there is a correlation between Score and Price

The R-sq(adj) value is high, which tells us that the regression equation explains a high percentage of the variation in the process (close 60%).

Step 4 Conclusion
It looks like that score is a strong predictor of a price for Napa wines.
Note:"Correlation does not imply causation" 

Wine Nerds: Is there Correlation between WS Scores & Prices for Sonoma Wines

This hypothesis testing is to try to understand if there is correlation between the average scores given by wine spectator and the average prices for wineries in Sonoma.

Step 1: Define the Hypothesis
Ho: There is no correlation between WS score and Price for Sonoma wines
H1: there is a correlation between WS score and price for Sonoma wines

Step 2 run the regression Analysis
The regression equation is  Sonoma Price = - 389 + 4.78 Sonoma Score

Predictor           Coef       StDev           T        P
Constant       -388.5       106.2      -3.66    0.001
Sonoma S        4.783       1.185       4.04    0.000
S = 9.461       R-Sq = 32.4%     R-Sq(adj) = 30.4%

Analysis of Variance
Source               DF          SS          MS          F            P
Regression         1      1458.3      1458.3     16.29    0.000
Residual Error    34      3043.3        89.5
Total             35      4501.6

Step 3 Explain the results
We reject the null hypothesis.

The P-value for Score  is <.05 which leads us to conclude that score is a good predictor of Price and there is correlation between Score and Price for Sonoma wines.

The R-sq(adj) value is low, which tells us that the regression equation can only explains about 30% of the variation, we therefore conclude that there are other factors that can explain variation.

Step 4 Conclusion
There is a correlation between scores and prices other factors are at play.
Note:"Correlation does not imply causation"